%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA150-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:34:02 PM UTC 2026
% Result : Unsatisfiable 1.44s 1.63s
% Output : Proof 2.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRA150-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.14/0.32 % Computer : n005.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 23:48:17 EDT 2026
% 0.14/0.32 % CPUTime :
% 1.44/1.63 % SZS status Unsatisfiable
% 1.44/1.63 % SZS output start Proof
% 1.44/1.63 tff(b_type, type, (
% 1.44/1.63 b: ( $i * $i ) > $o)).
% 1.44/1.63 tff(s_type, type, (
% 1.44/1.63 s: $i > $i)).
% 1.44/1.63 tff(elem_1_type, type, (
% 1.44/1.63 elem_1: $i)).
% 1.44/1.63 tff(z_type, type, (
% 1.44/1.63 z: $i)).
% 1.44/1.63 tff(r_type, type, (
% 1.44/1.63 r: ( $i * $i ) > $o)).
% 1.44/1.63 tff(inj_0_type, type, (
% 1.44/1.63 inj_0: $i > $i)).
% 1.44/1.63 tff(1,assumption,(~(s(s(s(z))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.63 tff(2,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 1.44/1.63 tff(3,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 1.44/1.63 tff(4,assumption,(~r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.44/1.63 tff(5,assumption,(~b(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.44/1.63 tff(6,plain,
% 1.44/1.63 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.44/1.63 inference(commutativity,[status(thm)],[])).
% 1.44/1.63 tff(7,plain,
% 1.44/1.63 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(z))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[6])).
% 1.44/1.63 tff(8,plain,
% 1.44/1.63 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(9,plain,
% 1.44/1.63 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(10,plain,
% 1.44/1.63 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(11,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sinj')).
% 1.44/1.63 tff(12,plain,
% 1.44/1.63 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[11, 10])).
% 1.44/1.63 tff(13,plain,(
% 1.44/1.63 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.44/1.63 inference(skolemize,[status(sab)],[12])).
% 1.44/1.63 tff(14,plain,
% 1.44/1.63 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[13, 9])).
% 1.44/1.63 tff(15,plain,
% 1.44/1.63 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[14, 8])).
% 1.44/1.63 tff(16,plain,
% 1.44/1.63 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(17,plain,
% 1.44/1.63 (inj_0(s(z)) = z),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[16, 15])).
% 1.44/1.63 tff(18,plain,
% 1.44/1.63 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(19,plain,
% 1.44/1.63 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[18, 15])).
% 1.44/1.63 tff(20,assumption,(s(s(z)) = s(s(s(elem!1)))), introduced(assumption)).
% 1.44/1.63 tff(21,plain,
% 1.44/1.63 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[20])).
% 1.44/1.63 tff(22,plain,
% 1.44/1.63 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(23,plain,
% 1.44/1.63 (inj_0(s(s(z))) = s(z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[22, 15])).
% 1.44/1.63 tff(24,plain,
% 1.44/1.63 (s(z) = inj_0(s(s(z)))),
% 1.44/1.63 inference(symmetry,[status(thm)],[23])).
% 1.44/1.63 tff(25,plain,
% 1.44/1.63 (s(z) = s(s(elem!1))),
% 1.44/1.63 inference(transitivity,[status(thm)],[24, 21, 19])).
% 1.44/1.63 tff(26,plain,
% 1.44/1.63 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[25])).
% 1.44/1.63 tff(27,plain,
% 1.44/1.63 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.44/1.63 inference(symmetry,[status(thm)],[26])).
% 1.44/1.63 tff(28,plain,
% 1.44/1.63 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(29,plain,
% 1.44/1.63 (inj_0(s(s(elem!1))) = s(elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[28, 15])).
% 1.44/1.63 tff(30,plain,
% 1.44/1.63 (s(elem!1) = inj_0(s(s(elem!1)))),
% 1.44/1.63 inference(symmetry,[status(thm)],[29])).
% 1.44/1.63 tff(31,plain,
% 1.44/1.63 (s(elem!1) = z),
% 1.44/1.63 inference(transitivity,[status(thm)],[30, 27, 17])).
% 1.44/1.63 tff(32,plain,
% 1.44/1.63 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 1.44/1.63 inference(bind,[status(th)],[])).
% 1.44/1.63 tff(33,plain,
% 1.44/1.63 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.44/1.63 inference(quant_intro,[status(thm)],[32])).
% 1.44/1.63 tff(34,plain,
% 1.44/1.63 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(35,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snz')).
% 1.44/1.63 tff(36,plain,
% 1.44/1.63 (![X: $i] : (~(s(X) = z))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[35, 34])).
% 1.44/1.63 tff(37,plain,(
% 1.44/1.63 ![X: $i] : (~(s(X) = z))),
% 1.44/1.63 inference(skolemize,[status(sab)],[36])).
% 1.44/1.63 tff(38,plain,
% 1.44/1.63 (![X: $i] : (~(s(X) = z))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[37, 33])).
% 1.44/1.63 tff(39,plain,
% 1.44/1.63 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(40,plain,
% 1.44/1.63 (~(s(elem!1) = z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[39, 38])).
% 1.44/1.63 tff(41,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[40, 31])).
% 1.44/1.63 tff(42,plain,(~(s(s(z)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(43,plain,
% 1.44/1.63 (~(s(s(s(elem!1))) = s(s(z)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[42, 7])).
% 1.44/1.63 tff(44,plain,
% 1.44/1.63 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.44/1.63 inference(bind,[status(th)],[])).
% 1.44/1.63 tff(45,plain,
% 1.44/1.63 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.44/1.63 inference(quant_intro,[status(thm)],[44])).
% 1.44/1.63 tff(46,plain,
% 1.44/1.63 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(47,plain,
% 1.44/1.63 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.44/1.63 inference(bind,[status(th)],[])).
% 1.44/1.63 tff(48,plain,
% 1.44/1.63 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.44/1.63 inference(quant_intro,[status(thm)],[47])).
% 1.44/1.63 tff(49,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rb')).
% 1.44/1.63 tff(50,plain,
% 1.44/1.63 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.44/1.63 tff(51,plain,
% 1.44/1.63 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[50, 46])).
% 1.44/1.63 tff(52,plain,(
% 1.44/1.63 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.44/1.63 inference(skolemize,[status(sab)],[51])).
% 1.44/1.63 tff(53,plain,
% 1.44/1.63 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[52, 45])).
% 1.44/1.63 tff(54,plain,
% 1.44/1.63 (((~![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))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(55,plain,
% 1.44/1.63 ((~![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))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(56,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.44/1.63 tff(57,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[56, 53, 43, 5, 4])).
% 1.44/1.63 tff(58,plain,(r(s(s(s(elem!1))), s(s(z))) | b(s(s(s(elem!1))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(59,plain,
% 1.44/1.63 (b(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[58, 4])).
% 1.44/1.63 tff(60,assumption,(b(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.44/1.63 tff(61,assumption,(b(z, s(z))), introduced(assumption)).
% 1.44/1.63 tff(62,plain,
% 1.44/1.63 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(63,plain,
% 1.44/1.63 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[62, 15])).
% 1.44/1.63 tff(64,assumption,(s(s(s(s(z)))) = s(s(z))), introduced(assumption)).
% 1.44/1.63 tff(65,plain,
% 1.44/1.63 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[64])).
% 1.44/1.63 tff(66,plain,
% 1.44/1.63 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[65])).
% 1.44/1.63 tff(67,plain,
% 1.44/1.63 (s(z) = s(s(s(z)))),
% 1.44/1.63 inference(transitivity,[status(thm)],[24, 66, 63])).
% 1.44/1.63 tff(68,assumption,(s(z) = s(s(s(z)))), introduced(assumption)).
% 1.44/1.63 tff(69,plain,
% 1.44/1.63 (inj_0(s(z)) = inj_0(s(s(s(z))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[68])).
% 1.44/1.63 tff(70,plain,
% 1.44/1.63 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.44/1.63 inference(symmetry,[status(thm)],[69])).
% 1.44/1.63 tff(71,plain,
% 1.44/1.63 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(72,plain,
% 1.44/1.63 (inj_0(s(s(s(z)))) = s(s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[71, 15])).
% 1.44/1.63 tff(73,plain,
% 1.44/1.63 (s(s(z)) = inj_0(s(s(s(z))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[72])).
% 1.44/1.63 tff(74,plain,
% 1.44/1.63 (s(s(z)) = z),
% 1.44/1.63 inference(transitivity,[status(thm)],[73, 70, 17])).
% 1.44/1.63 tff(75,plain,
% 1.44/1.63 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(76,plain,
% 1.44/1.63 (~(s(s(z)) = z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[75, 38])).
% 1.44/1.63 tff(77,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[76, 74])).
% 1.44/1.63 tff(78,plain,(~(s(z) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(79,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[78, 67])).
% 1.44/1.63 tff(80,plain,(~(s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(81,assumption,(r(s(z), z)), introduced(assumption)).
% 1.44/1.63 tff(82,assumption,(~b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.44/1.63 tff(83,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 1.44/1.63 tff(84,plain,
% 1.44/1.63 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(85,plain,
% 1.44/1.63 (inj_0(s(elem!1)) = elem!1),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[84, 15])).
% 1.44/1.63 tff(86,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.44/1.63 tff(87,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 1.44/1.63 tff(88,plain,
% 1.44/1.63 (^[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))))),
% 1.44/1.63 inference(bind,[status(th)],[])).
% 1.44/1.63 tff(89,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))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.44/1.63 inference(quant_intro,[status(thm)],[88])).
% 1.44/1.63 tff(90,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))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(91,plain,
% 1.44/1.63 (^[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)))))),
% 1.44/1.64 inference(bind,[status(th)],[])).
% 1.44/1.64 tff(92,plain,
% 1.44/1.64 (![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)))),
% 1.44/1.64 inference(quant_intro,[status(thm)],[91])).
% 1.44/1.64 tff(93,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/sandbox/benchmark/theBenchmark.p','axb')).
% 1.44/1.64 tff(94,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)))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[93, 92])).
% 1.44/1.64 tff(95,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)))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[94, 90])).
% 1.44/1.64 tff(96,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)))),
% 1.44/1.64 inference(skolemize,[status(sab)],[95])).
% 1.44/1.64 tff(97,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)))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[96, 89])).
% 1.44/1.64 tff(98,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(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z)), z)) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(99,plain,
% 1.44/1.64 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(100,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), s(s(s(z))))) | (~b(s(z), s(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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z)))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[99])).
% 1.44/1.64 tff(101,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), s(s(s(z))))) | (~b(s(z), s(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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[100, 98])).
% 1.44/1.64 tff(102,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), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(103,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.44/1.64 tff(104,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[103, 97, 61, 83, 87, 86])).
% 1.44/1.64 tff(105,plain,((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(106,plain,
% 1.44/1.64 (~b(s(s(z)), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[105, 86, 61, 83])).
% 1.44/1.64 tff(107,plain,
% 1.44/1.64 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 1.44/1.64 inference(commutativity,[status(thm)],[])).
% 1.44/1.64 tff(108,plain,
% 1.44/1.64 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 1.44/1.64 inference(symmetry,[status(thm)],[107])).
% 1.44/1.64 tff(109,plain,
% 1.44/1.64 ((~(s(z) = s(s(z)))) <=> (~(s(s(z)) = s(z)))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[108])).
% 1.44/1.64 tff(110,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 1.44/1.64 tff(111,plain,
% 1.44/1.64 (inj_0(s(z)) = inj_0(s(s(z)))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[110])).
% 1.44/1.64 tff(112,plain,
% 1.44/1.64 (inj_0(s(s(z))) = inj_0(s(z))),
% 1.44/1.64 inference(symmetry,[status(thm)],[111])).
% 1.44/1.64 tff(113,plain,
% 1.44/1.64 (s(s(z)) = s(z)),
% 1.44/1.64 inference(symmetry,[status(thm)],[110])).
% 1.44/1.64 tff(114,plain,
% 1.44/1.64 (s(s(z)) = z),
% 1.44/1.64 inference(transitivity,[status(thm)],[113, 24, 112, 17])).
% 1.44/1.64 tff(115,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[76, 114])).
% 1.44/1.64 tff(116,plain,(~(s(z) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(117,plain,
% 1.44/1.64 (~(s(s(z)) = s(z))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[116, 109])).
% 1.44/1.64 tff(118,plain,
% 1.44/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(119,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(120,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[119, 118])).
% 1.44/1.64 tff(121,plain,
% 1.44/1.64 ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[120, 53])).
% 1.44/1.64 tff(122,plain,
% 1.44/1.64 (b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[121, 117])).
% 1.44/1.64 tff(123,plain,
% 1.44/1.64 (r(s(s(z)), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[122, 106])).
% 1.44/1.64 tff(124,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.64 tff(125,assumption,(r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.44/1.64 tff(126,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.44/1.64 tff(127,assumption,(b(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.64 tff(128,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(s(s(s(elem!1))), 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(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(129,plain,
% 1.44/1.64 (((~b(z, s(z))) | (~b(z, 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(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(130,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(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(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[129])).
% 1.44/1.64 tff(131,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(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(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[130, 128])).
% 1.44/1.64 tff(132,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(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))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(133,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[132, 131])).
% 1.44/1.64 tff(134,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[133, 97, 61, 126, 83, 127])).
% 1.44/1.64 tff(135,plain,((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(136,plain,
% 1.44/1.64 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[135, 126, 83, 61])).
% 1.44/1.64 tff(137,assumption,(~r(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.64 tff(138,assumption,(~b(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.64 tff(139,plain,
% 1.44/1.64 (((~![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)))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(140,plain,
% 1.44/1.64 ((~![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)))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(141,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[140, 139])).
% 1.44/1.64 tff(142,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[141, 53, 42, 138, 137])).
% 1.44/1.64 tff(143,plain,(r(s(s(z)), s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(144,plain,
% 1.44/1.64 (r(s(s(z)), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[143, 136])).
% 1.44/1.64 tff(145,assumption,(r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.44/1.64 tff(146,plain,
% 1.44/1.64 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 1.44/1.64 inference(bind,[status(th)],[])).
% 1.44/1.64 tff(147,plain,
% 1.44/1.64 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.44/1.64 inference(quant_intro,[status(thm)],[146])).
% 1.44/1.64 tff(148,plain,
% 1.44/1.64 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(149,plain,
% 1.44/1.64 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X0, X3))) <=> (((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) | (~r(X0, X3))))), rewrite((((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) | (~r(X0, X3))) <=> ((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X0, X3))) <=> ((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))), ((((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X2, X3))) <=> (((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) | (~r(X2, X3))))), rewrite((((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) | (~r(X2, X3))) <=> ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))), ((((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X2, X3))) <=> ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))))),
% 1.44/1.64 inference(bind,[status(th)],[])).
% 1.44/1.64 tff(150,plain,
% 1.44/1.64 (![X0: $i, X3: $i, X2: $i, X1: $i] : (((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X2, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.44/1.64 inference(quant_intro,[status(thm)],[149])).
% 1.44/1.64 tff(151,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : (((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X2, X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axr')).
% 1.44/1.64 tff(152,plain,
% 1.44/1.64 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[151, 150])).
% 1.44/1.64 tff(153,plain,
% 1.44/1.64 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[152, 148])).
% 1.44/1.64 tff(154,plain,(
% 1.44/1.64 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.44/1.64 inference(skolemize,[status(sab)],[153])).
% 1.44/1.64 tff(155,plain,
% 1.44/1.64 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[154, 147])).
% 1.44/1.64 tff(156,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(157,plain,
% 1.44/1.64 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(158,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[157])).
% 1.44/1.64 tff(159,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[158, 156])).
% 1.44/1.64 tff(160,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(161,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[160, 159])).
% 1.44/1.64 tff(162,plain,
% 1.44/1.64 (~r(s(z), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[161, 155, 3, 145, 144])).
% 1.44/1.64 tff(163,assumption,(s(z) = s(s(s(elem!1)))), introduced(assumption)).
% 1.44/1.64 tff(164,plain,
% 1.44/1.64 (s(s(s(elem!1))) = s(z)),
% 1.44/1.64 inference(symmetry,[status(thm)],[163])).
% 1.44/1.64 tff(165,assumption,(s(s(s(elem!1))) = s(z)), introduced(assumption)).
% 1.44/1.64 tff(166,plain,
% 1.44/1.64 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[165])).
% 1.44/1.64 tff(167,plain,
% 1.44/1.64 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[19])).
% 1.44/1.64 tff(168,plain,
% 1.44/1.64 (s(s(elem!1)) = z),
% 1.44/1.64 inference(transitivity,[status(thm)],[167, 166, 17])).
% 1.44/1.64 tff(169,plain,
% 1.44/1.64 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(170,plain,
% 1.44/1.64 (~(s(s(elem!1)) = z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[169, 38])).
% 1.44/1.64 tff(171,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[170, 168])).
% 1.44/1.64 tff(172,plain,(~(s(s(s(elem!1))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(173,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[172, 164])).
% 1.44/1.64 tff(174,plain,(~(s(z) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(175,assumption,(~r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.64 tff(176,assumption,(~b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.64 tff(177,plain,
% 1.44/1.64 (((~![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)))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(178,plain,
% 1.44/1.64 ((~![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)))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(179,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[178, 177])).
% 1.44/1.64 tff(180,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[179, 53, 176, 175, 174])).
% 1.44/1.64 tff(181,plain,(b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(182,plain,
% 1.44/1.64 (b(s(z), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[181, 162])).
% 1.44/1.64 tff(183,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(z))) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(184,plain,
% 1.44/1.64 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(185,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(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(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(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[184])).
% 1.44/1.64 tff(186,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(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(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(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[185, 183])).
% 1.44/1.64 tff(187,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(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(188,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[187, 186])).
% 1.44/1.64 tff(189,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[188, 97, 182, 61, 126, 124])).
% 1.44/1.64 tff(190,plain,((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(191,plain,
% 1.44/1.64 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[190, 126, 124, 3, 61, 83])).
% 1.44/1.64 tff(192,plain,
% 1.44/1.64 (b(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[58, 191])).
% 1.44/1.64 tff(193,assumption,(b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.64 tff(194,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(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(195,plain,
% 1.44/1.64 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(196,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(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(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(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[195])).
% 1.44/1.65 tff(197,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(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(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(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[196, 194])).
% 1.44/1.65 tff(198,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(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(199,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[198, 197])).
% 1.44/1.65 tff(200,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[199, 97, 193, 61, 124, 60])).
% 1.44/1.65 tff(201,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(202,plain,
% 1.44/1.65 (~b(s(z), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[201, 192, 61, 124])).
% 1.44/1.65 tff(203,plain,
% 1.44/1.65 (r(s(z), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[181, 202])).
% 1.44/1.65 tff(204,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 1.44/1.65 tff(205,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(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(206,plain,
% 1.44/1.65 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(207,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(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[206])).
% 1.44/1.65 tff(208,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(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[207, 205])).
% 1.44/1.65 tff(209,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(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(210,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[209, 208])).
% 1.44/1.65 tff(211,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[210, 97, 124, 204, 60, 87])).
% 1.44/1.65 tff(212,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(213,plain,
% 1.44/1.65 (~b(z, s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[212, 192, 124, 87])).
% 1.44/1.65 tff(214,plain,
% 1.44/1.65 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 1.44/1.65 inference(commutativity,[status(thm)],[])).
% 1.44/1.65 tff(215,plain,
% 1.44/1.65 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 1.44/1.65 inference(symmetry,[status(thm)],[214])).
% 1.44/1.65 tff(216,plain,
% 1.44/1.65 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[215])).
% 1.44/1.65 tff(217,plain,
% 1.44/1.65 (~(z = s(s(z)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[76, 216])).
% 1.44/1.65 tff(218,plain,
% 1.44/1.65 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(219,plain,
% 1.44/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(220,plain,
% 1.44/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[219, 218])).
% 1.44/1.65 tff(221,plain,
% 1.44/1.65 ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[220, 53])).
% 1.44/1.65 tff(222,plain,
% 1.44/1.65 (b(z, s(s(z))) | r(z, s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[221, 217])).
% 1.44/1.65 tff(223,plain,
% 1.44/1.65 (r(z, s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[222, 213])).
% 1.44/1.65 tff(224,assumption,(r(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.65 tff(225,assumption,(r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.65 tff(226,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 1.44/1.65 tff(227,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(228,plain,
% 1.44/1.65 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(229,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[228])).
% 1.44/1.65 tff(230,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[229, 227])).
% 1.44/1.65 tff(231,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(232,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[231, 230])).
% 1.44/1.65 tff(233,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[232, 155, 226, 81, 3, 225, 224])).
% 1.44/1.65 tff(234,plain,((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(235,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[234, 223, 203, 3, 144, 81])).
% 1.44/1.65 tff(236,plain,((~b(s(s(s(elem!1))), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(237,plain,
% 1.44/1.65 (~b(s(s(s(elem!1))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[236, 87, 81, 124, 3, 61, 83])).
% 1.44/1.65 tff(238,assumption,(~r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.44/1.65 tff(239,assumption,(~b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.44/1.65 tff(240,plain,
% 1.44/1.65 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(241,plain,
% 1.44/1.65 (~(s(s(s(elem!1))) = z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[240, 38])).
% 1.44/1.65 tff(242,plain,
% 1.44/1.65 (((~![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))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(243,plain,
% 1.44/1.65 ((~![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))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(244,plain,
% 1.44/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[243, 242])).
% 1.44/1.65 tff(245,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[244, 53, 241, 239, 238])).
% 1.44/1.65 tff(246,plain,(r(s(s(s(elem!1))), z) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(247,plain,
% 1.44/1.65 (r(s(s(s(elem!1))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[246, 237])).
% 1.44/1.65 tff(248,plain,
% 1.44/1.65 (~b(s(z), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[105, 87, 61, 83])).
% 1.44/1.65 tff(249,plain,
% 1.44/1.65 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(250,plain,
% 1.44/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(251,plain,
% 1.44/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[250, 249])).
% 1.44/1.65 tff(252,plain,
% 1.44/1.65 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[251, 53])).
% 1.44/1.65 tff(253,plain,
% 1.44/1.65 (b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[252, 78])).
% 1.44/1.65 tff(254,plain,
% 1.44/1.65 (r(s(z), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[253, 248])).
% 1.44/1.65 tff(255,assumption,(b(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.44/1.65 tff(256,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(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z)), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(257,plain,
% 1.44/1.65 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(258,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), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[257])).
% 1.44/1.65 tff(259,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), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[258, 256])).
% 1.44/1.65 tff(260,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), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(261,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[260, 259])).
% 1.44/1.65 tff(262,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[261, 97, 61, 255, 83, 87])).
% 1.44/1.65 tff(263,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(264,plain,
% 1.44/1.65 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[263, 87, 83, 61])).
% 1.44/1.65 tff(265,plain,
% 1.44/1.65 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(commutativity,[status(thm)],[])).
% 1.44/1.65 tff(266,plain,
% 1.44/1.65 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(z) = s(s(s(s(elem!1))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[265])).
% 1.44/1.65 tff(267,assumption,(s(s(s(s(elem!1)))) = s(z)), introduced(assumption)).
% 1.44/1.65 tff(268,plain,
% 1.44/1.65 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[267])).
% 1.44/1.65 tff(269,plain,
% 1.44/1.65 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(270,plain,
% 1.44/1.65 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[269, 15])).
% 1.44/1.65 tff(271,plain,
% 1.44/1.65 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(symmetry,[status(thm)],[270])).
% 1.44/1.65 tff(272,plain,
% 1.44/1.65 (s(s(s(elem!1))) = z),
% 1.44/1.65 inference(transitivity,[status(thm)],[271, 268, 17])).
% 1.44/1.65 tff(273,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[241, 272])).
% 1.44/1.65 tff(274,plain,(~(s(s(s(s(elem!1)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(275,plain,
% 1.44/1.65 (~(s(z) = s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[274, 266])).
% 1.44/1.65 tff(276,plain,
% 1.44/1.65 (((~![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))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(277,plain,
% 1.44/1.65 ((~![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))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(278,plain,
% 1.44/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[277, 276])).
% 1.44/1.65 tff(279,plain,
% 1.44/1.65 ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[278, 53])).
% 1.44/1.65 tff(280,plain,
% 1.44/1.65 (b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[279, 275])).
% 1.44/1.65 tff(281,plain,
% 1.44/1.65 (r(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[280, 264])).
% 1.44/1.65 tff(282,assumption,(s(s(s(s(elem!1)))) = s(s(s(z)))), introduced(assumption)).
% 1.44/1.65 tff(283,plain,
% 1.44/1.65 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(z))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[282])).
% 1.44/1.65 tff(284,plain,
% 1.44/1.65 (s(s(s(elem!1))) = s(s(z))),
% 1.44/1.65 inference(transitivity,[status(thm)],[271, 283, 72])).
% 1.44/1.65 tff(285,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[43, 284])).
% 1.44/1.65 tff(286,plain,(~(s(s(s(s(elem!1)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(287,assumption,(r(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.44/1.65 tff(288,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.44/1.65 tff(289,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(290,plain,
% 1.44/1.65 (((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(291,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[290])).
% 1.44/1.65 tff(292,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[291, 289])).
% 1.44/1.65 tff(293,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(294,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[293, 292])).
% 1.44/1.65 tff(295,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[294, 155, 226, 81, 288, 3, 225])).
% 1.44/1.65 tff(296,plain,((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(297,plain,
% 1.44/1.65 (~r(z, s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[296, 225, 3, 288, 81])).
% 1.44/1.65 tff(298,plain,
% 1.44/1.65 (b(z, s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[222, 297])).
% 1.44/1.65 tff(299,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(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(300,plain,
% 1.44/1.65 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(301,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)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[300])).
% 1.44/1.65 tff(302,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)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[301, 299])).
% 1.44/1.65 tff(303,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)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(304,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[303, 302])).
% 1.44/1.65 tff(305,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[304, 97, 124, 204, 83, 60])).
% 1.44/1.66 tff(306,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(307,plain,
% 1.44/1.66 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[306, 298, 83, 124])).
% 1.44/1.66 tff(308,plain,
% 1.44/1.66 (r(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[58, 307])).
% 1.44/1.66 tff(309,assumption,(r(s(s(z)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.44/1.66 tff(310,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(311,plain,
% 1.44/1.66 (((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(312,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[311])).
% 1.44/1.66 tff(313,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[312, 310])).
% 1.44/1.66 tff(314,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(315,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[314, 313])).
% 1.44/1.66 tff(316,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[315, 155, 287, 309, 3, 225, 145])).
% 1.44/1.66 tff(317,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(318,plain,
% 1.44/1.66 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[317, 308, 287, 225, 3])).
% 1.44/1.66 tff(319,plain,
% 1.44/1.66 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(commutativity,[status(thm)],[])).
% 1.44/1.66 tff(320,plain,
% 1.44/1.66 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(z)))),
% 1.44/1.66 inference(symmetry,[status(thm)],[319])).
% 1.44/1.66 tff(321,assumption,(s(s(z)) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.66 tff(322,plain,
% 1.44/1.66 (s(s(s(s(elem!1)))) = s(s(z))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[321, 320])).
% 1.44/1.66 tff(323,assumption,(s(s(s(s(elem!1)))) = s(s(z))), introduced(assumption)).
% 1.44/1.66 tff(324,plain,
% 1.44/1.66 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(z)))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[323])).
% 1.44/1.66 tff(325,plain,
% 1.44/1.66 (s(s(s(elem!1))) = s(z)),
% 1.44/1.66 inference(transitivity,[status(thm)],[271, 324, 23])).
% 1.44/1.66 tff(326,assumption,(~(s(s(s(elem!1))) = s(z))), introduced(assumption)).
% 1.44/1.66 tff(327,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[326, 325])).
% 1.44/1.66 tff(328,plain,((~(s(s(s(s(elem!1)))) = s(s(z)))) | (s(s(s(elem!1))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(329,plain,
% 1.44/1.66 (~(s(s(s(s(elem!1)))) = s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[328, 172])).
% 1.44/1.66 tff(330,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[329, 322])).
% 1.44/1.66 tff(331,plain,(~(s(s(z)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(332,plain,
% 1.44/1.66 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(333,plain,
% 1.44/1.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(334,plain,
% 1.44/1.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[333, 332])).
% 1.44/1.66 tff(335,plain,
% 1.44/1.66 ((s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[334, 53])).
% 1.44/1.66 tff(336,plain,
% 1.44/1.66 (b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[335, 331])).
% 1.44/1.66 tff(337,plain,
% 1.44/1.66 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[336, 318])).
% 1.44/1.66 tff(338,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.44/1.66 tff(339,assumption,(b(s(s(z)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.44/1.66 tff(340,assumption,(s(s(s(elem!1))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.66 tff(341,plain,
% 1.44/1.66 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[340])).
% 1.44/1.66 tff(342,plain,
% 1.44/1.66 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.44/1.66 inference(symmetry,[status(thm)],[341])).
% 1.44/1.66 tff(343,plain,
% 1.44/1.66 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[340])).
% 1.44/1.66 tff(344,plain,
% 1.44/1.66 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(elem!1))))),
% 1.44/1.66 inference(symmetry,[status(thm)],[343])).
% 1.44/1.66 tff(345,plain,
% 1.44/1.66 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.44/1.66 inference(symmetry,[status(thm)],[340])).
% 1.44/1.66 tff(346,plain,
% 1.44/1.66 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.44/1.66 inference(transitivity,[status(thm)],[345, 271, 344, 19])).
% 1.44/1.66 tff(347,assumption,(~(s(s(s(s(elem!1)))) = s(s(elem!1)))), introduced(assumption)).
% 1.44/1.66 tff(348,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[347, 346])).
% 1.44/1.66 tff(349,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(350,plain,
% 1.44/1.66 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[349, 340])).
% 1.44/1.66 tff(351,plain,
% 1.44/1.66 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[350, 342])).
% 1.44/1.66 tff(352,assumption,(~(s(s(s(elem!1))) = s(s(elem!1)))), introduced(assumption)).
% 1.44/1.66 tff(353,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[352, 351])).
% 1.44/1.66 tff(354,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(355,plain,
% 1.44/1.66 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[354, 340])).
% 1.44/1.66 tff(356,assumption,(s(s(s(elem!1))) = s(s(elem!1))), introduced(assumption)).
% 1.44/1.66 tff(357,plain,
% 1.44/1.66 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.44/1.66 inference(symmetry,[status(thm)],[356])).
% 1.44/1.66 tff(358,plain,
% 1.44/1.66 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[356])).
% 1.44/1.66 tff(359,plain,
% 1.44/1.66 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.44/1.66 inference(transitivity,[status(thm)],[358, 356])).
% 1.44/1.66 tff(360,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[347, 359])).
% 1.44/1.66 tff(361,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(362,plain,
% 1.44/1.66 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[361, 356])).
% 1.44/1.66 tff(363,plain,
% 1.44/1.66 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.44/1.66 inference(transitivity,[status(thm)],[362, 357])).
% 1.44/1.66 tff(364,plain,
% 1.44/1.66 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(elem!1))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[363])).
% 1.44/1.66 tff(365,plain,
% 1.44/1.66 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(symmetry,[status(thm)],[364])).
% 1.44/1.66 tff(366,plain,
% 1.44/1.66 (b(z, s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[124, 365])).
% 1.44/1.66 tff(367,assumption,(~b(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.44/1.66 tff(368,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[367, 366])).
% 1.44/1.66 tff(369,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | b(z, s(s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(370,plain,
% 1.44/1.66 (b(z, s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[369, 355, 124])).
% 1.44/1.66 tff(371,assumption,(b(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 1.44/1.66 tff(372,assumption,(b(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.44/1.66 tff(373,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(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(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(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(374,plain,
% 1.44/1.66 (((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(375,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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[374])).
% 1.44/1.66 tff(376,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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[375, 373])).
% 1.44/1.66 tff(377,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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(378,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[377, 376])).
% 1.44/1.66 tff(379,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[378, 97, 372, 339, 83, 371])).
% 1.44/1.66 tff(380,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(381,plain,
% 1.44/1.66 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[380, 370, 339, 83])).
% 1.44/1.66 tff(382,plain,
% 1.44/1.66 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(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)))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(383,plain,
% 1.44/1.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(384,plain,
% 1.44/1.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[383, 382])).
% 1.44/1.66 tff(385,plain,
% 1.44/1.66 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[384, 53, 381, 286])).
% 1.44/1.66 tff(386,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 1.44/1.66 tff(387,assumption,(r(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 1.44/1.66 tff(388,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(389,plain,
% 1.44/1.66 (((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~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(s(s(z))), z)) | (~r(s(z), 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))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(390,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[389])).
% 1.44/1.66 tff(391,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[390, 388])).
% 1.44/1.66 tff(392,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~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)))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(393,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[392, 391])).
% 1.44/1.66 tff(394,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[393, 155, 287, 81, 387, 338, 386])).
% 1.44/1.66 tff(395,plain,((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(396,plain,
% 1.44/1.66 (~r(s(s(s(z))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[395, 385, 81, 287, 338])).
% 1.44/1.66 tff(397,plain,
% 1.44/1.66 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(398,plain,
% 1.44/1.66 (~(s(s(s(z))) = z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[397, 38])).
% 1.44/1.66 tff(399,plain,
% 1.44/1.66 (((~![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))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(400,plain,
% 1.44/1.66 ((~![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))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(401,plain,
% 1.44/1.66 ((~![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)),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[400, 399])).
% 1.44/1.66 tff(402,plain,
% 1.44/1.66 (b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[401, 53, 398])).
% 1.44/1.66 tff(403,plain,
% 1.44/1.66 (b(s(s(s(z))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[402, 396])).
% 1.44/1.66 tff(404,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(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(405,plain,
% 1.44/1.66 (((~b(z, s(z))) | (~b(z, 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(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(406,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(z))) | (~b(z, 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(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[405])).
% 1.44/1.66 tff(407,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(z))) | (~b(z, 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(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.44/1.66 inference(transitivity,[status(thm)],[406, 404])).
% 1.44/1.66 tff(408,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(z))) | (~b(z, 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)))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(409,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[408, 407])).
% 1.44/1.66 tff(410,plain,
% 1.44/1.66 (~b(s(s(s(z))), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[409, 97, 61, 83, 403])).
% 1.44/1.66 tff(411,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 1.44/1.66 tff(412,plain,
% 1.44/1.66 (s(s(z)) = s(s(s(z)))),
% 1.44/1.66 inference(symmetry,[status(thm)],[411])).
% 1.44/1.66 tff(413,plain,
% 1.44/1.66 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[412])).
% 1.44/1.66 tff(414,plain,
% 1.44/1.66 (s(z) = s(s(z))),
% 1.44/1.66 inference(transitivity,[status(thm)],[24, 413, 72])).
% 1.44/1.66 tff(415,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[116, 414])).
% 1.44/1.66 tff(416,plain,(~(s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(417,plain,
% 1.44/1.66 (((~![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))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(418,plain,
% 1.44/1.66 ((~![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))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(419,plain,
% 1.44/1.66 ((~![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)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[418, 417])).
% 1.44/1.66 tff(420,plain,
% 1.44/1.66 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[419, 53])).
% 1.44/1.66 tff(421,plain,
% 1.44/1.66 (b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[420, 416])).
% 1.44/1.66 tff(422,plain,
% 1.44/1.66 (r(s(s(s(z))), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[421, 410])).
% 1.44/1.66 tff(423,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(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(424,plain,
% 1.44/1.66 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(425,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(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(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(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[424])).
% 1.44/1.67 tff(426,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(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(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(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.44/1.67 inference(transitivity,[status(thm)],[425, 423])).
% 1.44/1.67 tff(427,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(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(428,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(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[427, 426])).
% 1.44/1.67 tff(429,plain,
% 1.44/1.67 (~b(s(s(z)), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[428, 97, 61, 83, 403])).
% 1.44/1.67 tff(430,plain,
% 1.44/1.67 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 1.44/1.67 inference(commutativity,[status(thm)],[])).
% 1.44/1.67 tff(431,plain,
% 1.44/1.67 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[430])).
% 1.44/1.67 tff(432,plain,
% 1.44/1.67 (~(s(s(z)) = s(s(s(z))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[416, 431])).
% 1.44/1.67 tff(433,plain,
% 1.44/1.67 (((~![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)))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(434,plain,
% 1.44/1.67 ((~![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)))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(435,plain,
% 1.44/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[434, 433])).
% 1.44/1.67 tff(436,plain,
% 1.44/1.67 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[435, 53])).
% 1.44/1.67 tff(437,plain,
% 1.44/1.67 (b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[436, 432])).
% 1.44/1.67 tff(438,plain,
% 1.44/1.67 (r(s(s(z)), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[437, 429])).
% 1.44/1.67 tff(439,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[340])).
% 1.44/1.67 tff(440,plain,
% 1.44/1.67 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.67 inference(symmetry,[status(thm)],[439])).
% 1.44/1.67 tff(441,assumption,(b(s(s(s(s(elem!1)))), s(s(z)))), introduced(assumption)).
% 1.44/1.67 tff(442,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[441, 440])).
% 1.44/1.67 tff(443,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5, 442])).
% 1.44/1.67 tff(444,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(445,plain,
% 1.44/1.67 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[444, 340, 5])).
% 1.44/1.67 tff(446,assumption,(~b(s(s(s(s(elem!1)))), s(s(z)))), introduced(assumption)).
% 1.44/1.67 tff(447,assumption,(~r(s(s(s(s(elem!1)))), s(s(z)))), introduced(assumption)).
% 1.44/1.67 tff(448,plain,
% 1.44/1.67 (((~![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))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(449,plain,
% 1.44/1.67 ((~![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))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(450,plain,
% 1.44/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[449, 448])).
% 1.44/1.67 tff(451,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[450, 53, 329, 447, 446])).
% 1.44/1.67 tff(452,plain,(b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(453,plain,
% 1.44/1.67 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[452, 445])).
% 1.44/1.67 tff(454,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(455,plain,
% 1.44/1.67 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(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(z)))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(456,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[455])).
% 1.44/1.67 tff(457,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[456, 454])).
% 1.44/1.67 tff(458,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(459,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[458, 457])).
% 1.44/1.67 tff(460,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[459, 155, 453, 385, 438, 422])).
% 1.44/1.67 tff(461,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(462,plain,
% 1.44/1.67 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[461, 337, 83, 81, 287, 338, 61, 124, 307])).
% 1.44/1.67 tff(463,assumption,(r(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.44/1.67 tff(464,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(465,plain,
% 1.44/1.67 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(466,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[465])).
% 1.44/1.67 tff(467,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[466, 464])).
% 1.44/1.67 tff(468,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(469,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[468, 467])).
% 1.44/1.67 tff(470,plain,
% 1.44/1.67 (~r(s(z), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[469, 155, 287, 463, 81, 288])).
% 1.44/1.67 tff(471,plain,
% 1.44/1.67 (b(s(z), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[181, 470])).
% 1.44/1.67 tff(472,assumption,(~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.44/1.67 tff(473,assumption,(b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.44/1.67 tff(474,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(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), 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(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(475,plain,
% 1.44/1.67 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(476,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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(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(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[475])).
% 1.44/1.67 tff(477,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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(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(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[476, 474])).
% 1.44/1.67 tff(478,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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(479,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[478, 477])).
% 1.44/1.67 tff(480,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[479, 97, 193, 61, 124, 473])).
% 1.44/1.67 tff(481,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(482,plain,
% 1.44/1.67 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[481, 471, 61, 124])).
% 1.44/1.67 tff(483,plain,
% 1.44/1.67 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(484,plain,
% 1.44/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(485,plain,
% 1.44/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[484, 483])).
% 1.44/1.67 tff(486,plain,
% 1.44/1.67 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[485, 53])).
% 1.44/1.67 tff(487,plain,
% 1.44/1.67 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[486, 482, 472])).
% 1.44/1.67 tff(488,assumption,(r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.44/1.67 tff(489,plain,
% 1.44/1.67 (((~![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)))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(490,plain,
% 1.44/1.67 ((~![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)))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(491,plain,
% 1.44/1.67 ((~![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))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[490, 489])).
% 1.44/1.67 tff(492,plain,
% 1.44/1.67 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[491, 53])).
% 1.44/1.67 tff(493,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[492, 172])).
% 1.44/1.67 tff(494,plain,
% 1.44/1.67 (r(s(s(s(elem!1))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[493, 82])).
% 1.44/1.67 tff(495,assumption,(r(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.44/1.67 tff(496,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(497,plain,
% 1.44/1.67 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(498,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[497])).
% 1.44/1.67 tff(499,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[498, 496])).
% 1.44/1.67 tff(500,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(501,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[500, 499])).
% 1.44/1.67 tff(502,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[501, 155, 125, 287, 488, 495])).
% 1.44/1.68 tff(503,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(504,plain,
% 1.44/1.68 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[503, 488, 494, 287])).
% 1.44/1.68 tff(505,assumption,(~r(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.44/1.68 tff(506,assumption,(~b(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.44/1.68 tff(507,plain,
% 1.44/1.68 (((~![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)))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(508,plain,
% 1.44/1.68 ((~![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)))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(509,plain,
% 1.44/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[508, 507])).
% 1.44/1.68 tff(510,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[509, 53, 506, 274, 505])).
% 1.44/1.68 tff(511,plain,(b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(512,plain,
% 1.44/1.68 (b(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[511, 504])).
% 1.44/1.68 tff(513,assumption,(b(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.44/1.68 tff(514,plain,
% 1.44/1.68 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[340])).
% 1.44/1.68 tff(515,plain,
% 1.44/1.68 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.44/1.68 inference(symmetry,[status(thm)],[514])).
% 1.44/1.68 tff(516,plain,
% 1.44/1.68 (b(s(s(s(elem!1))), s(z))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[513, 515])).
% 1.44/1.68 tff(517,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[82, 516])).
% 1.44/1.68 tff(518,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(z)) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(519,plain,
% 1.44/1.68 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[518, 513, 82])).
% 1.44/1.68 tff(520,assumption,(s(s(s(s(elem!1)))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.44/1.68 tff(521,plain,
% 1.44/1.68 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.44/1.68 inference(symmetry,[status(thm)],[520])).
% 1.44/1.68 tff(522,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[472, 521])).
% 1.44/1.68 tff(523,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(524,plain,
% 1.44/1.68 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[523, 519])).
% 1.44/1.68 tff(525,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(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(526,plain,
% 1.44/1.68 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(527,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(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(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(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[526])).
% 1.44/1.68 tff(528,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(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(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(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[527, 525])).
% 1.44/1.68 tff(529,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(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(530,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[529, 528])).
% 1.44/1.68 tff(531,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[530, 97, 193, 61, 372, 513])).
% 1.44/1.68 tff(532,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(533,plain,
% 1.44/1.68 (~b(s(z), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[532, 61, 372, 513])).
% 1.44/1.68 tff(534,plain,
% 1.44/1.68 (r(s(z), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[179, 53, 533, 174])).
% 1.44/1.68 tff(535,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 1.44/1.68 tff(536,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(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(537,plain,
% 1.44/1.68 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(538,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(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(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(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[537])).
% 1.44/1.68 tff(539,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(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(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(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[538, 536])).
% 1.44/1.68 tff(540,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(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(541,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[540, 539])).
% 1.44/1.68 tff(542,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[541, 97, 61, 372, 513, 535])).
% 1.44/1.68 tff(543,plain,((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(544,plain,
% 1.44/1.68 (~b(s(z), s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[543, 61, 372, 513])).
% 1.44/1.68 tff(545,plain,
% 1.44/1.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(546,plain,
% 1.44/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(547,plain,
% 1.44/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[546, 545])).
% 1.44/1.68 tff(548,plain,
% 1.44/1.68 (b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[547, 53, 116])).
% 1.44/1.68 tff(549,plain,
% 1.44/1.68 (r(s(z), s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[548, 544])).
% 1.44/1.68 tff(550,assumption,(b(s(z), z)), introduced(assumption)).
% 1.44/1.68 tff(551,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), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(552,plain,
% 1.44/1.68 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(553,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), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(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(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[552])).
% 1.44/1.68 tff(554,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), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(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(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[553, 551])).
% 1.44/1.68 tff(555,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), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(556,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[555, 554])).
% 1.44/1.68 tff(557,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[556, 97, 550, 61, 372, 513])).
% 1.44/1.68 tff(558,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(559,plain,
% 1.44/1.68 (~b(s(z), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[558, 61, 372, 513])).
% 1.44/1.68 tff(560,assumption,(~r(s(z), z)), introduced(assumption)).
% 1.44/1.68 tff(561,assumption,(~b(s(z), z)), introduced(assumption)).
% 1.44/1.68 tff(562,plain,
% 1.44/1.68 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(563,plain,
% 1.44/1.68 (~(s(z) = z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[562, 38])).
% 1.44/1.68 tff(564,plain,
% 1.44/1.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(565,plain,
% 1.44/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(566,plain,
% 1.44/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[565, 564])).
% 1.44/1.68 tff(567,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[566, 53, 563, 561, 560])).
% 1.44/1.68 tff(568,plain,(r(s(z), z) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(569,plain,
% 1.44/1.68 (r(s(z), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[568, 559])).
% 1.44/1.68 tff(570,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.68 tff(571,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(572,plain,
% 1.44/1.68 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(573,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[572])).
% 1.44/1.68 tff(574,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[573, 571])).
% 1.44/1.68 tff(575,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(576,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[575, 574])).
% 1.44/1.68 tff(577,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[576, 155, 570, 287, 488, 81, 225])).
% 1.44/1.68 tff(578,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(579,plain,
% 1.44/1.68 (~r(z, s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[578, 488, 287, 569, 534])).
% 1.44/1.68 tff(580,assumption,(z = s(s(s(elem!1)))), introduced(assumption)).
% 1.44/1.68 tff(581,plain,
% 1.44/1.68 (s(s(s(elem!1))) = z),
% 1.44/1.68 inference(symmetry,[status(thm)],[580])).
% 1.44/1.68 tff(582,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[241, 581])).
% 1.44/1.68 tff(583,plain,(~(z = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(584,assumption,(~b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.68 tff(585,assumption,(~r(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.68 tff(586,plain,
% 1.44/1.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(587,plain,
% 1.44/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(588,plain,
% 1.44/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[587, 586])).
% 1.44/1.68 tff(589,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[588, 53, 585, 584, 583])).
% 1.44/1.68 tff(590,plain,(b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(591,plain,
% 1.44/1.68 (b(z, s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[590, 579])).
% 1.44/1.68 tff(592,plain,
% 1.44/1.68 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 1.44/1.68 inference(commutativity,[status(thm)],[])).
% 1.44/1.68 tff(593,plain,
% 1.44/1.68 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(elem!1))))),
% 1.44/1.68 inference(symmetry,[status(thm)],[592])).
% 1.44/1.68 tff(594,plain,
% 1.44/1.68 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = s(s(s(elem!1)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[593])).
% 1.44/1.68 tff(595,plain,
% 1.44/1.68 (~(s(z) = s(s(s(elem!1))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[172, 594])).
% 1.44/1.68 tff(596,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(597,plain,
% 1.44/1.68 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(598,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[597])).
% 1.44/1.68 tff(599,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[598, 596])).
% 1.44/1.68 tff(600,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(601,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[600, 599])).
% 1.44/1.68 tff(602,plain,
% 1.44/1.68 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[601, 155, 125, 287, 488, 2])).
% 1.44/1.68 tff(603,plain,
% 1.44/1.68 (b(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[56, 53, 43, 602])).
% 1.44/1.68 tff(604,plain,
% 1.44/1.68 (~b(s(z), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[201, 603, 124, 61])).
% 1.44/1.68 tff(605,plain,
% 1.44/1.68 ((s(z) = s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[179, 53, 604])).
% 1.44/1.68 tff(606,plain,
% 1.44/1.68 (r(s(z), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[605, 595])).
% 1.44/1.68 tff(607,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(608,plain,
% 1.44/1.68 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(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(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(609,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[608])).
% 1.44/1.69 tff(610,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[609, 607])).
% 1.44/1.69 tff(611,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(612,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[611, 610])).
% 1.44/1.69 tff(613,plain,
% 1.44/1.69 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[612, 155, 125, 2, 606])).
% 1.44/1.69 tff(614,plain,
% 1.44/1.69 (b(s(s(z)), s(s(s(elem!1))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[141, 53, 42, 613])).
% 1.44/1.69 tff(615,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(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(616,plain,
% 1.44/1.69 (((~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(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(617,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(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(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(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[616])).
% 1.44/1.69 tff(618,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(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(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(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[617, 615])).
% 1.44/1.69 tff(619,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(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(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(620,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(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[619, 618])).
% 1.44/1.69 tff(621,plain,
% 1.44/1.69 (~b(s(s(z)), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[620, 97, 124, 603, 614])).
% 1.44/1.69 tff(622,plain,
% 1.44/1.69 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(623,plain,
% 1.44/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(624,plain,
% 1.44/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z)),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[623, 622])).
% 1.44/1.69 tff(625,plain,
% 1.44/1.69 (b(s(s(z)), z) | r(s(s(z)), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[624, 53, 76])).
% 1.44/1.69 tff(626,plain,
% 1.44/1.69 (r(s(s(z)), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[625, 621])).
% 1.44/1.69 tff(627,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(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(628,plain,
% 1.44/1.69 (((~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(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(629,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(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(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(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[628])).
% 1.44/1.69 tff(630,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(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(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(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[629, 627])).
% 1.44/1.69 tff(631,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(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(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(632,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(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[631, 630])).
% 1.44/1.69 tff(633,plain,
% 1.44/1.69 (~b(z, s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[632, 97, 124, 603, 614])).
% 1.44/1.69 tff(634,plain,
% 1.44/1.69 (r(z, s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[222, 633])).
% 1.44/1.69 tff(635,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(636,plain,
% 1.44/1.69 (((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(637,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(z))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[636])).
% 1.44/1.69 tff(638,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[637, 635])).
% 1.44/1.69 tff(639,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(640,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(z))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[639, 638])).
% 1.44/1.69 tff(641,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[640, 155, 634, 81, 626, 3])).
% 1.44/1.69 tff(642,plain,((~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(643,plain,
% 1.44/1.69 (~r(s(s(z)), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[642, 591, 287, 549, 125, 61, 569, 488])).
% 1.44/1.69 tff(644,plain,
% 1.44/1.69 (b(s(s(z)), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[122, 643])).
% 1.44/1.69 tff(645,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 1.44/1.69 tff(646,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(647,plain,
% 1.44/1.69 (((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(648,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[647])).
% 1.44/1.69 tff(649,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)))),
% 1.44/1.69 inference(transitivity,[status(thm)],[648, 646])).
% 1.44/1.69 tff(650,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(651,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[650, 649])).
% 1.44/1.69 tff(652,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[651, 155, 81, 645, 3, 225, 145])).
% 1.44/1.69 tff(653,plain,((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(654,plain,
% 1.44/1.69 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[653, 645, 225, 3, 81])).
% 1.44/1.69 tff(655,plain,
% 1.44/1.69 (b(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[58, 654])).
% 1.44/1.69 tff(656,plain,
% 1.44/1.69 (~b(z, s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[212, 655, 124, 87])).
% 1.44/1.69 tff(657,plain,
% 1.44/1.69 (r(z, s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[222, 656])).
% 1.44/1.69 tff(658,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[640, 155, 657, 81, 645, 3])).
% 1.44/1.69 tff(659,plain,((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(660,plain,
% 1.44/1.69 (~r(s(s(z)), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[659, 591, 549, 569, 644, 534])).
% 1.44/1.69 tff(661,plain,
% 1.44/1.69 (b(s(s(z)), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[625, 660])).
% 1.44/1.69 tff(662,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(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(663,plain,
% 1.44/1.69 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(664,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(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[663])).
% 1.44/1.69 tff(665,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(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[664, 662])).
% 1.44/1.69 tff(666,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(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(667,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[666, 665])).
% 1.44/1.69 tff(668,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[667, 97, 372, 339, 83, 513])).
% 1.44/1.69 tff(669,plain,((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(670,plain,
% 1.44/1.69 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[669, 661, 372, 513])).
% 1.44/1.69 tff(671,plain,
% 1.44/1.69 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[336, 670])).
% 1.44/1.69 tff(672,plain,
% 1.44/1.69 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[317, 671, 287, 534, 549])).
% 1.44/1.69 tff(673,plain,
% 1.44/1.69 (b(s(s(s(elem!1))), s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[58, 672])).
% 1.44/1.69 tff(674,plain,
% 1.44/1.69 (~b(z, s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[212, 673, 591, 644])).
% 1.44/1.69 tff(675,plain,
% 1.44/1.69 (r(z, s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[222, 674])).
% 1.44/1.69 tff(676,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(677,plain,
% 1.44/1.69 (((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(678,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))))),
% 1.44/1.70 inference(monotonicity,[status(thm)],[677])).
% 1.44/1.70 tff(679,plain,
% 1.44/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 1.44/1.70 inference(transitivity,[status(thm)],[678, 676])).
% 1.44/1.70 tff(680,plain,
% 1.44/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.44/1.70 inference(quant_inst,[status(thm)],[])).
% 1.44/1.70 tff(681,plain,
% 1.44/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))),
% 1.44/1.70 inference(modus_ponens,[status(thm)],[680, 679])).
% 1.44/1.70 tff(682,plain,
% 1.44/1.70 ($false),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[681, 155, 287, 671, 675, 569, 549])).
% 1.44/1.70 tff(683,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.70 tff(684,plain,
% 1.44/1.70 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[683, 61, 372, 513, 125, 287])).
% 1.44/1.70 tff(685,plain,
% 1.44/1.70 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[486, 684, 472])).
% 1.44/1.70 tff(686,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(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.70 inference(rewrite,[status(thm)],[])).
% 1.44/1.70 tff(687,plain,
% 1.44/1.70 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.70 inference(rewrite,[status(thm)],[])).
% 1.44/1.70 tff(688,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(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.44/1.70 inference(monotonicity,[status(thm)],[687])).
% 1.44/1.70 tff(689,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(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[688, 686])).
% 1.54/1.70 tff(690,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(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(691,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))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[690, 689])).
% 1.54/1.70 tff(692,plain,
% 1.54/1.70 (~b(s(s(s(elem!1))), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[691, 97, 372, 685, 513])).
% 1.54/1.70 tff(693,plain,
% 1.54/1.70 (r(s(s(s(elem!1))), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[246, 692])).
% 1.54/1.70 tff(694,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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(695,plain,
% 1.54/1.70 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(696,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(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[695])).
% 1.54/1.70 tff(697,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(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[696, 694])).
% 1.54/1.70 tff(698,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(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(699,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[698, 697])).
% 1.54/1.70 tff(700,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[699, 97, 124, 372, 473, 513])).
% 1.54/1.70 tff(701,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(702,plain,
% 1.54/1.70 (~b(z, s(s(s(elem!1))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[701, 685, 372, 513])).
% 1.54/1.70 tff(703,plain,
% 1.54/1.70 (r(z, s(s(s(elem!1))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[590, 702])).
% 1.54/1.70 tff(704,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(705,plain,
% 1.54/1.70 (((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(706,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)) | (~r(s(s(s(elem!1))), z))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[705])).
% 1.54/1.70 tff(707,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.70 inference(transitivity,[status(thm)],[706, 704])).
% 1.54/1.70 tff(708,plain,
% 1.54/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(709,plain,
% 1.54/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[708, 707])).
% 1.54/1.70 tff(710,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[709, 155, 703, 569, 693, 534])).
% 1.54/1.70 tff(711,plain,((~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(712,plain,
% 1.54/1.70 (~b(z, s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[711, 513, 372, 519, 494, 287])).
% 1.54/1.70 tff(713,assumption,(z = s(z)), introduced(assumption)).
% 1.54/1.70 tff(714,plain,
% 1.54/1.70 (s(z) = z),
% 1.54/1.70 inference(symmetry,[status(thm)],[713])).
% 1.54/1.70 tff(715,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[563, 714])).
% 1.54/1.70 tff(716,plain,(~(z = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(717,assumption,(~b(z, s(z))), introduced(assumption)).
% 1.54/1.70 tff(718,assumption,(~r(z, s(z))), introduced(assumption)).
% 1.54/1.70 tff(719,plain,
% 1.54/1.70 (((~![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)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(720,plain,
% 1.54/1.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(721,plain,
% 1.54/1.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[720, 719])).
% 1.54/1.70 tff(722,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[721, 53, 718, 717, 716])).
% 1.54/1.70 tff(723,plain,(b(z, s(z)) | r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(724,plain,
% 1.54/1.70 (r(z, s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[723, 712])).
% 1.54/1.70 tff(725,plain,
% 1.54/1.70 (~b(s(s(s(elem!1))), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[691, 97, 372, 473, 513])).
% 1.54/1.70 tff(726,plain,
% 1.54/1.70 (r(s(s(s(elem!1))), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[246, 725])).
% 1.54/1.70 tff(727,plain,
% 1.54/1.70 (~b(z, s(s(s(elem!1))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[701, 473, 372, 513])).
% 1.54/1.70 tff(728,plain,
% 1.54/1.70 (r(z, s(s(s(elem!1))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[590, 727])).
% 1.54/1.70 tff(729,assumption,(r(z, s(z))), introduced(assumption)).
% 1.54/1.70 tff(730,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(731,plain,
% 1.54/1.70 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(732,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[731])).
% 1.54/1.70 tff(733,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[732, 730])).
% 1.54/1.70 tff(734,plain,
% 1.54/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(735,plain,
% 1.54/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[734, 733])).
% 1.54/1.70 tff(736,plain,
% 1.54/1.70 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[735, 155, 570, 288, 645])).
% 1.54/1.70 tff(737,plain,
% 1.54/1.70 (b(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[141, 53, 42, 736])).
% 1.54/1.70 tff(738,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(739,plain,
% 1.54/1.70 (((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(740,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[739])).
% 1.54/1.70 tff(741,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.70 inference(transitivity,[status(thm)],[740, 738])).
% 1.54/1.70 tff(742,plain,
% 1.54/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(743,plain,
% 1.54/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[742, 741])).
% 1.54/1.70 tff(744,plain,
% 1.54/1.70 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[743, 155, 125, 729, 288, 645])).
% 1.54/1.70 tff(745,plain,
% 1.54/1.70 (b(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[58, 744])).
% 1.54/1.70 tff(746,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(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), 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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(747,plain,
% 1.54/1.70 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(748,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(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[747])).
% 1.54/1.71 tff(749,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(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[748, 746])).
% 1.54/1.71 tff(750,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(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(751,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[750, 749])).
% 1.54/1.71 tff(752,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[751, 97, 473, 339, 60, 513])).
% 1.54/1.71 tff(753,plain,((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(754,plain,
% 1.54/1.71 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[753, 745, 473, 513])).
% 1.54/1.71 tff(755,plain,
% 1.54/1.71 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[336, 754])).
% 1.54/1.71 tff(756,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(757,plain,
% 1.54/1.71 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(758,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[757])).
% 1.54/1.71 tff(759,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[758, 756])).
% 1.54/1.71 tff(760,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(761,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[760, 759])).
% 1.54/1.71 tff(762,plain,
% 1.54/1.71 (~r(s(s(z)), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[761, 155, 729, 287, 755, 645])).
% 1.54/1.71 tff(763,plain,
% 1.54/1.71 (b(s(s(z)), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[122, 762])).
% 1.54/1.71 tff(764,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(765,plain,
% 1.54/1.71 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(766,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[765])).
% 1.54/1.71 tff(767,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[766, 764])).
% 1.54/1.71 tff(768,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(769,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[768, 767])).
% 1.54/1.71 tff(770,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[769, 155, 125, 729, 570, 225])).
% 1.54/1.71 tff(771,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(772,plain,
% 1.54/1.71 (~r(s(z), s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[771, 570, 729, 125])).
% 1.54/1.71 tff(773,plain,
% 1.54/1.71 (b(s(z), s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[181, 772])).
% 1.54/1.71 tff(774,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(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(775,plain,
% 1.54/1.71 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(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(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(776,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(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(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(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[775])).
% 1.54/1.71 tff(777,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(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(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(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[776, 774])).
% 1.54/1.71 tff(778,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(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(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))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(779,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[778, 777])).
% 1.54/1.71 tff(780,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[779, 97, 773, 745, 763, 737])).
% 1.54/1.71 tff(781,plain,((~r(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(782,plain,
% 1.54/1.71 (~r(s(s(z)), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[781, 473, 287, 729, 513, 728, 726, 125])).
% 1.54/1.71 tff(783,plain,
% 1.54/1.71 (b(s(s(z)), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[625, 782])).
% 1.54/1.71 tff(784,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(785,plain,
% 1.54/1.71 (((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(786,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[785])).
% 1.54/1.71 tff(787,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[786, 784])).
% 1.54/1.71 tff(788,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(789,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[788, 787])).
% 1.54/1.71 tff(790,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[789, 155, 125, 729, 81, 288])).
% 1.54/1.71 tff(791,plain,((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(792,plain,
% 1.54/1.71 (~r(s(z), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[791, 726, 729, 125])).
% 1.54/1.71 tff(793,plain,
% 1.54/1.71 (b(s(z), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[568, 792])).
% 1.54/1.71 tff(794,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(s(z), s(s(z)))) | (~b(s(s(z)), 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(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(795,plain,
% 1.54/1.71 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(796,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(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(z), 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(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[795])).
% 1.54/1.71 tff(797,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(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(z), 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(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[796, 794])).
% 1.54/1.71 tff(798,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(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(799,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(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[798, 797])).
% 1.54/1.71 tff(800,plain,
% 1.54/1.71 (~b(s(z), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[799, 97, 793, 372, 783])).
% 1.54/1.71 tff(801,plain,
% 1.54/1.71 (r(s(z), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[548, 800])).
% 1.54/1.71 tff(802,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.71 tff(803,plain,
% 1.54/1.71 (~r(s(z), s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[771, 728, 729, 125])).
% 1.54/1.71 tff(804,plain,
% 1.54/1.71 (b(s(z), s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[181, 803])).
% 1.54/1.71 tff(805,assumption,(b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.71 tff(806,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(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(807,plain,
% 1.54/1.71 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(808,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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~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(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[807])).
% 1.54/1.71 tff(809,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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~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(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[808, 806])).
% 1.54/1.71 tff(810,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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(811,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[810, 809])).
% 1.54/1.71 tff(812,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[811, 97, 193, 550, 372, 473, 805, 513])).
% 1.54/1.71 tff(813,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(814,plain,
% 1.54/1.71 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[813, 793, 804, 372, 473, 513])).
% 1.54/1.71 tff(815,assumption,(~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.71 tff(816,assumption,(~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.71 tff(817,plain,
% 1.54/1.71 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(818,plain,
% 1.54/1.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(819,plain,
% 1.54/1.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[818, 817])).
% 1.54/1.71 tff(820,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[819, 53, 816, 802, 815])).
% 1.54/1.71 tff(821,plain,(r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(822,plain,
% 1.54/1.71 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[821, 814, 802])).
% 1.54/1.71 tff(823,assumption,(r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.71 tff(824,assumption,(r(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.54/1.71 tff(825,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(826,plain,
% 1.54/1.72 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(827,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[826])).
% 1.54/1.72 tff(828,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[827, 825])).
% 1.54/1.72 tff(829,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(830,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[829, 828])).
% 1.54/1.72 tff(831,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[830, 155, 570, 288, 824, 823])).
% 1.54/1.72 tff(832,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(833,plain,
% 1.54/1.72 (~r(s(s(s(s(elem!1)))), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[832, 822, 726, 728])).
% 1.54/1.72 tff(834,assumption,(~b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.54/1.72 tff(835,assumption,(~r(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.54/1.72 tff(836,plain,
% 1.54/1.72 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(837,plain,
% 1.54/1.72 (~(s(s(s(s(elem!1)))) = z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[836, 38])).
% 1.54/1.72 tff(838,plain,
% 1.54/1.72 (((~![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))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(839,plain,
% 1.54/1.72 ((~![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))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(840,plain,
% 1.54/1.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[839, 838])).
% 1.54/1.72 tff(841,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[840, 53, 837, 835, 834])).
% 1.54/1.72 tff(842,plain,(b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(843,plain,
% 1.54/1.72 (b(s(s(s(s(elem!1)))), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[842, 833])).
% 1.54/1.72 tff(844,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(s(z)), s(z))) | (~b(s(s(z)), 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(z)), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(845,plain,
% 1.54/1.72 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(846,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(s(s(elem!1)))))) | (~b(z, s(s(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(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[845])).
% 1.54/1.72 tff(847,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(s(s(elem!1)))))) | (~b(z, s(s(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(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[846, 844])).
% 1.54/1.72 tff(848,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(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(849,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(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1))))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[848, 847])).
% 1.54/1.72 tff(850,plain,
% 1.54/1.72 (~b(s(s(z)), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[849, 97, 793, 372, 783])).
% 1.54/1.72 tff(851,plain,
% 1.54/1.72 (r(s(s(z)), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[122, 850])).
% 1.54/1.72 tff(852,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(853,plain,
% 1.54/1.72 (((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(854,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[853])).
% 1.54/1.72 tff(855,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[854, 852])).
% 1.54/1.72 tff(856,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(857,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[856, 855])).
% 1.54/1.72 tff(858,plain,
% 1.54/1.72 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[857, 155, 125, 226, 726, 2])).
% 1.54/1.72 tff(859,plain,
% 1.54/1.72 (b(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[58, 858])).
% 1.54/1.72 tff(860,plain,
% 1.54/1.72 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[753, 859, 473, 513])).
% 1.54/1.72 tff(861,plain,
% 1.54/1.72 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[336, 860])).
% 1.54/1.72 tff(862,plain,
% 1.54/1.72 (~r(s(s(z)), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[761, 155, 729, 287, 861, 2])).
% 1.54/1.72 tff(863,plain,
% 1.54/1.72 (b(s(s(z)), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[625, 862])).
% 1.54/1.72 tff(864,plain,
% 1.54/1.72 (~b(s(z), s(s(z)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[799, 97, 550, 372, 863])).
% 1.54/1.72 tff(865,plain,
% 1.54/1.72 (r(s(z), s(s(z)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[548, 864])).
% 1.54/1.72 tff(866,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(867,plain,
% 1.54/1.72 (((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(868,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[867])).
% 1.54/1.72 tff(869,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[868, 866])).
% 1.54/1.72 tff(870,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(871,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[870, 869])).
% 1.54/1.72 tff(872,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[871, 155, 729, 226, 2, 865])).
% 1.54/1.72 tff(873,plain,((~r(z, s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(874,plain,
% 1.54/1.72 (~r(z, s(s(z)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[873, 851, 793, 729, 372, 287, 473, 513, 125])).
% 1.54/1.72 tff(875,plain,
% 1.54/1.72 (b(z, s(s(z)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[222, 874])).
% 1.54/1.72 tff(876,assumption,(b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.54/1.72 tff(877,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(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, 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(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(878,plain,
% 1.54/1.72 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(879,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(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, 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(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[878])).
% 1.54/1.72 tff(880,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(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, 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(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[879, 877])).
% 1.54/1.72 tff(881,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(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(882,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[881, 880])).
% 1.54/1.72 tff(883,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[882, 97, 204, 83, 876, 441])).
% 1.54/1.72 tff(884,plain,((~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))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(885,plain,
% 1.54/1.72 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[884, 875, 783, 843])).
% 1.54/1.72 tff(886,plain,
% 1.54/1.72 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[452, 885])).
% 1.54/1.72 tff(887,plain,
% 1.54/1.72 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[669, 783, 372, 513])).
% 1.54/1.72 tff(888,plain,
% 1.54/1.72 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[336, 887])).
% 1.54/1.72 tff(889,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(890,plain,
% 1.54/1.72 (((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(891,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[890])).
% 1.54/1.72 tff(892,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[891, 889])).
% 1.54/1.72 tff(893,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(894,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[893, 892])).
% 1.54/1.72 tff(895,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[894, 155, 287, 888, 886, 801])).
% 1.54/1.72 tff(896,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(897,plain,
% 1.54/1.72 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[896, 724, 287, 372, 513, 494, 524])).
% 1.54/1.72 tff(898,plain,
% 1.54/1.72 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[486, 897, 519])).
% 1.54/1.72 tff(899,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(900,plain,
% 1.54/1.73 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(901,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[900])).
% 1.54/1.73 tff(902,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[901, 899])).
% 1.54/1.73 tff(903,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(904,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[903, 902])).
% 1.54/1.73 tff(905,plain,
% 1.54/1.73 (~r(s(s(s(elem!1))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[904, 155, 125, 729, 287, 488])).
% 1.54/1.73 tff(906,plain,
% 1.54/1.73 (b(s(s(s(elem!1))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[246, 905])).
% 1.54/1.73 tff(907,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(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(908,plain,
% 1.54/1.73 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(909,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(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[908])).
% 1.54/1.73 tff(910,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(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[909, 907])).
% 1.54/1.73 tff(911,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(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(912,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[911, 910])).
% 1.54/1.73 tff(913,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[912, 97, 126, 124, 372, 805])).
% 1.54/1.73 tff(914,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(915,plain,
% 1.54/1.73 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[914, 124, 906, 372])).
% 1.54/1.73 tff(916,plain,
% 1.54/1.73 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[821, 915, 802])).
% 1.54/1.73 tff(917,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(918,plain,
% 1.54/1.73 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(919,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[918])).
% 1.54/1.73 tff(920,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[919, 917])).
% 1.54/1.73 tff(921,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(922,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[921, 920])).
% 1.54/1.73 tff(923,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[922, 155, 287, 488, 823, 225])).
% 1.54/1.73 tff(924,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(925,plain,
% 1.54/1.73 (~r(s(z), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[924, 916, 488, 287])).
% 1.54/1.73 tff(926,plain,
% 1.54/1.73 (b(s(z), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[181, 925])).
% 1.54/1.73 tff(927,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), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(928,plain,
% 1.54/1.73 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(929,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), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[928])).
% 1.54/1.73 tff(930,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), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[929, 927])).
% 1.54/1.73 tff(931,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), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(932,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), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[931, 930])).
% 1.54/1.73 tff(933,plain,
% 1.54/1.73 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[932, 97, 193, 513, 87])).
% 1.54/1.73 tff(934,plain,
% 1.54/1.73 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[336, 933])).
% 1.54/1.73 tff(935,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(936,plain,
% 1.54/1.73 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(937,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[936])).
% 1.54/1.73 tff(938,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[937, 935])).
% 1.54/1.73 tff(939,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(940,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[939, 938])).
% 1.54/1.73 tff(941,plain,
% 1.54/1.73 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[940, 155, 488, 934, 823])).
% 1.54/1.73 tff(942,plain,
% 1.54/1.73 (b(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[141, 53, 42, 941])).
% 1.54/1.73 tff(943,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(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(944,plain,
% 1.54/1.73 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), 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(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(945,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(elem!1))), z)) | (~b(s(s(s(elem!1))), 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(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[944])).
% 1.54/1.73 tff(946,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(elem!1))), z)) | (~b(s(s(s(elem!1))), 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(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[945, 943])).
% 1.54/1.73 tff(947,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(elem!1))), z)) | (~b(s(s(s(elem!1))), 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))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(948,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[947, 946])).
% 1.54/1.73 tff(949,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[948, 97, 193, 126, 87, 942])).
% 1.54/1.73 tff(950,plain,((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(951,plain,
% 1.54/1.73 (~b(s(s(z)), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[950, 926, 906, 488, 916, 513])).
% 1.54/1.73 tff(952,plain,
% 1.54/1.73 (r(s(s(z)), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[122, 951])).
% 1.54/1.73 tff(953,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(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(954,plain,
% 1.54/1.73 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(955,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(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[954])).
% 1.54/1.73 tff(956,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(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[955, 953])).
% 1.54/1.73 tff(957,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(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(958,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(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[957, 956])).
% 1.54/1.73 tff(959,plain,
% 1.54/1.73 (~b(s(z), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[958, 97, 926, 906, 124])).
% 1.54/1.73 tff(960,plain,
% 1.54/1.73 (r(s(z), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[568, 959])).
% 1.54/1.73 tff(961,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(962,plain,
% 1.54/1.73 (((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(963,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[962])).
% 1.54/1.73 tff(964,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[963, 961])).
% 1.54/1.74 tff(965,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(966,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[965, 964])).
% 1.54/1.74 tff(967,plain,
% 1.54/1.74 (~r(s(s(z)), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[966, 155, 729, 960, 952])).
% 1.54/1.74 tff(968,plain,
% 1.54/1.74 (b(s(s(z)), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[625, 967])).
% 1.54/1.74 tff(969,plain,
% 1.54/1.74 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[669, 968, 372, 513])).
% 1.54/1.74 tff(970,plain,
% 1.54/1.74 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[336, 969])).
% 1.54/1.74 tff(971,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(972,plain,
% 1.54/1.74 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(973,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[972])).
% 1.54/1.74 tff(974,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[973, 971])).
% 1.54/1.74 tff(975,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(976,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[975, 974])).
% 1.54/1.74 tff(977,plain,
% 1.54/1.74 ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[976, 155, 125, 916, 952])).
% 1.54/1.74 tff(978,plain,
% 1.54/1.74 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[977, 970])).
% 1.54/1.74 tff(979,plain,
% 1.54/1.74 (b(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[141, 53, 42, 978])).
% 1.54/1.74 tff(980,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(elem!1))))) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(981,plain,
% 1.54/1.74 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~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(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(982,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(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~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(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[981])).
% 1.54/1.74 tff(983,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(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~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(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[982, 980])).
% 1.54/1.74 tff(984,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(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~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))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(985,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[984, 983])).
% 1.54/1.74 tff(986,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[985, 97, 906, 124, 968, 979])).
% 1.54/1.74 tff(987,plain,((~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(988,plain,
% 1.54/1.74 (~b(z, s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[987, 513, 372, 494, 724, 898, 287, 524])).
% 1.54/1.74 tff(989,plain,
% 1.54/1.74 (r(z, s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[590, 988])).
% 1.54/1.74 tff(990,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(991,plain,
% 1.54/1.74 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(992,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[991])).
% 1.54/1.74 tff(993,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[992, 990])).
% 1.54/1.74 tff(994,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(995,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[994, 993])).
% 1.54/1.74 tff(996,plain,
% 1.54/1.74 ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[995, 155, 570, 488, 309])).
% 1.54/1.74 tff(997,plain,
% 1.54/1.74 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[996, 645])).
% 1.54/1.74 tff(998,plain,
% 1.54/1.74 (b(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[141, 53, 42, 997])).
% 1.54/1.74 tff(999,plain,
% 1.54/1.74 ((~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[761, 155, 729, 287, 309])).
% 1.54/1.74 tff(1000,plain,
% 1.54/1.74 (~r(s(s(z)), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[999, 645])).
% 1.54/1.74 tff(1001,plain,
% 1.54/1.74 (b(s(s(z)), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[122, 1000])).
% 1.54/1.74 tff(1002,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[948, 97, 193, 126, 1001, 998])).
% 1.54/1.74 tff(1003,plain,((~r(s(s(z)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(1004,plain,
% 1.54/1.74 (~r(s(s(z)), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1003, 309, 906, 570, 488, 773, 729, 287])).
% 1.54/1.74 tff(1005,plain,
% 1.54/1.74 (b(s(s(z)), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[625, 1004])).
% 1.54/1.74 tff(1006,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(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(1007,plain,
% 1.54/1.74 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~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))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(1008,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(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~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))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[1007])).
% 1.54/1.74 tff(1009,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(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~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))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[1008, 1006])).
% 1.54/1.74 tff(1010,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(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~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)))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(1011,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(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 1.54/1.74 tff(1012,plain,
% 1.54/1.74 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1011, 97, 906, 372, 1005])).
% 1.54/1.74 tff(1013,plain,
% 1.54/1.74 (r(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[58, 1012])).
% 1.54/1.74 tff(1014,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(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(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))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(1015,plain,
% 1.54/1.74 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(1016,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(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[1015])).
% 1.54/1.74 tff(1017,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(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[1016, 1014])).
% 1.54/1.74 tff(1018,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(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~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))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(1019,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(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 1.54/1.74 tff(1020,plain,
% 1.54/1.74 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1019, 97, 906, 372, 1005])).
% 1.54/1.74 tff(1021,plain,
% 1.54/1.74 (r(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[141, 53, 42, 1020])).
% 1.54/1.74 tff(1022,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(1023,plain,
% 1.54/1.74 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~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(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(1024,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[1023])).
% 1.54/1.74 tff(1025,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[1024, 1022])).
% 1.54/1.75 tff(1026,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(1027,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1026, 1025])).
% 1.54/1.75 tff(1028,plain,
% 1.54/1.75 ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1027, 155, 125, 287, 309])).
% 1.54/1.75 tff(1029,plain,
% 1.54/1.75 (~r(s(s(z)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1028, 1021])).
% 1.54/1.75 tff(1030,plain,
% 1.54/1.75 (b(s(s(z)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[122, 1029])).
% 1.54/1.75 tff(1031,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(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1032,plain,
% 1.54/1.75 (((~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(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1033,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(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), 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(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[1032])).
% 1.54/1.75 tff(1034,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(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), 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(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[1033, 1031])).
% 1.54/1.75 tff(1035,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(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(1036,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(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 1.54/1.75 tff(1037,plain,
% 1.54/1.75 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1036, 97, 773, 513, 1030])).
% 1.54/1.75 tff(1038,plain,
% 1.54/1.75 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[452, 1037])).
% 1.54/1.75 tff(1039,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1040,plain,
% 1.54/1.75 (((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(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(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1041,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[1040])).
% 1.54/1.75 tff(1042,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[1041, 1039])).
% 1.54/1.75 tff(1043,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(1044,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 1.54/1.75 tff(1045,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1044, 155, 488, 309, 1038, 1013])).
% 1.54/1.75 tff(1046,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(1047,plain,
% 1.54/1.75 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1046, 898, 513, 494, 287, 372, 989, 724])).
% 1.54/1.75 tff(1048,plain,
% 1.54/1.75 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[336, 1047])).
% 1.54/1.75 tff(1049,plain,
% 1.54/1.75 (~b(s(s(z)), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[669, 1048, 372, 513])).
% 1.54/1.75 tff(1050,plain,
% 1.54/1.75 (r(s(s(z)), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[625, 1049])).
% 1.54/1.75 tff(1051,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(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1052,plain,
% 1.54/1.75 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1053,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(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(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(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[1052])).
% 1.54/1.75 tff(1054,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(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(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(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[1053, 1051])).
% 1.54/1.75 tff(1055,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(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(1056,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(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1055, 1054])).
% 1.54/1.75 tff(1057,plain,
% 1.54/1.75 (~b(z, s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1056, 97, 372, 1048, 513])).
% 1.54/1.75 tff(1058,plain,
% 1.54/1.75 (r(z, s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[222, 1057])).
% 1.54/1.75 tff(1059,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1060,plain,
% 1.54/1.75 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~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(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1061,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[1060])).
% 1.54/1.75 tff(1062,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[1061, 1059])).
% 1.54/1.75 tff(1063,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(1064,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1063, 1062])).
% 1.54/1.75 tff(1065,plain,
% 1.54/1.75 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1064, 155, 125, 570, 645, 2])).
% 1.54/1.75 tff(1066,plain,
% 1.54/1.75 (b(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[141, 53, 42, 1065])).
% 1.54/1.75 tff(1067,plain,
% 1.54/1.75 (b(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[58, 602])).
% 1.54/1.75 tff(1068,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(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1069,plain,
% 1.54/1.75 (((~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(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(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1070,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(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(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(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[1069])).
% 1.54/1.75 tff(1071,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(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(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(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[1070, 1068])).
% 1.54/1.75 tff(1072,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(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(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(1073,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 1.54/1.75 tff(1074,plain,
% 1.54/1.75 (~b(s(z), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1073, 97, 773, 1067, 1066])).
% 1.54/1.75 tff(1075,plain,
% 1.54/1.75 (r(s(z), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[548, 1074])).
% 1.54/1.75 tff(1076,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[871, 155, 729, 226, 2, 1075])).
% 1.54/1.75 tff(1077,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(1078,plain,
% 1.54/1.75 (~r(s(s(z)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1077, 724, 1058, 494, 989, 1050, 287, 898])).
% 1.54/1.75 tff(1079,plain,
% 1.54/1.75 (b(s(s(z)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[122, 1078])).
% 1.54/1.75 tff(1080,plain,
% 1.54/1.75 (~r(s(z), s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[771, 989, 724, 494])).
% 1.54/1.75 tff(1081,plain,
% 1.54/1.75 (b(s(z), s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[181, 1080])).
% 1.54/1.75 tff(1082,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[932, 97, 1081, 1048, 513, 1079])).
% 1.54/1.75 tff(1083,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(1084,plain,
% 1.54/1.75 (~b(z, s(s(s(s(elem!1)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1083, 512, 287, 82])).
% 1.54/1.75 tff(1085,plain,
% 1.54/1.75 ((z = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 1.54/1.75 inference(commutativity,[status(thm)],[])).
% 1.54/1.75 tff(1086,plain,
% 1.54/1.75 ((s(s(s(s(elem!1)))) = z) <=> (z = s(s(s(s(elem!1)))))),
% 1.54/1.75 inference(symmetry,[status(thm)],[1085])).
% 1.54/1.75 tff(1087,plain,
% 1.54/1.75 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(z = s(s(s(s(elem!1))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[1086])).
% 1.54/1.75 tff(1088,plain,
% 1.54/1.75 (~(z = s(s(s(s(elem!1)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[837, 1087])).
% 1.54/1.75 tff(1089,plain,
% 1.54/1.75 (((~![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))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(1090,plain,
% 1.54/1.75 ((~![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))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(1091,plain,
% 1.54/1.75 ((~![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)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 1.54/1.76 tff(1092,plain,
% 1.54/1.76 ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1091, 53])).
% 1.54/1.76 tff(1093,plain,
% 1.54/1.76 (b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1092, 1088])).
% 1.54/1.76 tff(1094,plain,
% 1.54/1.76 (r(z, s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1093, 1084])).
% 1.54/1.76 tff(1095,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1096,plain,
% 1.54/1.76 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1097,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1096])).
% 1.54/1.76 tff(1098,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[1097, 1095])).
% 1.54/1.76 tff(1099,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(1100,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1099, 1098])).
% 1.54/1.76 tff(1101,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1100, 155, 494, 1094, 488, 81, 288])).
% 1.54/1.76 tff(1102,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(1103,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1102, 487, 81, 288, 287])).
% 1.54/1.76 tff(1104,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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1105,plain,
% 1.54/1.76 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1106,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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1105])).
% 1.54/1.76 tff(1107,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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[1106, 1104])).
% 1.54/1.76 tff(1108,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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(1109,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 1.54/1.76 tff(1110,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1109, 97, 1103, 471, 61, 124])).
% 1.54/1.76 tff(1111,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(1112,plain,
% 1.54/1.76 (~r(z, s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1111, 462, 124, 81, 287, 61, 288])).
% 1.54/1.76 tff(1113,plain,
% 1.54/1.76 (b(z, s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1093, 1112])).
% 1.54/1.76 tff(1114,plain,
% 1.54/1.76 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[380, 1113, 337, 83])).
% 1.54/1.76 tff(1115,plain,
% 1.54/1.76 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[669, 1113, 83, 337])).
% 1.54/1.76 tff(1116,plain,
% 1.54/1.76 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[523, 462])).
% 1.54/1.76 tff(1117,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(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1118,plain,
% 1.54/1.76 (((~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(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1119,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(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1118])).
% 1.54/1.76 tff(1120,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(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[1119, 1117])).
% 1.54/1.76 tff(1121,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(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(1122,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 1.54/1.76 tff(1123,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1122, 97, 372, 339, 805, 83])).
% 1.54/1.76 tff(1124,plain,((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(1125,plain,
% 1.54/1.76 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1124, 1113, 83, 337])).
% 1.54/1.76 tff(1126,plain,
% 1.54/1.76 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[821, 1125, 1116])).
% 1.54/1.76 tff(1127,plain,
% 1.54/1.76 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[924, 1126, 225, 287])).
% 1.54/1.76 tff(1128,plain,
% 1.54/1.76 (r(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[511, 1115])).
% 1.54/1.76 tff(1129,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1130,plain,
% 1.54/1.76 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1131,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1130])).
% 1.54/1.76 tff(1132,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[1131, 1129])).
% 1.54/1.76 tff(1133,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(1134,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1133, 1132])).
% 1.54/1.76 tff(1135,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1134, 155, 125, 823, 495, 225])).
% 1.54/1.76 tff(1136,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(1137,plain,
% 1.54/1.76 (~r(s(s(s(elem!1))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1136, 1126, 1128, 225])).
% 1.54/1.76 tff(1138,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[493, 1137])).
% 1.54/1.76 tff(1139,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.54/1.76 tff(1140,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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1141,plain,
% 1.54/1.76 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1142,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), s(s(z)))) | (~b(s(z), s(s(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1141])).
% 1.54/1.76 tff(1143,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), s(s(z)))) | (~b(s(z), s(s(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[1142, 1140])).
% 1.54/1.76 tff(1144,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), s(s(z)))) | (~b(s(z), s(s(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))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(1145,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1144, 1143])).
% 1.54/1.76 tff(1146,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1145, 97, 1139, 61, 124, 535])).
% 1.54/1.76 tff(1147,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(1148,plain,
% 1.54/1.76 (~b(s(z), s(s(z)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1147, 1139, 61, 124])).
% 1.54/1.76 tff(1149,plain,
% 1.54/1.76 (r(s(z), s(s(z)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[548, 1148])).
% 1.54/1.76 tff(1150,assumption,(~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.54/1.76 tff(1151,plain,
% 1.54/1.76 ((~b(s(s(s(s(elem!1)))), s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[515])).
% 1.54/1.76 tff(1152,plain,
% 1.54/1.76 (~b(s(s(s(elem!1))), s(z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[506, 1151])).
% 1.54/1.76 tff(1153,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1139, 1152])).
% 1.54/1.76 tff(1154,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | b(s(s(s(s(elem!1)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(1155,plain,
% 1.54/1.76 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1154, 1139, 506])).
% 1.54/1.76 tff(1156,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[486, 1155, 1150])).
% 1.54/1.76 tff(1157,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(s(elem!1))))) | (~b(s(z), z)) | (~b(s(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(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1158,plain,
% 1.54/1.76 (((~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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1159,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(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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1158])).
% 1.54/1.76 tff(1160,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(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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[1159, 1157])).
% 1.54/1.76 tff(1161,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(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))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(1162,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1161, 1160])).
% 1.54/1.76 tff(1163,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1162, 97, 1139, 550, 61, 124])).
% 1.54/1.76 tff(1164,plain,((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(1165,plain,
% 1.54/1.76 (~b(s(z), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1164, 1139, 61, 124])).
% 1.54/1.76 tff(1166,plain,
% 1.54/1.76 (r(s(z), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[568, 1165])).
% 1.54/1.76 tff(1167,plain,
% 1.54/1.76 (r(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[141, 53, 42, 138])).
% 1.54/1.76 tff(1168,plain,
% 1.54/1.76 (~r(z, s(s(z)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[234, 1167, 3, 225, 81])).
% 1.54/1.76 tff(1169,plain,
% 1.54/1.76 (b(z, s(s(z)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[222, 1168])).
% 1.54/1.76 tff(1170,assumption,(r(s(s(s(s(elem!1)))), s(s(z)))), introduced(assumption)).
% 1.54/1.76 tff(1171,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1172,plain,
% 1.54/1.76 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(1173,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1172])).
% 1.54/1.76 tff(1174,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[1173, 1171])).
% 1.54/1.77 tff(1175,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(1176,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1175, 1174])).
% 1.54/1.77 tff(1177,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1176, 155, 287, 1170, 3, 225, 224])).
% 1.54/1.77 tff(1178,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(1179,plain,
% 1.54/1.77 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1178, 1167, 3, 225, 287])).
% 1.54/1.77 tff(1180,plain,
% 1.54/1.77 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[452, 1179])).
% 1.54/1.77 tff(1181,plain,
% 1.54/1.77 (~b(s(s(s(s(elem!1)))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[884, 1180, 83, 1169])).
% 1.54/1.77 tff(1182,plain,
% 1.54/1.77 (r(s(s(s(s(elem!1)))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[842, 1181])).
% 1.54/1.77 tff(1183,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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1184,plain,
% 1.54/1.77 (((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1185,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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1184])).
% 1.54/1.77 tff(1186,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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[1185, 1183])).
% 1.54/1.77 tff(1187,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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(1188,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 1.54/1.77 tff(1189,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1188, 97, 124, 372, 473, 441])).
% 1.54/1.77 tff(1190,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(1191,plain,
% 1.54/1.77 (~b(z, s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1190, 1180, 473, 124])).
% 1.54/1.77 tff(1192,plain,
% 1.54/1.77 (r(z, s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1093, 1191])).
% 1.54/1.77 tff(1193,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1194,plain,
% 1.54/1.77 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~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(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1195,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1194])).
% 1.54/1.77 tff(1196,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[1195, 1193])).
% 1.54/1.77 tff(1197,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(1198,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1197, 1196])).
% 1.54/1.77 tff(1199,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1198, 155, 287, 1192, 81, 1182])).
% 1.54/1.77 tff(1200,plain,((~b(s(s(z)), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | b(s(s(z)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(1201,plain,
% 1.54/1.77 (~b(s(s(z)), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1200, 1166, 287, 1156, 124, 1149, 225, 138])).
% 1.54/1.77 tff(1202,plain,
% 1.54/1.77 (r(s(s(z)), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[625, 1201])).
% 1.54/1.77 tff(1203,plain,
% 1.54/1.77 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1178, 1167, 1149, 225, 287])).
% 1.54/1.77 tff(1204,plain,
% 1.54/1.77 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[452, 1203])).
% 1.54/1.77 tff(1205,plain,
% 1.54/1.77 (~b(z, s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1190, 1204, 1156, 124])).
% 1.54/1.77 tff(1206,plain,
% 1.54/1.77 (r(z, s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1093, 1205])).
% 1.54/1.77 tff(1207,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1208,plain,
% 1.54/1.77 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1209,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1208])).
% 1.54/1.77 tff(1210,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[1209, 1207])).
% 1.54/1.77 tff(1211,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(1212,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1211, 1210])).
% 1.54/1.77 tff(1213,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1212, 155, 287, 1206, 1166, 1202, 1149])).
% 1.54/1.77 tff(1214,plain,((~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | b(s(s(z)), s(s(s(elem!1)))) | (~b(z, s(z))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(1215,plain,
% 1.54/1.77 (b(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1214, 1138, 124, 225, 287, 61, 1127, 1115])).
% 1.54/1.77 tff(1216,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 1.54/1.77 tff(1217,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(elem!1))), s(z))) | (~b(z, s(z))) | (~b(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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z, s(z))) | (~b(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)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1218,plain,
% 1.54/1.77 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), 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(elem!1))), s(z))) | (~b(z, s(z))) | (~b(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)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1219,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(z))) | (~b(s(s(s(elem!1))), 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(elem!1))), s(z))) | (~b(z, s(z))) | (~b(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))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1218])).
% 1.54/1.77 tff(1220,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(z))) | (~b(s(s(s(elem!1))), 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(elem!1))), s(z))) | (~b(z, s(z))) | (~b(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)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[1219, 1217])).
% 1.54/1.77 tff(1221,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(z))) | (~b(s(s(s(elem!1))), 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)))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(1222,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(elem!1))), s(z))) | (~b(z, s(z))) | (~b(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))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1221, 1220])).
% 1.54/1.77 tff(1223,plain,
% 1.54/1.77 (~b(s(s(s(z))), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1222, 97, 1139, 61, 83, 127, 1216])).
% 1.54/1.77 tff(1224,plain,
% 1.54/1.77 (r(s(s(s(z))), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[421, 1223])).
% 1.54/1.77 tff(1225,plain,
% 1.54/1.77 (~b(s(s(z)), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[428, 97, 61, 83, 1216])).
% 1.54/1.77 tff(1226,plain,
% 1.54/1.77 (r(s(s(z)), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[437, 1225])).
% 1.54/1.77 tff(1227,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1228,plain,
% 1.54/1.77 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1229,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1228])).
% 1.54/1.77 tff(1230,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[1229, 1227])).
% 1.54/1.77 tff(1231,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(1232,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 1.54/1.77 tff(1233,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1232, 155, 3, 338, 1226, 1224])).
% 1.54/1.77 tff(1234,plain,((~b(s(s(s(z))), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(1235,plain,
% 1.54/1.77 (~b(s(s(s(z))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1234, 1138, 338, 61, 83, 3, 1215])).
% 1.54/1.77 tff(1236,plain,
% 1.54/1.77 (r(s(s(s(z))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[402, 1235])).
% 1.54/1.77 tff(1237,plain,
% 1.54/1.77 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[395, 1236, 81, 287, 338])).
% 1.54/1.77 tff(1238,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[384, 53, 1237, 1114, 286])).
% 1.54/1.77 tff(1239,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(1240,plain,
% 1.54/1.77 (~r(s(z), s(s(s(elem!1))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1239, 281, 81, 254, 61, 83, 3, 124, 247])).
% 1.54/1.77 tff(1241,plain,
% 1.54/1.77 (b(s(z), s(s(s(elem!1))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[181, 1240])).
% 1.54/1.77 tff(1242,plain,
% 1.54/1.77 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[340])).
% 1.54/1.77 tff(1243,plain,
% 1.54/1.77 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(elem!1))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[1242])).
% 1.54/1.77 tff(1244,plain,
% 1.54/1.77 ((~b(s(z), s(s(s(s(elem!1)))))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1243])).
% 1.54/1.77 tff(1245,assumption,(~b(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.54/1.77 tff(1246,plain,
% 1.54/1.77 (~b(s(z), s(s(s(elem!1))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 1.54/1.77 tff(1247,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[193, 1246])).
% 1.54/1.77 tff(1248,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(1249,plain,
% 1.54/1.77 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1248, 1241, 264])).
% 1.54/1.77 tff(1250,plain,
% 1.54/1.77 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[481, 1241, 61, 124])).
% 1.54/1.77 tff(1251,plain,
% 1.54/1.77 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[486, 1250, 1249])).
% 1.54/1.77 tff(1252,plain,
% 1.54/1.77 (b(s(s(s(elem!1))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1102, 1251, 81, 281, 247])).
% 1.54/1.77 tff(1253,plain,
% 1.54/1.77 (((~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(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(1254,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(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[1253])).
% 1.54/1.78 tff(1255,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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[1254, 1104])).
% 1.54/1.78 tff(1256,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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~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))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(1257,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[1256, 1255])).
% 1.54/1.78 tff(1258,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1257, 97, 1252, 1241, 61, 124])).
% 1.54/1.78 tff(1259,plain,((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(s(z)), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(1260,plain,
% 1.54/1.78 (~b(s(s(z)), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1259, 124, 61, 81, 83, 3])).
% 1.54/1.78 tff(1261,plain,
% 1.54/1.78 (r(s(s(z)), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[122, 1260])).
% 1.54/1.78 tff(1262,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), 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)))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(1263,plain,
% 1.54/1.78 (((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~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(s(z)), 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)))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(1264,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[1263])).
% 1.54/1.78 tff(1265,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), 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)))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[1264, 1262])).
% 1.54/1.78 tff(1266,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(1267,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[1266, 1265])).
% 1.54/1.78 tff(1268,plain,
% 1.54/1.78 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1267, 155, 125, 1261, 3])).
% 1.54/1.78 tff(1269,plain,
% 1.54/1.78 (b(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[58, 1268])).
% 1.54/1.78 tff(1270,plain,
% 1.54/1.78 (~b(s(z), s(s(s(elem!1))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[201, 1269, 61, 124])).
% 1.54/1.78 tff(1271,plain,
% 1.54/1.78 (r(s(z), s(s(s(elem!1))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[181, 1270])).
% 1.54/1.78 tff(1272,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[612, 155, 125, 2, 225, 224])).
% 1.54/1.78 tff(1273,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(1274,plain,
% 1.54/1.78 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1273, 1271, 1261, 125])).
% 1.54/1.78 tff(1275,plain,
% 1.54/1.78 (b(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[143, 1274])).
% 1.54/1.78 tff(1276,plain,
% 1.54/1.78 (~b(z, s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[306, 1269, 83, 124])).
% 1.54/1.78 tff(1277,plain,
% 1.54/1.78 (r(z, s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[222, 1276])).
% 1.54/1.78 tff(1278,plain,
% 1.54/1.78 (~r(s(s(s(elem!1))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[296, 1277, 3, 1271, 81])).
% 1.54/1.78 tff(1279,plain,
% 1.54/1.78 (b(s(s(s(elem!1))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[246, 1278])).
% 1.54/1.78 tff(1280,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[135, 1279, 1275, 83, 61])).
% 1.54/1.78 tff(1281,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(1282,plain,
% 1.54/1.78 (~r(s(s(s(elem!1))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1281, 124, 61, 3, 81, 83])).
% 1.54/1.78 tff(1283,plain,
% 1.54/1.78 (b(s(s(s(elem!1))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[493, 1282])).
% 1.54/1.78 tff(1284,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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(1285,plain,
% 1.54/1.78 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(1286,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(z), s(s(s(z))))) | (~b(s(z), s(s(s(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[1285])).
% 1.54/1.78 tff(1287,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(z), s(s(s(z))))) | (~b(s(z), s(s(s(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[1286, 1284])).
% 1.54/1.78 tff(1288,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(z), s(s(s(z))))) | (~b(s(z), s(s(s(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))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(1289,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[1288, 1287])).
% 1.54/1.78 tff(1290,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1289, 97, 1139, 61, 124, 86])).
% 1.54/1.78 tff(1291,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(1292,plain,
% 1.54/1.78 (~b(s(z), s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1291, 1283, 61, 124])).
% 1.54/1.78 tff(1293,plain,
% 1.54/1.78 (r(s(z), s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[253, 1292])).
% 1.54/1.78 tff(1294,plain,
% 1.54/1.78 (~b(s(s(s(z))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[409, 97, 61, 83, 1216])).
% 1.54/1.78 tff(1295,plain,
% 1.54/1.78 (r(s(s(s(z))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[421, 1294])).
% 1.54/1.78 tff(1296,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1232, 155, 3, 338, 1226, 1295])).
% 1.54/1.78 tff(1297,plain,((~b(s(s(s(z))), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(1298,plain,
% 1.54/1.78 (~b(s(s(s(z))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1297, 1293, 3, 61, 83])).
% 1.54/1.78 tff(1299,plain,
% 1.54/1.78 (r(s(s(s(z))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[402, 1298])).
% 1.54/1.78 tff(1300,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 1.54/1.78 tff(1301,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(z, s(s(s(z))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(1302,plain,
% 1.54/1.78 (((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(1303,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(z, s(s(s(z)))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[1302])).
% 1.54/1.78 tff(1304,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(z, s(s(s(z))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[1303, 1301])).
% 1.54/1.78 tff(1305,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(1306,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 1.54/1.78 tff(1307,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1306, 155, 81, 1300, 338, 386])).
% 1.54/1.78 tff(1308,plain,((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(1309,plain,
% 1.54/1.78 (~r(z, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1308, 1299, 1293, 81])).
% 1.54/1.78 tff(1310,plain,
% 1.54/1.78 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 1.54/1.78 inference(commutativity,[status(thm)],[])).
% 1.54/1.78 tff(1311,plain,
% 1.54/1.78 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 1.54/1.78 inference(symmetry,[status(thm)],[1310])).
% 1.54/1.78 tff(1312,plain,
% 1.54/1.78 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[1311])).
% 1.54/1.78 tff(1313,plain,
% 1.54/1.78 (~(z = s(s(s(z))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[398, 1312])).
% 1.54/1.78 tff(1314,plain,
% 1.54/1.78 (((~![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)))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(1315,plain,
% 1.54/1.78 ((~![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)))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(1316,plain,
% 1.54/1.78 ((~![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))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 1.54/1.78 tff(1317,plain,
% 1.54/1.78 ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1316, 53])).
% 1.54/1.78 tff(1318,plain,
% 1.54/1.78 (b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1317, 1313])).
% 1.54/1.78 tff(1319,plain,
% 1.54/1.78 (b(z, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1318, 1309])).
% 1.54/1.78 tff(1320,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(1321,plain,
% 1.54/1.78 (((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(1322,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z)))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[1321])).
% 1.54/1.78 tff(1323,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[1322, 1320])).
% 1.54/1.78 tff(1324,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(1325,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 1.54/1.78 tff(1326,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1325, 155, 226, 81, 3, 338, 386])).
% 1.54/1.78 tff(1327,plain,((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(1328,plain,
% 1.54/1.78 (~r(z, s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1327, 1293, 3, 81, 1299])).
% 1.54/1.78 tff(1329,plain,
% 1.54/1.78 (b(z, s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[222, 1328])).
% 1.54/1.78 tff(1330,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 1.54/1.78 tff(1331,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.54/1.78 tff(1332,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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(1333,plain,
% 1.54/1.78 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(1334,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)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[1333])).
% 1.54/1.78 tff(1335,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)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[1334, 1332])).
% 1.54/1.78 tff(1336,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)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(1337,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[1336, 1335])).
% 1.54/1.78 tff(1338,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1337, 97, 204, 83, 1331, 1330])).
% 1.54/1.78 tff(1339,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(1340,plain,
% 1.54/1.78 (~b(s(s(s(z))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1339, 1329, 83, 1319])).
% 1.54/1.78 tff(1341,plain,
% 1.54/1.78 (r(s(s(s(z))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[421, 1340])).
% 1.54/1.78 tff(1342,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(1343,plain,
% 1.54/1.78 (((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(1344,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[1343])).
% 1.54/1.78 tff(1345,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[1344, 1342])).
% 1.54/1.78 tff(1346,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(1347,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[1346, 1345])).
% 1.54/1.78 tff(1348,plain,
% 1.54/1.79 ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1347, 155, 81, 1261, 1299])).
% 1.54/1.79 tff(1349,plain,
% 1.54/1.79 (~r(s(s(s(z))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1348, 1341])).
% 1.54/1.79 tff(1350,plain,
% 1.54/1.79 ((s(s(s(z))) = s(z)) <=> (s(z) = s(s(s(z))))),
% 1.54/1.79 inference(commutativity,[status(thm)],[])).
% 1.54/1.79 tff(1351,plain,
% 1.54/1.79 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 1.54/1.79 inference(symmetry,[status(thm)],[1350])).
% 1.54/1.79 tff(1352,plain,
% 1.54/1.79 ((~(s(z) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(z)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1351])).
% 1.54/1.79 tff(1353,plain,
% 1.54/1.79 (~(s(s(s(z))) = s(z))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[78, 1352])).
% 1.54/1.79 tff(1354,plain,
% 1.54/1.79 (((~![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)))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(1355,plain,
% 1.54/1.79 ((~![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)))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(1356,plain,
% 1.54/1.79 ((~![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))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1355, 1354])).
% 1.54/1.79 tff(1357,plain,
% 1.54/1.79 ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1356, 53])).
% 1.54/1.79 tff(1358,plain,
% 1.54/1.79 (b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1357, 1353])).
% 1.54/1.79 tff(1359,plain,
% 1.54/1.79 (b(s(s(s(z))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1358, 1349])).
% 1.54/1.79 tff(1360,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.54/1.79 tff(1361,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.54/1.79 tff(1362,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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(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(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(1363,plain,
% 1.54/1.79 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(1364,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))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1363])).
% 1.54/1.79 tff(1365,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))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[1364, 1362])).
% 1.54/1.79 tff(1366,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))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(1367,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 1.54/1.79 tff(1368,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1367, 97, 1139, 124, 83, 1361, 1360, 1330])).
% 1.54/1.79 tff(1369,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(1370,plain,
% 1.54/1.79 (~b(s(s(z)), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1369, 1283, 124, 83, 1359, 1319])).
% 1.54/1.79 tff(1371,plain,
% 1.54/1.79 (r(s(s(z)), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[437, 1370])).
% 1.54/1.79 tff(1372,plain,
% 1.54/1.79 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(1373,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1372])).
% 1.54/1.79 tff(1374,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[1373, 1227])).
% 1.54/1.79 tff(1375,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(1376,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 1.54/1.79 tff(1377,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1376, 155, 3, 1293, 1371, 1341])).
% 1.54/1.79 tff(1378,plain,((~b(z, s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(1379,plain,
% 1.54/1.79 (~b(z, s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1378, 83, 3, 81, 61])).
% 1.54/1.79 tff(1380,plain,
% 1.54/1.79 (r(z, s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[590, 1379])).
% 1.54/1.79 tff(1381,plain,
% 1.54/1.79 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1267, 155, 494, 123, 3])).
% 1.54/1.79 tff(1382,plain,
% 1.54/1.79 (b(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[58, 1381])).
% 1.54/1.79 tff(1383,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(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(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(1384,plain,
% 1.54/1.79 (((~b(z, s(z))) | (~b(z, 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(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(1385,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(z))) | (~b(z, 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(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1384])).
% 1.54/1.79 tff(1386,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(z))) | (~b(z, 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(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[1385, 1383])).
% 1.54/1.79 tff(1387,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(z))) | (~b(z, 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)))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(1388,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1387, 1386])).
% 1.54/1.79 tff(1389,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1388, 97, 61, 126, 60, 83])).
% 1.54/1.79 tff(1390,plain,((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(1391,plain,
% 1.54/1.79 (~b(s(s(s(elem!1))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1390, 1382, 61, 83])).
% 1.54/1.79 tff(1392,plain,
% 1.54/1.79 (r(s(s(s(elem!1))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[246, 1391])).
% 1.54/1.79 tff(1393,assumption,(s(s(s(z))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.54/1.79 tff(1394,plain,
% 1.54/1.79 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1393])).
% 1.54/1.79 tff(1395,plain,
% 1.54/1.79 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.54/1.79 inference(symmetry,[status(thm)],[1394])).
% 1.54/1.79 tff(1396,plain,
% 1.54/1.79 (s(s(elem!1)) = s(s(z))),
% 1.54/1.79 inference(transitivity,[status(thm)],[167, 1395, 72])).
% 1.54/1.79 tff(1397,plain,
% 1.54/1.79 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(elem!1))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1396])).
% 1.54/1.79 tff(1398,plain,
% 1.54/1.79 (r(s(s(z)), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.54/1.79 inference(symmetry,[status(thm)],[1397])).
% 1.54/1.79 tff(1399,plain,
% 1.54/1.79 (s(s(z)) = s(s(elem!1))),
% 1.54/1.79 inference(transitivity,[status(thm)],[73, 1394, 19])).
% 1.54/1.79 tff(1400,plain,
% 1.54/1.79 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1399])).
% 1.54/1.79 tff(1401,plain,
% 1.54/1.79 (s(z) = s(elem!1)),
% 1.54/1.79 inference(transitivity,[status(thm)],[24, 1400, 29])).
% 1.54/1.79 tff(1402,plain,
% 1.54/1.79 (r(s(s(z)), s(z)) <=> r(s(s(z)), s(elem!1))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1401])).
% 1.54/1.79 tff(1403,plain,
% 1.54/1.79 (r(s(s(z)), s(elem!1))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[2, 1402])).
% 1.54/1.79 tff(1404,plain,
% 1.54/1.79 (r(s(s(elem!1)), s(elem!1))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1403, 1398])).
% 1.54/1.79 tff(1405,plain,
% 1.54/1.79 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(z)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1396])).
% 1.54/1.79 tff(1406,plain,
% 1.54/1.79 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.54/1.79 inference(symmetry,[status(thm)],[1405])).
% 1.54/1.79 tff(1407,plain,
% 1.54/1.79 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1401])).
% 1.54/1.79 tff(1408,plain,
% 1.54/1.79 (r(s(elem!1), s(s(z)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3, 1407])).
% 1.54/1.79 tff(1409,plain,
% 1.54/1.79 (r(s(elem!1), s(s(elem!1)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1408, 1406])).
% 1.54/1.79 tff(1410,plain,
% 1.54/1.79 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.54/1.79 inference(symmetry,[status(thm)],[1400])).
% 1.54/1.79 tff(1411,plain,
% 1.54/1.79 (s(elem!1) = s(z)),
% 1.54/1.79 inference(transitivity,[status(thm)],[30, 1410, 23])).
% 1.54/1.79 tff(1412,plain,
% 1.54/1.79 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1411])).
% 1.54/1.79 tff(1413,plain,
% 1.54/1.79 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.54/1.79 inference(symmetry,[status(thm)],[1412])).
% 1.54/1.79 tff(1414,plain,
% 1.54/1.79 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(commutativity,[status(thm)],[])).
% 1.54/1.79 tff(1415,plain,
% 1.54/1.79 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1393])).
% 1.54/1.79 tff(1416,plain,
% 1.54/1.79 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[1415, 1414])).
% 1.54/1.79 tff(1417,plain,
% 1.54/1.79 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1416])).
% 1.54/1.79 tff(1418,plain,
% 1.54/1.79 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[286, 1417])).
% 1.54/1.79 tff(1419,plain,
% 1.54/1.79 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(1420,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)) | (~r(s(s(s(elem!1))), z))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1419])).
% 1.54/1.79 tff(1421,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.79 inference(transitivity,[status(thm)],[1420, 704])).
% 1.54/1.79 tff(1422,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(1423,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1422, 1421])).
% 1.54/1.79 tff(1424,plain,
% 1.54/1.79 (~r(s(z), s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1423, 155, 570, 81, 288])).
% 1.54/1.79 tff(1425,plain,
% 1.54/1.79 (b(s(z), s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[181, 1424])).
% 1.54/1.79 tff(1426,plain,
% 1.54/1.79 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1399])).
% 1.54/1.79 tff(1427,plain,
% 1.54/1.79 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.54/1.79 inference(symmetry,[status(thm)],[1426])).
% 1.54/1.79 tff(1428,plain,
% 1.54/1.79 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.54/1.79 inference(commutativity,[status(thm)],[])).
% 1.54/1.79 tff(1429,plain,
% 1.54/1.79 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1399])).
% 1.54/1.79 tff(1430,plain,
% 1.54/1.79 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.54/1.79 inference(transitivity,[status(thm)],[1429, 1428])).
% 1.54/1.79 tff(1431,plain,
% 1.54/1.79 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1430])).
% 1.54/1.79 tff(1432,plain,
% 1.54/1.79 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[331, 1431])).
% 1.54/1.79 tff(1433,assumption,(r(s(s(z)), s(elem!1))), introduced(assumption)).
% 1.54/1.79 tff(1434,plain,
% 1.54/1.79 (r(s(s(elem!1)), s(elem!1))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1433, 1398])).
% 1.54/1.79 tff(1435,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1100, 155, 125, 463, 488, 81, 288])).
% 1.54/1.79 tff(1436,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(1437,plain,
% 1.54/1.79 (~r(z, s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1436, 488, 494, 81, 288])).
% 1.54/1.79 tff(1438,plain,
% 1.54/1.79 (b(z, s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1093, 1437])).
% 1.54/1.79 tff(1439,plain,
% 1.54/1.79 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[532, 1438, 61, 193])).
% 1.54/1.79 tff(1440,plain,
% 1.54/1.79 (r(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[511, 1439])).
% 1.54/1.79 tff(1441,plain,
% 1.54/1.79 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1440, 1413])).
% 1.54/1.79 tff(1442,plain,
% 1.54/1.79 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1401])).
% 1.54/1.79 tff(1443,plain,
% 1.54/1.79 (z = inj_0(s(z))),
% 1.54/1.79 inference(symmetry,[status(thm)],[17])).
% 1.54/1.79 tff(1444,plain,
% 1.54/1.79 (z = elem!1),
% 1.54/1.79 inference(transitivity,[status(thm)],[1443, 1442, 85])).
% 1.54/1.79 tff(1445,plain,
% 1.54/1.79 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1444])).
% 1.54/1.79 tff(1446,plain,
% 1.54/1.79 (r(s(z), z) <=> r(s(elem!1), z)),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1401])).
% 1.54/1.79 tff(1447,plain,
% 1.54/1.79 (r(s(elem!1), z)),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[81, 1446])).
% 1.54/1.79 tff(1448,plain,
% 1.54/1.79 (r(s(elem!1), elem!1)),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1447, 1445])).
% 1.54/1.79 tff(1449,plain,
% 1.54/1.79 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.54/1.79 inference(symmetry,[status(thm)],[1442])).
% 1.54/1.79 tff(1450,plain,
% 1.54/1.79 (elem!1 = inj_0(s(elem!1))),
% 1.54/1.79 inference(symmetry,[status(thm)],[85])).
% 1.54/1.79 tff(1451,plain,
% 1.54/1.79 (elem!1 = z),
% 1.54/1.79 inference(transitivity,[status(thm)],[1450, 1449, 17])).
% 1.54/1.79 tff(1452,plain,
% 1.54/1.79 ((s(s(s(s(elem!1)))) = elem!1) <=> (s(s(s(s(elem!1)))) = z)),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1451])).
% 1.54/1.79 tff(1453,plain,
% 1.54/1.79 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.54/1.79 inference(symmetry,[status(thm)],[1452])).
% 1.54/1.79 tff(1454,plain,
% 1.54/1.79 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1453])).
% 1.54/1.79 tff(1455,plain,
% 1.54/1.79 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[837, 1454])).
% 1.54/1.79 tff(1456,plain,
% 1.54/1.79 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1102, 488, 81, 82, 288])).
% 1.54/1.79 tff(1457,plain,
% 1.54/1.79 (b(s(z), s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[280, 1456])).
% 1.54/1.79 tff(1458,assumption,(b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.54/1.79 tff(1459,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(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(1460,plain,
% 1.54/1.79 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(1461,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(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1460])).
% 1.54/1.79 tff(1462,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(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[1461, 1459])).
% 1.54/1.79 tff(1463,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(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(1464,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1463, 1462])).
% 1.54/1.79 tff(1465,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1464, 97, 61, 255, 372, 1458])).
% 1.54/1.79 tff(1466,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(1467,plain,
% 1.54/1.79 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1466, 1438, 61, 1457])).
% 1.54/1.79 tff(1468,plain,
% 1.54/1.79 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(1469,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(1470,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.80 inference(modus_ponens,[status(thm)],[1469, 1468])).
% 1.54/1.80 tff(1471,plain,
% 1.54/1.80 ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[1470, 53])).
% 1.54/1.80 tff(1472,plain,
% 1.54/1.80 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[1471, 1467, 1455])).
% 1.54/1.80 tff(1473,plain,
% 1.54/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.54/1.80 tff(1474,plain,
% 1.54/1.80 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.54/1.80 tff(1475,plain,
% 1.54/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.54/1.80 inference(monotonicity,[status(thm)],[1474])).
% 1.54/1.80 tff(1476,plain,
% 1.54/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.54/1.80 inference(transitivity,[status(thm)],[1475, 1473])).
% 1.54/1.80 tff(1477,plain,
% 1.54/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(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)))))),
% 1.54/1.80 inference(quant_inst,[status(thm)],[])).
% 1.54/1.80 tff(1478,plain,
% 1.54/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.54/1.80 inference(modus_ponens,[status(thm)],[1477, 1476])).
% 1.54/1.80 tff(1479,plain,
% 1.54/1.80 ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[1478, 155, 1472, 1448])).
% 1.54/1.80 tff(1480,plain,
% 1.54/1.80 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[1479, 1441, 1434])).
% 1.54/1.80 tff(1481,plain,
% 1.54/1.80 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(1482,plain,
% 1.64/1.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(1483,plain,
% 1.64/1.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[1482, 1481])).
% 1.64/1.80 tff(1484,plain,
% 1.64/1.80 ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1483, 53])).
% 1.64/1.80 tff(1485,plain,
% 1.64/1.80 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1484, 1480, 1432])).
% 1.64/1.80 tff(1486,plain,
% 1.64/1.80 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[1485, 1427])).
% 1.64/1.80 tff(1487,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(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~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(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(1488,plain,
% 1.64/1.80 (((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(1489,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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1488])).
% 1.64/1.80 tff(1490,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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[1489, 1487])).
% 1.64/1.80 tff(1491,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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(1492,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[1491, 1490])).
% 1.64/1.80 tff(1493,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1492, 97, 61, 255, 372, 441])).
% 1.64/1.80 tff(1494,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(1495,plain,
% 1.64/1.80 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1494, 1438, 61, 1457])).
% 1.64/1.80 tff(1496,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1495, 1486])).
% 1.64/1.80 tff(1497,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(z)), s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(1498,plain,
% 1.64/1.80 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1497, 1393, 1403, 61, 1425, 81, 288, 82])).
% 1.64/1.80 tff(1499,plain,
% 1.64/1.80 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[486, 1498, 1418])).
% 1.64/1.80 tff(1500,plain,
% 1.64/1.80 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1396])).
% 1.64/1.80 tff(1501,plain,
% 1.64/1.80 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[1500])).
% 1.64/1.80 tff(1502,plain,
% 1.64/1.80 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1267, 155, 494, 2, 3])).
% 1.64/1.80 tff(1503,plain,
% 1.64/1.80 (b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[58, 1502])).
% 1.64/1.80 tff(1504,plain,
% 1.64/1.80 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[1503, 1501])).
% 1.64/1.80 tff(1505,plain,
% 1.64/1.80 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[1428])).
% 1.64/1.80 tff(1506,plain,
% 1.64/1.80 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[1430, 1505])).
% 1.64/1.80 tff(1507,plain,
% 1.64/1.80 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1506])).
% 1.64/1.80 tff(1508,plain,
% 1.64/1.80 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[331, 1507])).
% 1.64/1.80 tff(1509,plain,
% 1.64/1.80 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1444])).
% 1.64/1.80 tff(1510,plain,
% 1.64/1.80 (r(elem!1, s(s(s(elem!1))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[570, 1509])).
% 1.64/1.80 tff(1511,plain,
% 1.64/1.80 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1444])).
% 1.64/1.80 tff(1512,plain,
% 1.64/1.80 (r(s(s(s(elem!1))), elem!1)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[288, 1511])).
% 1.64/1.80 tff(1513,plain,
% 1.64/1.80 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1411])).
% 1.64/1.80 tff(1514,plain,
% 1.64/1.80 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[1513])).
% 1.64/1.80 tff(1515,plain,
% 1.64/1.80 (b(s(elem!1), s(s(s(elem!1))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[1425, 1514])).
% 1.64/1.80 tff(1516,plain,
% 1.64/1.80 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1411])).
% 1.64/1.80 tff(1517,plain,
% 1.64/1.80 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[1516])).
% 1.64/1.80 tff(1518,plain,
% 1.64/1.80 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1411])).
% 1.64/1.80 tff(1519,plain,
% 1.64/1.80 ((~r(s(elem!1), s(s(s(s(elem!1)))))) <=> (~r(s(z), s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1518])).
% 1.64/1.80 tff(1520,assumption,(r(s(elem!1), s(s(z)))), introduced(assumption)).
% 1.64/1.80 tff(1521,plain,
% 1.64/1.80 (r(s(elem!1), s(s(elem!1)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[1520, 1406])).
% 1.64/1.80 tff(1522,assumption,(r(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.64/1.80 tff(1523,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.80 tff(1524,plain,
% 1.64/1.80 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1396])).
% 1.64/1.80 tff(1525,plain,
% 1.64/1.80 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[1524])).
% 1.64/1.80 tff(1526,plain,
% 1.64/1.80 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1525])).
% 1.64/1.80 tff(1527,plain,
% 1.64/1.80 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[43, 1526])).
% 1.64/1.80 tff(1528,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.64/1.80 tff(1529,assumption,(b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.64/1.80 tff(1530,plain,
% 1.64/1.80 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.64/1.80 inference(commutativity,[status(thm)],[])).
% 1.64/1.80 tff(1531,plain,
% 1.64/1.80 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[1530])).
% 1.64/1.80 tff(1532,plain,
% 1.64/1.80 ((~(s(s(s(elem!1))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1531])).
% 1.64/1.80 tff(1533,plain,
% 1.64/1.80 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[352, 1532])).
% 1.64/1.80 tff(1534,assumption,(z = elem!1), introduced(assumption)).
% 1.64/1.80 tff(1535,plain,
% 1.64/1.80 (s(z) = s(elem!1)),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1534])).
% 1.64/1.80 tff(1536,plain,
% 1.64/1.80 (s(s(z)) = s(s(elem!1))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1535])).
% 1.64/1.80 tff(1537,plain,
% 1.64/1.80 (s(s(elem!1)) = s(s(z))),
% 1.64/1.80 inference(symmetry,[status(thm)],[1536])).
% 1.64/1.80 tff(1538,plain,
% 1.64/1.80 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1537])).
% 1.64/1.80 tff(1539,plain,
% 1.64/1.80 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.64/1.80 inference(symmetry,[status(thm)],[1538])).
% 1.64/1.80 tff(1540,plain,
% 1.64/1.80 (elem!1 = z),
% 1.64/1.80 inference(symmetry,[status(thm)],[1534])).
% 1.64/1.80 tff(1541,plain,
% 1.64/1.80 ((s(s(z)) = elem!1) <=> (s(s(z)) = z)),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1540])).
% 1.64/1.80 tff(1542,plain,
% 1.64/1.80 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 1.64/1.80 inference(symmetry,[status(thm)],[1541])).
% 1.64/1.80 tff(1543,plain,
% 1.64/1.80 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1542])).
% 1.64/1.80 tff(1544,plain,
% 1.64/1.80 (~(s(s(z)) = elem!1)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[76, 1543])).
% 1.64/1.80 tff(1545,assumption,(b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.64/1.80 tff(1546,plain,
% 1.64/1.80 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1537])).
% 1.64/1.80 tff(1547,plain,
% 1.64/1.80 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.64/1.80 inference(symmetry,[status(thm)],[1546])).
% 1.64/1.80 tff(1548,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 1.64/1.80 tff(1549,plain,
% 1.64/1.80 (b(s(s(elem!1)), elem!1)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[1548, 1547])).
% 1.64/1.80 tff(1550,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(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(1551,plain,
% 1.64/1.80 (((~b(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(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(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(1552,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)), elem!1)) | (~b(s(s(elem!1)), 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(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1551])).
% 1.64/1.80 tff(1553,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)), elem!1)) | (~b(s(s(elem!1)), 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(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[1552, 1550])).
% 1.64/1.80 tff(1554,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)), elem!1)) | (~b(s(s(elem!1)), 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)))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(1555,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[1554, 1553])).
% 1.64/1.80 tff(1556,plain,
% 1.64/1.80 (~b(s(s(elem!1)), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1555, 97, 1545, 473, 1529])).
% 1.64/1.80 tff(1557,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1556, 1549])).
% 1.64/1.80 tff(1558,plain,((~b(s(s(z)), elem!1)) | (~(z = 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))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(1559,plain,
% 1.64/1.80 (~b(s(s(z)), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1558, 1529, 1545, 473, 1534])).
% 1.64/1.80 tff(1560,plain,
% 1.64/1.80 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(1561,plain,
% 1.64/1.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(1562,plain,
% 1.64/1.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[1561, 1560])).
% 1.64/1.80 tff(1563,plain,
% 1.64/1.80 ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1562, 53])).
% 1.64/1.80 tff(1564,plain,
% 1.64/1.80 (r(s(s(z)), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1563, 1559, 1544])).
% 1.64/1.80 tff(1565,plain,
% 1.64/1.80 (r(s(s(elem!1)), elem!1)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[1564, 1539])).
% 1.64/1.80 tff(1566,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(1567,plain,
% 1.64/1.80 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(1568,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[1567])).
% 1.64/1.80 tff(1569,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[1568, 1566])).
% 1.64/1.80 tff(1570,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(1571,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[1570, 1569])).
% 1.64/1.80 tff(1572,plain,
% 1.64/1.80 ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1571, 155, 1528, 1523])).
% 1.64/1.80 tff(1573,plain,
% 1.64/1.80 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1572, 1565])).
% 1.64/1.80 tff(1574,plain,
% 1.64/1.80 (((~![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)))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(1575,plain,
% 1.64/1.80 ((~![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)))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(1576,plain,
% 1.64/1.80 ((~![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))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[1575, 1574])).
% 1.64/1.80 tff(1577,plain,
% 1.64/1.80 ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1576, 53, 1573])).
% 1.64/1.80 tff(1578,plain,
% 1.64/1.80 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1577, 1533])).
% 1.64/1.80 tff(1579,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(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(1580,plain,
% 1.64/1.81 (((~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(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)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(1581,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(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(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))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[1580])).
% 1.64/1.81 tff(1582,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(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(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)))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[1581, 1579])).
% 1.64/1.81 tff(1583,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(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)))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(1584,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[1583, 1582])).
% 1.64/1.81 tff(1585,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1584, 97, 1545, 473, 1529, 1578])).
% 1.64/1.81 tff(1586,plain,((~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)))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(1587,plain,
% 1.64/1.81 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1586, 473, 1529, 1528, 1527, 1523, 1444])).
% 1.64/1.81 tff(1588,plain,
% 1.64/1.81 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1484, 1587, 1432])).
% 1.64/1.81 tff(1589,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(1590,plain,
% 1.64/1.81 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(1591,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[1590])).
% 1.64/1.81 tff(1592,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[1591, 1589])).
% 1.64/1.81 tff(1593,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(1594,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[1593, 1592])).
% 1.64/1.81 tff(1595,plain,
% 1.64/1.81 ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1594, 155, 1588, 1522])).
% 1.64/1.81 tff(1596,plain,
% 1.64/1.81 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1595, 1521])).
% 1.64/1.81 tff(1597,plain,
% 1.64/1.81 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[1596, 1519])).
% 1.64/1.81 tff(1598,plain,
% 1.64/1.81 (b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[280, 1597])).
% 1.64/1.81 tff(1599,plain,
% 1.64/1.81 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[1598, 1517])).
% 1.64/1.81 tff(1600,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(1601,plain,
% 1.64/1.81 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(1602,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[1601])).
% 1.64/1.81 tff(1603,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[1602, 1600])).
% 1.64/1.81 tff(1604,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(1605,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[1604, 1603])).
% 1.64/1.81 tff(1606,plain,
% 1.64/1.81 ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1605, 155, 1588])).
% 1.64/1.81 tff(1607,plain,
% 1.64/1.81 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1606, 1521, 1434])).
% 1.64/1.81 tff(1608,plain,
% 1.64/1.81 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(z))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[1411])).
% 1.64/1.81 tff(1609,plain,
% 1.64/1.81 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(z) = s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[1608, 265])).
% 1.64/1.81 tff(1610,plain,
% 1.64/1.81 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.64/1.81 inference(symmetry,[status(thm)],[1609])).
% 1.64/1.81 tff(1611,plain,
% 1.64/1.81 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[1610])).
% 1.64/1.81 tff(1612,plain,
% 1.64/1.81 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[275, 1611])).
% 1.64/1.81 tff(1613,plain,
% 1.64/1.81 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(1614,plain,
% 1.64/1.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(1615,plain,
% 1.64/1.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 1.64/1.81 tff(1616,plain,
% 1.64/1.81 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1615, 53, 1612, 1607])).
% 1.64/1.81 tff(1617,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.81 tff(1618,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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(1619,plain,
% 1.64/1.81 (((~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(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))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(1620,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(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(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)))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[1619])).
% 1.64/1.81 tff(1621,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(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(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))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[1620, 1618])).
% 1.64/1.81 tff(1622,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(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))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(1623,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[1622, 1621])).
% 1.64/1.81 tff(1624,plain,
% 1.64/1.81 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1623, 97, 473, 1617, 1616])).
% 1.64/1.81 tff(1625,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1624, 1599])).
% 1.64/1.81 tff(1626,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(1627,plain,
% 1.64/1.81 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1626, 1499, 1515, 1393, 1403, 1408, 1504, 1512, 1510])).
% 1.64/1.81 tff(1628,plain,
% 1.64/1.81 (((~![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))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(1629,plain,
% 1.64/1.81 ((~![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))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(1630,plain,
% 1.64/1.81 ((~![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)))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[1629, 1628])).
% 1.64/1.81 tff(1631,plain,
% 1.64/1.81 ((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)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1630, 53])).
% 1.64/1.81 tff(1632,plain,
% 1.64/1.81 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1631, 1627, 1508])).
% 1.64/1.81 tff(1633,assumption,(b(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.64/1.81 tff(1634,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(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(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(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(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(1635,plain,
% 1.64/1.81 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(1636,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(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[1635])).
% 1.64/1.81 tff(1637,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(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[1636, 1634])).
% 1.64/1.81 tff(1638,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(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(1639,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[1638, 1637])).
% 1.64/1.81 tff(1640,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1639, 97, 1633, 473, 1529, 513])).
% 1.64/1.81 tff(1641,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(1642,plain,
% 1.64/1.81 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1641, 1632, 1504, 1499])).
% 1.64/1.81 tff(1643,plain,
% 1.64/1.81 (r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[511, 1642])).
% 1.64/1.81 tff(1644,plain,
% 1.64/1.81 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[1643, 1413])).
% 1.64/1.81 tff(1645,plain,
% 1.64/1.81 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1586, 1499, 1504, 1512, 1527, 1510, 1444])).
% 1.64/1.81 tff(1646,plain,
% 1.64/1.81 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1484, 1645, 1432])).
% 1.64/1.81 tff(1647,plain,
% 1.64/1.81 ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1605, 155, 1646])).
% 1.64/1.81 tff(1648,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1647, 1644, 1409, 1404])).
% 1.64/1.81 tff(1649,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | b(s(s(s(elem!1))), s(z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(1650,plain,
% 1.64/1.81 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1649, 1392, 81, 61, 82, 1380, 3, 123])).
% 1.64/1.81 tff(1651,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(1652,plain,
% 1.64/1.81 (((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(1653,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[1652])).
% 1.64/1.81 tff(1654,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[1653, 1651])).
% 1.64/1.82 tff(1655,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(1656,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[1655, 1654])).
% 1.64/1.82 tff(1657,plain,
% 1.64/1.82 (~r(s(s(s(z))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1656, 155, 123, 3, 1295])).
% 1.64/1.82 tff(1658,plain,
% 1.64/1.82 (b(s(s(s(z))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1358, 1657])).
% 1.64/1.82 tff(1659,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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(1660,plain,
% 1.64/1.82 (((~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(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(1661,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(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(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[1660])).
% 1.64/1.82 tff(1662,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(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(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[1661, 1659])).
% 1.64/1.82 tff(1663,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(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)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(1664,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[1663, 1662])).
% 1.64/1.82 tff(1665,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1664, 97, 61, 1658, 86, 1216])).
% 1.64/1.82 tff(1666,plain,((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(1667,plain,
% 1.64/1.82 (~b(s(s(s(z))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1666, 86, 61, 3, 83])).
% 1.64/1.82 tff(1668,plain,
% 1.64/1.82 (r(s(s(s(z))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[402, 1667])).
% 1.64/1.82 tff(1669,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(1670,plain,
% 1.64/1.82 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(1671,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[1670])).
% 1.64/1.82 tff(1672,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[1671, 1669])).
% 1.64/1.82 tff(1673,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(1674,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 1.64/1.82 tff(1675,plain,
% 1.64/1.82 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1674, 155, 1380, 1392, 1668])).
% 1.64/1.82 tff(1676,plain,
% 1.64/1.82 (((~![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)))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(1677,plain,
% 1.64/1.82 ((~![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)))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(1678,plain,
% 1.64/1.82 ((~![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))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[1677, 1676])).
% 1.64/1.82 tff(1679,plain,
% 1.64/1.82 ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1678, 53, 1675])).
% 1.64/1.82 tff(1680,plain,
% 1.64/1.82 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1679, 1650])).
% 1.64/1.82 tff(1681,plain,
% 1.64/1.82 (~r(s(z), s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1423, 155, 1380, 81, 1392])).
% 1.64/1.82 tff(1682,plain,
% 1.64/1.82 (b(s(z), s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[181, 1681])).
% 1.64/1.82 tff(1683,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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(1684,plain,
% 1.64/1.82 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(1685,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(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[1684])).
% 1.64/1.82 tff(1686,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(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[1685, 1683])).
% 1.64/1.82 tff(1687,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(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(1688,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[1687, 1686])).
% 1.64/1.82 tff(1689,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1688, 97, 1682, 1382, 86, 1680])).
% 1.64/1.82 tff(1690,plain,(b(s(s(s(elem!1))), s(z)) | (~b(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(1691,plain,
% 1.64/1.82 (b(s(s(s(elem!1))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1690, 86, 81, 61, 3, 83])).
% 1.64/1.82 tff(1692,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(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), 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(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(1693,plain,
% 1.64/1.82 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~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(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(1694,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(s(z))))) | (~b(s(z), s(s(s(z))))) | (~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(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(z)))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[1693])).
% 1.64/1.82 tff(1695,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(s(z))))) | (~b(s(z), s(s(s(z))))) | (~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(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[1694, 1692])).
% 1.64/1.82 tff(1696,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(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(1697,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(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(z)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[1696, 1695])).
% 1.64/1.82 tff(1698,plain,
% 1.64/1.82 (~b(s(s(s(elem!1))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1697, 97, 1691, 61, 86])).
% 1.64/1.82 tff(1699,plain,
% 1.64/1.82 (r(s(s(s(elem!1))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[246, 1698])).
% 1.64/1.82 tff(1700,plain,
% 1.64/1.82 (~r(s(z), s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1423, 155, 1380, 81, 1699])).
% 1.64/1.82 tff(1701,plain,
% 1.64/1.82 (b(s(z), s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[181, 1700])).
% 1.64/1.82 tff(1702,assumption,(b(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.82 tff(1703,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(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(1704,plain,
% 1.64/1.82 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(1705,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(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[1704])).
% 1.64/1.82 tff(1706,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(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[1705, 1703])).
% 1.64/1.82 tff(1707,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(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(1708,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[1707, 1706])).
% 1.64/1.82 tff(1709,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1708, 97, 1139, 193, 86, 1702])).
% 1.64/1.82 tff(1710,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(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(1711,plain,
% 1.64/1.82 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1710, 1691, 1701, 86])).
% 1.64/1.82 tff(1712,plain,
% 1.64/1.82 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1674, 155, 1380, 1699, 1668])).
% 1.64/1.82 tff(1713,plain,
% 1.64/1.82 ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1678, 53, 1712])).
% 1.64/1.82 tff(1714,plain,
% 1.64/1.82 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1713, 1711])).
% 1.64/1.82 tff(1715,plain,
% 1.64/1.82 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[1714])).
% 1.64/1.82 tff(1716,plain,
% 1.64/1.82 (s(s(z)) = s(s(elem!1))),
% 1.64/1.82 inference(transitivity,[status(thm)],[73, 1715, 19])).
% 1.64/1.82 tff(1717,plain,
% 1.64/1.82 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[1716])).
% 1.64/1.82 tff(1718,plain,
% 1.64/1.82 (s(z) = s(elem!1)),
% 1.64/1.82 inference(transitivity,[status(thm)],[24, 1717, 29])).
% 1.64/1.82 tff(1719,plain,
% 1.64/1.82 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[1718])).
% 1.64/1.82 tff(1720,plain,
% 1.64/1.82 (z = elem!1),
% 1.64/1.82 inference(transitivity,[status(thm)],[1443, 1719, 85])).
% 1.64/1.82 tff(1721,plain,
% 1.64/1.82 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.64/1.82 inference(monotonicity,[status(thm)],[1720])).
% 1.64/1.82 tff(1722,plain,
% 1.64/1.82 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 1.64/1.82 inference(monotonicity,[status(thm)],[1716])).
% 1.64/1.82 tff(1723,plain,
% 1.64/1.82 (b(s(s(elem!1)), z)),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[83, 1722])).
% 1.64/1.82 tff(1724,plain,
% 1.64/1.82 (b(s(s(elem!1)), elem!1)),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[1723, 1721])).
% 1.64/1.82 tff(1725,assumption,(s(s(s(s(elem!1)))) = s(s(elem!1))), introduced(assumption)).
% 1.64/1.82 tff(1726,plain,
% 1.64/1.82 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[1725])).
% 1.64/1.82 tff(1727,plain,
% 1.64/1.82 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[1726])).
% 1.64/1.82 tff(1728,plain,
% 1.64/1.82 (s(elem!1) = s(s(s(elem!1)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[30, 1727, 270])).
% 1.64/1.82 tff(1729,plain,
% 1.64/1.82 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[1728])).
% 1.64/1.82 tff(1730,plain,
% 1.64/1.82 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.64/1.82 inference(symmetry,[status(thm)],[1729])).
% 1.64/1.82 tff(1731,plain,
% 1.64/1.82 (s(s(s(s(elem!1)))) = elem!1),
% 1.64/1.82 inference(transitivity,[status(thm)],[1725, 167, 1730, 85])).
% 1.64/1.82 tff(1732,assumption,(~(s(s(s(s(elem!1)))) = elem!1)), introduced(assumption)).
% 1.64/1.82 tff(1733,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1732, 1731])).
% 1.64/1.82 tff(1734,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (s(s(s(s(elem!1)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(1735,plain,
% 1.64/1.82 (s(s(s(s(elem!1)))) = elem!1),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1734, 350])).
% 1.64/1.82 tff(1736,plain,
% 1.64/1.82 (elem!1 = s(s(s(s(elem!1))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[1735])).
% 1.64/1.82 tff(1737,assumption,(s(s(s(z))) = elem!1), introduced(assumption)).
% 1.64/1.82 tff(1738,plain,
% 1.64/1.82 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[1737, 1736])).
% 1.64/1.82 tff(1739,plain,
% 1.64/1.82 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[1738])).
% 1.64/1.82 tff(1740,plain,
% 1.64/1.82 (s(s(z)) = s(s(s(s(elem!1))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[73, 1739, 270, 340])).
% 1.64/1.82 tff(1741,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[331, 1740])).
% 1.64/1.82 tff(1742,plain,((~(s(s(s(z))) = elem!1)) | (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(1743,plain,
% 1.64/1.82 (~(s(s(s(z))) = elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1742, 340])).
% 1.64/1.82 tff(1744,plain,
% 1.64/1.82 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[1736])).
% 1.64/1.82 tff(1745,plain,
% 1.64/1.82 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), elem!1)),
% 1.64/1.82 inference(symmetry,[status(thm)],[1744])).
% 1.64/1.82 tff(1746,plain,
% 1.64/1.82 ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(z))), elem!1))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[1745])).
% 1.64/1.82 tff(1747,plain,
% 1.64/1.82 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[340])).
% 1.64/1.82 tff(1748,plain,
% 1.64/1.82 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[1747])).
% 1.64/1.82 tff(1749,assumption,(~r(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.82 tff(1750,plain,
% 1.64/1.82 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[1749, 1748])).
% 1.64/1.82 tff(1751,plain,
% 1.64/1.82 (~r(s(s(s(z))), elem!1)),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[1750, 1746])).
% 1.64/1.82 tff(1752,plain,
% 1.64/1.82 (((~![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))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(1753,plain,
% 1.64/1.82 ((~![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))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(1754,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 1.64/1.82 tff(1755,plain,
% 1.64/1.82 ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1754, 53])).
% 1.64/1.82 tff(1756,plain,
% 1.64/1.82 (b(s(s(s(z))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1755, 1751, 1743])).
% 1.64/1.82 tff(1757,assumption,(s(s(s(s(elem!1)))) = elem!1), introduced(assumption)).
% 1.64/1.82 tff(1758,plain,
% 1.64/1.82 (elem!1 = s(s(s(s(elem!1))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[1757])).
% 1.64/1.82 tff(1759,plain,
% 1.64/1.82 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[1758])).
% 1.64/1.82 tff(1760,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.64/1.82 tff(1761,plain,
% 1.64/1.82 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[1760, 1759])).
% 1.64/1.82 tff(1762,assumption,(~b(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.64/1.82 tff(1763,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1762, 1761])).
% 1.64/1.82 tff(1764,plain,((~b(s(s(s(z))), elem!1)) | b(s(s(s(z))), s(s(s(s(elem!1))))) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(1765,plain,
% 1.64/1.83 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1764, 1756, 1735])).
% 1.64/1.83 tff(1766,plain,
% 1.64/1.83 (b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1154, 340, 1139])).
% 1.64/1.83 tff(1767,plain,
% 1.64/1.83 (b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1248, 340, 193])).
% 1.64/1.83 tff(1768,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(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(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(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(1769,plain,
% 1.64/1.83 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(1770,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(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z)))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[1769])).
% 1.64/1.83 tff(1771,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(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[1770, 1768])).
% 1.64/1.83 tff(1772,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(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(1773,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z)))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[1772, 1771])).
% 1.64/1.83 tff(1774,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1773, 97, 1767, 1766, 86, 1765])).
% 1.64/1.83 tff(1775,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | r(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)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(1776,plain,
% 1.64/1.83 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1775, 86, 1712, 1691, 1701])).
% 1.64/1.83 tff(1777,plain,
% 1.64/1.83 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[523, 1776])).
% 1.64/1.83 tff(1778,plain,
% 1.64/1.83 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.64/1.83 inference(symmetry,[status(thm)],[1715])).
% 1.64/1.83 tff(1779,plain,
% 1.64/1.83 (s(s(elem!1)) = s(s(z))),
% 1.64/1.83 inference(transitivity,[status(thm)],[167, 1778, 72])).
% 1.64/1.83 tff(1780,plain,
% 1.64/1.83 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[1779])).
% 1.64/1.83 tff(1781,plain,
% 1.64/1.83 (r(s(s(z)), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.64/1.83 inference(symmetry,[status(thm)],[1780])).
% 1.64/1.83 tff(1782,plain,
% 1.64/1.83 (r(s(s(z)), s(z)) <=> r(s(s(z)), s(elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[1718])).
% 1.64/1.83 tff(1783,plain,
% 1.64/1.83 (r(s(s(z)), s(elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[123, 1782])).
% 1.64/1.83 tff(1784,plain,
% 1.64/1.83 (r(s(s(elem!1)), s(elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[1783, 1781])).
% 1.64/1.83 tff(1785,plain,
% 1.64/1.83 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[1718])).
% 1.64/1.83 tff(1786,plain,
% 1.64/1.83 (r(s(elem!1), s(s(z)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[3, 1785])).
% 1.64/1.83 tff(1787,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(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(1788,plain,
% 1.64/1.83 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(1789,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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, 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(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[1788])).
% 1.64/1.83 tff(1790,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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, 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(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[1789, 1787])).
% 1.64/1.83 tff(1791,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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(1792,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[1791, 1790])).
% 1.64/1.83 tff(1793,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1792, 97, 193, 61, 513, 876])).
% 1.64/1.83 tff(1794,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(1795,plain,
% 1.64/1.83 (~b(s(s(s(s(elem!1)))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1794, 513, 61, 193])).
% 1.64/1.83 tff(1796,plain,
% 1.64/1.83 (r(s(s(s(s(elem!1)))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[842, 1795])).
% 1.64/1.83 tff(1797,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(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(1798,plain,
% 1.64/1.83 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(1799,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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[1798])).
% 1.64/1.83 tff(1800,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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[1799, 1797])).
% 1.64/1.83 tff(1801,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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(1802,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[1801, 1800])).
% 1.64/1.83 tff(1803,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1802, 97, 1139, 193, 805, 513])).
% 1.64/1.83 tff(1804,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(1805,plain,
% 1.64/1.83 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1804, 513, 1139, 193])).
% 1.64/1.83 tff(1806,plain,
% 1.64/1.83 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[821, 1805, 802])).
% 1.64/1.83 tff(1807,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[832, 1806, 1796, 570, 288])).
% 1.64/1.83 tff(1808,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(1809,plain,
% 1.64/1.83 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1808, 1699, 1380, 1777, 1691, 1701, 61])).
% 1.64/1.83 tff(1810,plain,
% 1.64/1.83 (r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[511, 1809])).
% 1.64/1.83 tff(1811,plain,
% 1.64/1.83 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[495, 1413])).
% 1.64/1.83 tff(1812,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.64/1.83 tff(1813,assumption,(r(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.64/1.83 tff(1814,plain,
% 1.64/1.83 ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1605, 155, 1813, 1812])).
% 1.64/1.83 tff(1815,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1814, 1521, 1811])).
% 1.64/1.83 tff(1816,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(1817,plain,
% 1.64/1.83 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1816, 1810, 1786, 1714, 1784])).
% 1.64/1.83 tff(1818,plain,
% 1.64/1.83 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[1399])).
% 1.64/1.83 tff(1819,plain,
% 1.64/1.83 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[1170, 1818])).
% 1.64/1.83 tff(1820,assumption,(~r(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.64/1.83 tff(1821,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1820, 1819])).
% 1.64/1.83 tff(1822,plain,(r(s(s(s(s(elem!1)))), s(s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~(s(s(s(z))) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(1823,plain,
% 1.64/1.83 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1822, 1817, 1714])).
% 1.64/1.83 tff(1824,plain,
% 1.64/1.83 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[452, 1823])).
% 1.64/1.83 tff(1825,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(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(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(1826,plain,
% 1.64/1.83 (((~b(z, s(z))) | (~b(z, 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(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(1827,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(z))) | (~b(z, 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(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[1826])).
% 1.64/1.83 tff(1828,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(z))) | (~b(z, 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(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[1827, 1825])).
% 1.64/1.83 tff(1829,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(z))) | (~b(z, 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)))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(1830,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[1829, 1828])).
% 1.64/1.83 tff(1831,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1830, 97, 61, 83, 876, 441])).
% 1.64/1.83 tff(1832,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(1833,plain,
% 1.64/1.83 (~b(s(s(s(s(elem!1)))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1832, 1824, 83, 61])).
% 1.64/1.83 tff(1834,plain,
% 1.64/1.83 (r(s(s(s(s(elem!1)))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[842, 1833])).
% 1.64/1.83 tff(1835,plain,
% 1.64/1.83 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[832, 1834, 1380, 1699])).
% 1.64/1.83 tff(1836,plain,
% 1.64/1.83 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[821, 1835, 1777])).
% 1.64/1.83 tff(1837,plain,
% 1.64/1.83 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[1779])).
% 1.64/1.83 tff(1838,plain,
% 1.64/1.83 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.83 inference(symmetry,[status(thm)],[1837])).
% 1.64/1.83 tff(1839,plain,
% 1.64/1.83 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.64/1.83 inference(symmetry,[status(thm)],[1393])).
% 1.64/1.83 tff(1840,plain,
% 1.64/1.83 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[1839])).
% 1.64/1.83 tff(1841,plain,
% 1.64/1.83 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.64/1.83 inference(symmetry,[status(thm)],[1840])).
% 1.64/1.83 tff(1842,plain,
% 1.64/1.83 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[1841])).
% 1.64/1.83 tff(1843,assumption,(~b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.64/1.83 tff(1844,plain,
% 1.64/1.83 (~b(s(s(s(elem!1))), s(z))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[1843, 1842])).
% 1.64/1.83 tff(1845,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1139, 1844])).
% 1.64/1.83 tff(1846,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(1847,plain,
% 1.64/1.83 (b(s(s(s(z))), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1846, 1714, 1691])).
% 1.64/1.83 tff(1848,plain,
% 1.64/1.83 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[1716])).
% 1.64/1.83 tff(1849,plain,
% 1.64/1.83 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.64/1.83 inference(transitivity,[status(thm)],[1848, 1428])).
% 1.64/1.83 tff(1850,plain,
% 1.64/1.83 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[1849])).
% 1.64/1.83 tff(1851,plain,
% 1.64/1.83 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[331, 1850])).
% 1.64/1.83 tff(1852,plain,
% 1.64/1.83 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1484, 1817, 1851])).
% 1.64/1.83 tff(1853,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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(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(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(1854,plain,
% 1.64/1.83 (((~b(s(s(s(s(elem!1)))), 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(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(1855,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(s(elem!1)))), 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(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[1854])).
% 1.64/1.83 tff(1856,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(s(elem!1)))), 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(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[1855, 1853])).
% 1.64/1.83 tff(1857,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(s(elem!1)))), 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(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(1858,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[1857, 1856])).
% 1.64/1.83 tff(1859,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1858, 97, 1139, 1545, 255, 473])).
% 1.64/1.83 tff(1860,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(1861,plain,
% 1.64/1.83 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1860, 255, 1139, 1545])).
% 1.64/1.83 tff(1862,plain,
% 1.64/1.83 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[486, 1861, 472])).
% 1.64/1.83 tff(1863,plain,
% 1.64/1.83 (~b(z, s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1494, 255, 61, 441])).
% 1.64/1.83 tff(1864,plain,
% 1.64/1.83 (r(z, s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1093, 1863])).
% 1.64/1.83 tff(1865,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(1866,plain,
% 1.64/1.84 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(1867,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1866])).
% 1.64/1.84 tff(1868,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[1867, 1865])).
% 1.64/1.84 tff(1869,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(1870,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[1869, 1868])).
% 1.64/1.84 tff(1871,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1870, 155, 463, 488, 288, 824])).
% 1.64/1.84 tff(1872,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(1873,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1872, 1864, 1862, 288, 824])).
% 1.64/1.84 tff(1874,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(1875,plain,
% 1.64/1.84 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1874, 1699, 1834, 1776, 61, 1824, 1691, 1852])).
% 1.64/1.84 tff(1876,plain,
% 1.64/1.84 (r(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[280, 1875])).
% 1.64/1.84 tff(1877,plain,
% 1.64/1.84 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1822, 1820, 1393])).
% 1.64/1.84 tff(1878,plain,
% 1.64/1.84 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[452, 1877])).
% 1.64/1.84 tff(1879,plain,
% 1.64/1.84 (~b(s(s(s(s(elem!1)))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1832, 1878, 83, 61])).
% 1.64/1.84 tff(1880,plain,
% 1.64/1.84 (r(s(s(s(s(elem!1)))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[842, 1879])).
% 1.64/1.84 tff(1881,plain,
% 1.64/1.84 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[832, 1880, 1380, 288])).
% 1.64/1.84 tff(1882,plain,
% 1.64/1.84 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[821, 1881, 802])).
% 1.64/1.84 tff(1883,plain,
% 1.64/1.84 ((elem!1 = z) <=> (z = elem!1)),
% 1.64/1.84 inference(commutativity,[status(thm)],[])).
% 1.64/1.84 tff(1884,plain,
% 1.64/1.84 ((z = elem!1) <=> (elem!1 = z)),
% 1.64/1.84 inference(symmetry,[status(thm)],[1883])).
% 1.64/1.84 tff(1885,plain,
% 1.64/1.84 (elem!1 = z),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[1534, 1884])).
% 1.64/1.84 tff(1886,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.64/1.84 tff(1887,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1886, 1885])).
% 1.64/1.84 tff(1888,plain,((~(z = elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(1889,plain,
% 1.64/1.84 (elem!1 = z),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1888, 1444])).
% 1.64/1.84 tff(1890,plain,
% 1.64/1.84 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1399])).
% 1.64/1.84 tff(1891,plain,
% 1.64/1.84 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 1.64/1.84 inference(symmetry,[status(thm)],[1890])).
% 1.64/1.84 tff(1892,plain,
% 1.64/1.84 (b(elem!1, s(s(z))) <=> b(z, s(s(elem!1)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1451, 1399])).
% 1.64/1.84 tff(1893,plain,
% 1.64/1.84 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1396])).
% 1.64/1.84 tff(1894,plain,
% 1.64/1.84 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(z)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[1893, 1892, 1891])).
% 1.64/1.84 tff(1895,plain,
% 1.64/1.84 ((~b(elem!1, s(s(elem!1)))) <=> (~b(z, s(s(z))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1894])).
% 1.64/1.84 tff(1896,plain,
% 1.64/1.84 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1444])).
% 1.64/1.84 tff(1897,plain,
% 1.64/1.84 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1399])).
% 1.64/1.84 tff(1898,plain,
% 1.64/1.84 (b(s(s(elem!1)), z)),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[83, 1897])).
% 1.64/1.84 tff(1899,plain,
% 1.64/1.84 (b(s(s(elem!1)), elem!1)),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[1898, 1896])).
% 1.64/1.84 tff(1900,plain,
% 1.64/1.84 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.64/1.84 inference(commutativity,[status(thm)],[])).
% 1.64/1.84 tff(1901,plain,
% 1.64/1.84 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[1900])).
% 1.64/1.84 tff(1902,plain,
% 1.64/1.84 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[1453, 1901])).
% 1.64/1.84 tff(1903,plain,
% 1.64/1.84 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1902])).
% 1.64/1.84 tff(1904,plain,
% 1.64/1.84 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[837, 1903])).
% 1.64/1.84 tff(1905,plain,
% 1.64/1.84 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[1518])).
% 1.64/1.84 tff(1906,plain,
% 1.64/1.84 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[287, 1905])).
% 1.64/1.84 tff(1907,assumption,(~r(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.64/1.84 tff(1908,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1907, 1906])).
% 1.64/1.84 tff(1909,plain,(r(s(elem!1), s(s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~(s(s(s(z))) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(1910,plain,
% 1.64/1.84 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1909, 287, 1393])).
% 1.64/1.84 tff(1911,plain,
% 1.64/1.84 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1484, 1820, 1432])).
% 1.64/1.84 tff(1912,assumption,(r(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.64/1.84 tff(1913,assumption,(~(elem!1 = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.64/1.84 tff(1914,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.64/1.84 tff(1915,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.64/1.84 tff(1916,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(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $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(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(1917,plain,
% 1.64/1.84 (((~b(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(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(1918,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)), 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(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1917])).
% 1.64/1.84 tff(1919,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)), 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(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[1918, 1916])).
% 1.64/1.84 tff(1920,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)), 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(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(1921,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(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[1920, 1919])).
% 1.64/1.84 tff(1922,plain,
% 1.64/1.84 ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1921, 97, 1545, 1915])).
% 1.64/1.84 tff(1923,plain,
% 1.64/1.84 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1922, 1914])).
% 1.64/1.84 tff(1924,assumption,(~r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.64/1.84 tff(1925,assumption,(~b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.64/1.84 tff(1926,plain,
% 1.64/1.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(1927,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(1928,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1)))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[1927, 1926])).
% 1.64/1.84 tff(1929,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1928, 53, 1925, 1924, 1913])).
% 1.64/1.84 tff(1930,plain,(r(elem!1, s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(1931,plain,
% 1.64/1.84 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1930, 1923, 1913])).
% 1.64/1.84 tff(1932,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 1.64/1.84 tff(1933,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(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(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(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(1934,plain,
% 1.64/1.84 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(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)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(1935,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)), 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(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1934])).
% 1.64/1.84 tff(1936,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)), 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(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[1935, 1933])).
% 1.64/1.84 tff(1937,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)), 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)))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(1938,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(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 1.64/1.84 tff(1939,plain,
% 1.64/1.84 ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1938, 97, 1545, 1915])).
% 1.64/1.84 tff(1940,plain,
% 1.64/1.84 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1939, 1914])).
% 1.64/1.84 tff(1941,plain,
% 1.64/1.84 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1471, 1940, 1732])).
% 1.64/1.84 tff(1942,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(1943,plain,
% 1.64/1.84 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(1944,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1943])).
% 1.64/1.84 tff(1945,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[1944, 1942])).
% 1.64/1.84 tff(1946,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(1947,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[1946, 1945])).
% 1.64/1.84 tff(1948,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1947, 155, 1941, 1932, 1931, 1912])).
% 1.64/1.84 tff(1949,plain,((~b(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = elem!1) | (elem!1 = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(1950,plain,
% 1.64/1.84 (~b(elem!1, s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1949, 1911, 1910, 1455, 1904, 1448, 1899])).
% 1.64/1.84 tff(1951,plain,
% 1.64/1.84 (~b(z, s(s(z)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[1950, 1895])).
% 1.64/1.84 tff(1952,plain,
% 1.64/1.84 (r(z, s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[222, 1951])).
% 1.64/1.84 tff(1953,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[681, 155, 287, 309, 226, 81, 3])).
% 1.64/1.84 tff(1954,plain,((~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(1955,plain,
% 1.64/1.84 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1954, 1952, 81, 287, 3])).
% 1.64/1.84 tff(1956,plain,
% 1.64/1.84 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[336, 1955])).
% 1.64/1.84 tff(1957,plain,
% 1.64/1.84 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1393])).
% 1.64/1.84 tff(1958,plain,
% 1.64/1.84 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[1957])).
% 1.64/1.84 tff(1959,plain,
% 1.64/1.84 (r(z, s(s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[1380, 1958])).
% 1.64/1.84 tff(1960,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.64/1.84 tff(1961,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.64/1.84 tff(1962,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(1963,plain,
% 1.64/1.84 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(1964,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1963])).
% 1.64/1.84 tff(1965,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[1964, 1962])).
% 1.64/1.84 tff(1966,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(1967,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[1966, 1965])).
% 1.64/1.84 tff(1968,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1967, 155, 226, 1300, 1961, 1960])).
% 1.64/1.84 tff(1969,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(1970,plain,
% 1.64/1.84 (~r(s(s(z)), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1969, 1952, 1960, 1959])).
% 1.64/1.84 tff(1971,plain,
% 1.64/1.84 (b(s(s(z)), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[437, 1970])).
% 1.64/1.84 tff(1972,assumption,(elem!1 = z), introduced(assumption)).
% 1.64/1.84 tff(1973,plain,
% 1.64/1.84 (s(elem!1) = s(z)),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1972])).
% 1.64/1.84 tff(1974,plain,
% 1.64/1.84 (s(s(elem!1)) = s(s(z))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1973])).
% 1.64/1.84 tff(1975,plain,
% 1.64/1.84 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1974])).
% 1.64/1.84 tff(1976,plain,
% 1.64/1.84 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.64/1.84 inference(symmetry,[status(thm)],[1975])).
% 1.64/1.84 tff(1977,plain,
% 1.64/1.84 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1976])).
% 1.64/1.84 tff(1978,plain,
% 1.64/1.84 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[1977])).
% 1.64/1.84 tff(1979,plain,
% 1.64/1.84 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[805, 1978])).
% 1.64/1.84 tff(1980,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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(1981,plain,
% 1.64/1.85 (((~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(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(1982,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))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(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)), 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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1981])).
% 1.64/1.85 tff(1983,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))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(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)), 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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[1982, 1980])).
% 1.64/1.85 tff(1984,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))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(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)), s(s(s(s(elem!1)))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(1985,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1984, 1983])).
% 1.64/1.85 tff(1986,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1985, 97, 339, 1361, 1360, 1979])).
% 1.64/1.85 tff(1987,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(1988,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1987, 1971, 1956, 1360, 1889, 1882])).
% 1.64/1.85 tff(1989,plain,(r(s(s(s(s(elem!1)))), s(s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(1990,plain,
% 1.64/1.85 (~r(s(s(s(z))), s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1989, 1876, 1817, 81, 1847, 3, 1714, 1777, 1699, 83, 61])).
% 1.64/1.85 tff(1991,plain,
% 1.64/1.85 (b(s(s(s(z))), s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[421, 1990])).
% 1.64/1.85 tff(1992,plain,
% 1.64/1.85 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1393])).
% 1.64/1.85 tff(1993,plain,
% 1.64/1.85 (b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1331, 1992])).
% 1.64/1.85 tff(1994,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5, 1993])).
% 1.64/1.85 tff(1995,plain,((~b(s(s(s(z))), s(s(z)))) | b(s(s(s(elem!1))), s(s(z))) | (~(s(s(s(z))) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(1996,plain,
% 1.64/1.85 (b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1995, 1991, 1714])).
% 1.64/1.85 tff(1997,plain,
% 1.64/1.85 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1996, 1838])).
% 1.64/1.85 tff(1998,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(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(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(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(1999,plain,
% 1.64/1.85 (((~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(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(2000,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)), 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(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1999])).
% 1.64/1.85 tff(2001,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)), 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(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[2000, 1998])).
% 1.64/1.85 tff(2002,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)), 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))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(2003,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[2002, 2001])).
% 1.64/1.85 tff(2004,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2003, 97, 1852, 1997, 1836, 1724])).
% 1.64/1.85 tff(2005,plain,((~b(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(2006,plain,
% 1.64/1.85 (~b(s(z), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2005, 83, 3, 81, 61])).
% 1.64/1.85 tff(2007,plain,
% 1.64/1.85 (r(s(z), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[253, 2006])).
% 1.64/1.85 tff(2008,plain,
% 1.64/1.85 (~b(s(s(s(z))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1297, 2007, 3, 61, 83])).
% 1.64/1.85 tff(2009,plain,
% 1.64/1.85 (r(s(s(s(z))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[402, 2008])).
% 1.64/1.85 tff(2010,plain,
% 1.64/1.85 (~r(z, s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1327, 2009, 3, 81, 2007])).
% 1.64/1.85 tff(2011,plain,
% 1.64/1.85 (b(z, s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[222, 2010])).
% 1.64/1.85 tff(2012,plain,
% 1.64/1.85 (~r(z, s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1308, 2009, 2007, 81])).
% 1.64/1.85 tff(2013,plain,
% 1.64/1.85 (b(z, s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1318, 2012])).
% 1.64/1.85 tff(2014,plain,
% 1.64/1.85 (~b(s(s(s(z))), s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1339, 2013, 83, 2011])).
% 1.64/1.85 tff(2015,plain,
% 1.64/1.85 (r(s(s(s(z))), s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[421, 2014])).
% 1.64/1.85 tff(2016,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(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(2017,plain,
% 1.64/1.85 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(2018,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(s(elem!1))))) | (~b(s(z), s(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(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[2017])).
% 1.64/1.85 tff(2019,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(s(elem!1))))) | (~b(s(z), s(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(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.64/1.85 inference(transitivity,[status(thm)],[2018, 2016])).
% 1.64/1.85 tff(2020,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(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~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(2021,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[2020, 2019])).
% 1.64/1.85 tff(2022,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2021, 97, 193, 61, 83, 87])).
% 1.64/1.85 tff(2023,plain,((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(2024,plain,
% 1.64/1.85 (~b(s(s(z)), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2023, 193, 61, 83])).
% 1.64/1.85 tff(2025,plain,
% 1.64/1.85 (r(s(s(z)), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[122, 2024])).
% 1.64/1.85 tff(2026,plain,
% 1.64/1.85 (~r(s(s(s(z))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1347, 155, 81, 2025, 1960, 386])).
% 1.64/1.85 tff(2027,plain,
% 1.64/1.85 (b(s(s(s(z))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1358, 2026])).
% 1.64/1.85 tff(2028,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(z), s(s(s(elem!1))))) | (~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(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(2029,plain,
% 1.64/1.85 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~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(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(2030,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(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~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(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[2029])).
% 1.64/1.85 tff(2031,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(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~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(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[2030, 2028])).
% 1.64/1.85 tff(2032,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(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(2033,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[2032, 2031])).
% 1.64/1.85 tff(2034,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2033, 97, 193, 61, 2027, 1330])).
% 1.64/1.85 tff(2035,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(2036,plain,
% 1.64/1.85 (~b(s(z), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2035, 2013, 61, 81, 2015, 2009, 83])).
% 1.64/1.85 tff(2037,plain,
% 1.64/1.85 (r(s(z), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[181, 2036])).
% 1.64/1.85 tff(2038,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(2039,plain,
% 1.64/1.85 (((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(2040,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[2039])).
% 1.64/1.85 tff(2041,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[2040, 2038])).
% 1.64/1.85 tff(2042,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(2043,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[2042, 2041])).
% 1.64/1.85 tff(2044,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2043, 155, 1380, 81, 2007, 2037, 2009])).
% 1.64/1.85 tff(2045,plain,((~b(s(s(z)), z)) | (~r(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(2046,plain,
% 1.64/1.85 (~b(s(s(z)), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2045, 61, 81, 3])).
% 1.64/1.85 tff(2047,plain,
% 1.64/1.85 (r(s(s(z)), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[625, 2046])).
% 1.64/1.85 tff(2048,plain,
% 1.64/1.85 (((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(2049,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(z))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[2048])).
% 1.64/1.85 tff(2050,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[2049, 635])).
% 1.64/1.85 tff(2051,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(2052,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(z))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[2051, 2050])).
% 1.64/1.86 tff(2053,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2052, 155, 226, 81, 645, 3])).
% 1.64/1.86 tff(2054,plain,((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(2055,plain,
% 1.64/1.86 (~r(z, s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2054, 2047, 81, 3])).
% 1.64/1.86 tff(2056,plain,
% 1.64/1.86 (b(z, s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[222, 2055])).
% 1.64/1.86 tff(2057,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(2058,plain,
% 1.64/1.86 (((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(2059,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[2058])).
% 1.64/1.86 tff(2060,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)))),
% 1.64/1.86 inference(transitivity,[status(thm)],[2059, 2057])).
% 1.64/1.86 tff(2061,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(2062,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[2061, 2060])).
% 1.64/1.86 tff(2063,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2062, 155, 570, 81, 645, 3, 225])).
% 1.64/1.86 tff(2064,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(2065,plain,
% 1.64/1.86 (~r(z, s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2064, 225, 2047, 3, 81])).
% 1.64/1.86 tff(2066,plain,
% 1.64/1.86 (b(z, s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[590, 2065])).
% 1.64/1.86 tff(2067,plain,
% 1.64/1.86 (~b(s(s(z)), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[659, 2066, 81, 2047, 225, 3])).
% 1.64/1.86 tff(2068,plain,
% 1.64/1.86 (r(s(s(z)), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[122, 2067])).
% 1.64/1.86 tff(2069,plain,
% 1.64/1.86 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[653, 225, 81, 2047, 3])).
% 1.64/1.86 tff(2070,plain,
% 1.64/1.86 (b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[58, 2069])).
% 1.64/1.86 tff(2071,plain,
% 1.64/1.86 (((~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(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(2072,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(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[2071])).
% 1.64/1.86 tff(2073,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(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[2072, 627])).
% 1.64/1.86 tff(2074,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(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(2075,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[2074, 2073])).
% 1.64/1.86 tff(2076,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2075, 97, 124, 204, 60, 127])).
% 1.64/1.86 tff(2077,plain,((~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(2078,plain,
% 1.64/1.86 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2077, 2066, 2056, 2070])).
% 1.64/1.86 tff(2079,plain,
% 1.64/1.86 (r(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[143, 2078])).
% 1.64/1.86 tff(2080,plain,
% 1.64/1.86 (~r(s(s(s(elem!1))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1273, 2079, 225, 2068])).
% 1.64/1.86 tff(2081,plain,
% 1.64/1.86 (b(s(s(s(elem!1))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[493, 2080])).
% 1.64/1.86 tff(2082,plain,
% 1.64/1.86 (~b(s(z), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1291, 2081, 61, 2066])).
% 1.64/1.86 tff(2083,plain,
% 1.64/1.86 (r(s(z), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[253, 2082])).
% 1.64/1.86 tff(2084,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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(2085,plain,
% 1.64/1.86 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(2086,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(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[2085])).
% 1.64/1.86 tff(2087,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(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[2086, 2084])).
% 1.64/1.86 tff(2088,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(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(2089,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[2088, 2087])).
% 1.64/1.86 tff(2090,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2089, 97, 1139, 61, 124, 255])).
% 1.64/1.86 tff(2091,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(2092,plain,
% 1.64/1.86 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2091, 2081, 2066, 61])).
% 1.64/1.86 tff(2093,plain,
% 1.64/1.86 (r(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[280, 2092])).
% 1.64/1.86 tff(2094,plain,
% 1.64/1.86 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1178, 2093, 3, 225, 2079])).
% 1.64/1.86 tff(2095,plain,
% 1.64/1.86 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[452, 2094])).
% 1.64/1.86 tff(2096,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(2097,plain,
% 1.64/1.86 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(2098,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[2097])).
% 1.64/1.86 tff(2099,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[2098, 2096])).
% 1.64/1.86 tff(2100,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(2101,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[2100, 2099])).
% 1.64/1.86 tff(2102,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2101, 155, 287, 488, 3, 225, 224])).
% 1.64/1.86 tff(2103,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(2104,plain,
% 1.64/1.86 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2103, 2093, 3, 225, 2079])).
% 1.64/1.86 tff(2105,plain,
% 1.64/1.86 (r(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[143, 138])).
% 1.64/1.86 tff(2106,plain,
% 1.64/1.86 (~r(s(s(s(elem!1))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1273, 2105, 225, 2])).
% 1.64/1.86 tff(2107,plain,
% 1.64/1.86 (b(s(s(s(elem!1))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[493, 2106])).
% 1.64/1.86 tff(2108,plain,
% 1.64/1.86 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2091, 2107, 124, 61])).
% 1.64/1.86 tff(2109,plain,
% 1.64/1.86 (r(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[280, 2108])).
% 1.64/1.86 tff(2110,plain,
% 1.64/1.86 (b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1214, 1150, 225, 124, 2107, 61, 138, 2109])).
% 1.64/1.86 tff(2111,plain,
% 1.64/1.86 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[486, 1150, 472])).
% 1.64/1.86 tff(2112,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(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(2113,plain,
% 1.64/1.86 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(2114,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(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[2113])).
% 1.64/1.86 tff(2115,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(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[2114, 2112])).
% 1.64/1.86 tff(2116,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(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(2117,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(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[2116, 2115])).
% 1.64/1.86 tff(2118,plain,
% 1.64/1.86 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2117, 97, 473, 339, 513])).
% 1.64/1.86 tff(2119,plain,
% 1.64/1.86 (r(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[141, 53, 42, 2118])).
% 1.64/1.86 tff(2120,plain,
% 1.64/1.86 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[751, 97, 473, 339, 513])).
% 1.64/1.86 tff(2121,plain,
% 1.64/1.86 (r(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[58, 2120])).
% 1.64/1.86 tff(2122,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(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(2123,plain,
% 1.64/1.86 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(2124,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(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(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))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[2123])).
% 1.64/1.86 tff(2125,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(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(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))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[2124, 2122])).
% 1.64/1.86 tff(2126,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(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(2127,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[2126, 2125])).
% 1.64/1.86 tff(2128,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2127, 97, 1139, 473, 513, 535])).
% 1.64/1.86 tff(2129,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(2130,plain,
% 1.64/1.86 (~b(s(z), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2129, 473, 1139, 513])).
% 1.64/1.86 tff(2131,plain,
% 1.64/1.86 (r(s(z), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[548, 2130])).
% 1.64/1.86 tff(2132,plain,
% 1.64/1.86 (~r(s(z), s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[161, 155, 2131, 2121, 2119])).
% 1.64/1.86 tff(2133,plain,
% 1.64/1.86 (b(s(z), s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[179, 53, 2132, 174])).
% 1.64/1.86 tff(2134,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(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(2135,plain,
% 1.64/1.86 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(2136,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(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(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))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[2135])).
% 1.64/1.87 tff(2137,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(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(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))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[2136, 2134])).
% 1.64/1.87 tff(2138,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(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(2139,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[2138, 2137])).
% 1.64/1.87 tff(2140,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2139, 97, 1139, 2133, 473, 513])).
% 1.64/1.87 tff(2141,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(2142,plain,
% 1.64/1.87 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2141, 2111, 2107, 2110])).
% 1.64/1.87 tff(2143,plain,
% 1.64/1.87 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[336, 2142])).
% 1.64/1.87 tff(2144,plain,
% 1.64/1.87 (~b(z, s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1190, 2111, 124, 441])).
% 1.64/1.87 tff(2145,plain,
% 1.64/1.87 (r(z, s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1093, 2144])).
% 1.64/1.87 tff(2146,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(2147,plain,
% 1.64/1.87 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(2148,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[2147])).
% 1.64/1.87 tff(2149,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[2148, 2146])).
% 1.64/1.87 tff(2150,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(2151,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[2150, 2149])).
% 1.64/1.87 tff(2152,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2151, 155, 463, 309, 81, 645, 2])).
% 1.64/1.87 tff(2153,plain,((~r(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(2154,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2153, 2145, 2143, 81, 645, 2])).
% 1.64/1.87 tff(2155,plain,(r(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | b(s(s(z)), s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(2156,plain,
% 1.64/1.87 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2155, 2104, 2047, 2068, 2066, 2095, 225, 61, 2078, 81])).
% 1.64/1.87 tff(2157,plain,
% 1.64/1.87 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[340])).
% 1.64/1.87 tff(2158,plain,
% 1.64/1.87 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.87 inference(symmetry,[status(thm)],[2157])).
% 1.64/1.87 tff(2159,plain,
% 1.64/1.87 (b(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[339, 2158])).
% 1.64/1.87 tff(2160,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[138, 2159])).
% 1.64/1.87 tff(2161,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | b(s(s(z)), s(s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(2162,plain,
% 1.64/1.87 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2161, 2156, 2078])).
% 1.64/1.87 tff(2163,plain,
% 1.64/1.87 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[336, 2162])).
% 1.64/1.87 tff(2164,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(2165,plain,
% 1.64/1.87 (((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~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(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(2166,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[2165])).
% 1.64/1.87 tff(2167,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[2166, 2164])).
% 1.64/1.87 tff(2168,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(2169,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[2168, 2167])).
% 1.64/1.87 tff(2170,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2169, 155, 287, 309, 3, 338, 1960])).
% 1.64/1.87 tff(2171,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(2172,plain,
% 1.64/1.87 (~r(s(s(s(z))), s(s(z)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2171, 2163, 2083, 3, 2093])).
% 1.64/1.87 tff(2173,plain,
% 1.64/1.87 (b(s(s(s(z))), s(s(z)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[421, 2172])).
% 1.64/1.87 tff(2174,plain,
% 1.64/1.87 (~r(z, s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1308, 386, 338, 81])).
% 1.64/1.87 tff(2175,plain,
% 1.64/1.87 (b(z, s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1318, 2174])).
% 1.64/1.87 tff(2176,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(2177,plain,
% 1.64/1.87 (((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(2178,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[2177])).
% 1.64/1.87 tff(2179,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[2178, 2176])).
% 1.64/1.87 tff(2180,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(2181,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[2180, 2179])).
% 1.64/1.87 tff(2182,plain,
% 1.64/1.87 (~r(s(s(z)), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2181, 155, 645, 2, 338, 386])).
% 1.64/1.87 tff(2183,plain,
% 1.64/1.87 (b(s(s(z)), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[437, 2182])).
% 1.64/1.87 tff(2184,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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(2185,plain,
% 1.64/1.87 (((~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(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(2186,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))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(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(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[2185])).
% 1.64/1.87 tff(2187,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))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(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(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[2186, 2184])).
% 1.64/1.87 tff(2188,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))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(2189,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[2188, 2187])).
% 1.64/1.87 tff(2190,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2189, 97, 204, 2183, 1331, 2175])).
% 1.64/1.87 tff(2191,plain,((~r(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(2192,plain,
% 1.64/1.87 (~r(s(s(s(z))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2191, 2173, 2056, 2047, 2068, 2083, 81])).
% 1.64/1.87 tff(2193,plain,
% 1.64/1.87 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[349, 2156])).
% 1.64/1.87 tff(2194,plain,
% 1.64/1.87 (s(s(s(s(elem!1)))) = elem!1),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1734, 2193])).
% 1.64/1.87 tff(2195,plain,
% 1.64/1.87 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[354, 2156])).
% 1.64/1.87 tff(2196,plain,
% 1.64/1.87 (b(z, s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[369, 2195, 2066])).
% 1.64/1.87 tff(2197,plain,
% 1.64/1.87 (~(s(s(s(z))) = elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1742, 2156])).
% 1.64/1.87 tff(2198,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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(2199,plain,
% 1.64/1.87 (((~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(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(2200,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(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(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[2199])).
% 1.64/1.87 tff(2201,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(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(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.64/1.87 inference(transitivity,[status(thm)],[2200, 2198])).
% 1.64/1.87 tff(2202,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(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)))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(2203,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[2202, 2201])).
% 1.64/1.87 tff(2204,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2203, 97, 204, 1361, 1331, 1216])).
% 1.64/1.87 tff(2205,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(2206,plain,
% 1.64/1.87 (~b(s(s(z)), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2205, 1216, 1331, 204])).
% 1.64/1.87 tff(2207,plain,
% 1.64/1.87 (r(s(s(z)), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[437, 2206])).
% 1.64/1.87 tff(2208,assumption,(~(s(s(s(z))) = elem!1)), introduced(assumption)).
% 1.64/1.87 tff(2209,plain,
% 1.64/1.87 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), elem!1)),
% 1.64/1.87 inference(monotonicity,[status(thm)],[1757])).
% 1.64/1.87 tff(2210,plain,
% 1.64/1.87 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(symmetry,[status(thm)],[2209])).
% 1.64/1.87 tff(2211,plain,
% 1.64/1.87 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[1758])).
% 1.64/1.88 tff(2212,plain,
% 1.64/1.88 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), elem!1)),
% 1.64/1.88 inference(symmetry,[status(thm)],[2211])).
% 1.64/1.88 tff(2213,plain,
% 1.64/1.88 ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(z))), elem!1))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[2212])).
% 1.64/1.88 tff(2214,assumption,(~r(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.64/1.88 tff(2215,plain,
% 1.64/1.88 (~r(s(s(s(z))), elem!1)),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[2214, 2213])).
% 1.64/1.88 tff(2216,plain,
% 1.64/1.88 (b(s(s(s(z))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1755, 2215, 2208])).
% 1.64/1.88 tff(2217,plain,
% 1.64/1.88 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[2216, 2210])).
% 1.64/1.88 tff(2218,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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(2219,plain,
% 1.64/1.88 (((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(2220,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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[2219])).
% 1.64/1.88 tff(2221,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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))),
% 1.64/1.88 inference(transitivity,[status(thm)],[2220, 2218])).
% 1.64/1.88 tff(2222,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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(2223,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[2222, 2221])).
% 1.64/1.88 tff(2224,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2223, 97, 372, 441, 1216, 2217])).
% 1.64/1.88 tff(2225,plain,((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(s(s(z))) = elem!1) | r(s(s(s(z))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(2226,plain,
% 1.64/1.88 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2225, 1216, 441, 372, 2208, 1757])).
% 1.64/1.88 tff(2227,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(2228,plain,
% 1.64/1.88 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(2229,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[2228])).
% 1.64/1.88 tff(2230,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[2229, 2227])).
% 1.64/1.88 tff(2231,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(2232,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[2231, 2230])).
% 1.64/1.88 tff(2233,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2232, 155, 287, 3, 2226, 338, 2207])).
% 1.64/1.88 tff(2234,plain,((~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (s(s(s(z))) = elem!1) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(2235,plain,
% 1.64/1.88 (~b(s(s(s(z))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2234, 2173, 3, 2083, 2095, 2093, 2197, 2196, 2194, 2056])).
% 1.64/1.88 tff(2236,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[402, 2235, 2192])).
% 1.64/1.88 tff(2237,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(2238,plain,
% 1.64/1.88 (~r(s(z), s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2237, 61, 81, 3])).
% 1.64/1.88 tff(2239,plain,
% 1.64/1.88 (b(s(z), s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[181, 2238])).
% 1.64/1.88 tff(2240,plain,
% 1.64/1.88 (~b(z, s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[201, 60, 61, 2239])).
% 1.64/1.88 tff(2241,plain,
% 1.64/1.88 (r(z, s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[590, 2240])).
% 1.64/1.88 tff(2242,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(z))) | (~b(s(z), s(s(s(elem!1))))) | (~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(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(2243,plain,
% 1.64/1.88 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(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(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(2244,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(elem!1))))) | (~b(s(z), s(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(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[2243])).
% 1.64/1.88 tff(2245,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(elem!1))))) | (~b(s(z), s(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(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[2244, 2242])).
% 1.64/1.88 tff(2246,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(elem!1))))) | (~b(s(z), s(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)))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(2247,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[2246, 2245])).
% 1.64/1.88 tff(2248,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2247, 97, 193, 61, 204, 87])).
% 1.64/1.88 tff(2249,plain,((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(2250,plain,
% 1.64/1.88 (~b(s(s(z)), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2249, 2239, 61, 2056])).
% 1.64/1.88 tff(2251,plain,
% 1.64/1.88 (r(s(s(z)), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[122, 2250])).
% 1.64/1.88 tff(2252,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1064, 155, 125, 570, 645, 2, 224])).
% 1.64/1.88 tff(2253,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(2254,plain,
% 1.64/1.88 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2253, 494, 2047, 2251, 2241])).
% 1.64/1.88 tff(2255,plain,
% 1.64/1.88 (b(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[143, 2254])).
% 1.64/1.88 tff(2256,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(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(2257,plain,
% 1.64/1.88 (((~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))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(2258,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(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))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[2257])).
% 1.64/1.88 tff(2259,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(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))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[2258, 2256])).
% 1.64/1.88 tff(2260,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(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)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(2261,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(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[2260, 2259])).
% 1.64/1.88 tff(2262,plain,
% 1.64/1.88 (~b(s(s(s(elem!1))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2261, 97, 2056, 60, 2255])).
% 1.64/1.88 tff(2263,plain,
% 1.64/1.88 (r(s(s(s(elem!1))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[246, 2262])).
% 1.64/1.88 tff(2264,plain,
% 1.64/1.88 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1649, 2263, 81, 2251, 82, 2241, 3, 61])).
% 1.64/1.88 tff(2265,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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(2266,plain,
% 1.64/1.88 (((~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(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~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)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(2267,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(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)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[2266])).
% 1.64/1.88 tff(2268,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(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)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[2267, 2265])).
% 1.64/1.88 tff(2269,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(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)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(2270,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(elem!1))))) | (~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)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[2269, 2268])).
% 1.64/1.88 tff(2271,plain,
% 1.64/1.88 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2270, 97, 60, 1331, 127])).
% 1.64/1.88 tff(2272,plain,
% 1.64/1.88 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1678, 53, 1, 2271])).
% 1.64/1.88 tff(2273,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(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(2274,plain,
% 1.64/1.88 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(2275,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(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(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(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[2274])).
% 1.64/1.88 tff(2276,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(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(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(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.64/1.88 inference(transitivity,[status(thm)],[2275, 2273])).
% 1.64/1.88 tff(2277,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(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(2278,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[2277, 2276])).
% 1.64/1.88 tff(2279,plain,
% 1.64/1.88 (~b(s(s(s(z))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2278, 97, 193, 61, 204, 1331, 127])).
% 1.64/1.88 tff(2280,plain,
% 1.64/1.88 (r(s(s(s(z))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[402, 2279])).
% 1.64/1.88 tff(2281,plain,
% 1.64/1.88 (~b(s(s(s(elem!1))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2261, 97, 204, 60, 127])).
% 1.64/1.88 tff(2282,plain,
% 1.64/1.88 (r(s(s(s(elem!1))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[246, 2281])).
% 1.64/1.88 tff(2283,plain,
% 1.64/1.88 (~b(z, s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[201, 60, 61, 193])).
% 1.64/1.88 tff(2284,plain,
% 1.64/1.88 (r(z, s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[590, 2283])).
% 1.64/1.88 tff(2285,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1674, 155, 2284, 2282, 2280, 2272])).
% 1.64/1.88 tff(2286,plain,((~b(s(s(s(z))), s(s(z)))) | (s(s(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))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(2287,plain,
% 1.64/1.88 (~b(s(s(s(z))), s(s(z)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2286, 2264, 60, 2255, 2239, 61, 2056])).
% 1.64/1.88 tff(2288,plain,
% 1.64/1.88 (r(s(s(s(z))), s(s(z)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[421, 2287])).
% 1.64/1.88 tff(2289,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(2290,plain,
% 1.64/1.88 (((~r(s(s(z)), z)) | (~r(s(z), z)) | (~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(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(2291,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[2290])).
% 1.64/1.88 tff(2292,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[2291, 2289])).
% 1.64/1.89 tff(2293,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(2294,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[2293, 2292])).
% 1.64/1.89 tff(2295,plain,
% 1.64/1.89 (~r(s(z), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2294, 155, 81, 2047, 3, 2288])).
% 1.64/1.89 tff(2296,plain,
% 1.64/1.89 (b(s(z), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[253, 2295])).
% 1.64/1.89 tff(2297,plain,
% 1.64/1.89 (~r(s(s(s(z))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1656, 155, 2251, 3, 2288])).
% 1.64/1.89 tff(2298,plain,
% 1.64/1.89 (b(s(s(s(z))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1358, 2297])).
% 1.64/1.89 tff(2299,plain,
% 1.64/1.89 (~b(s(s(s(z))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1664, 97, 61, 2298, 2296])).
% 1.64/1.89 tff(2300,plain,
% 1.64/1.89 (r(s(s(s(z))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[402, 2299])).
% 1.64/1.89 tff(2301,plain,
% 1.64/1.89 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1674, 155, 2241, 2263, 2300])).
% 1.64/1.89 tff(2302,plain,
% 1.64/1.89 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1678, 53, 2264, 2301])).
% 1.64/1.89 tff(2303,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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(2304,plain,
% 1.64/1.89 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(2305,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(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2304])).
% 1.64/1.89 tff(2306,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(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[2305, 2303])).
% 1.64/1.89 tff(2307,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(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(2308,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[2307, 2306])).
% 1.64/1.89 tff(2309,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2308, 97, 2239, 60, 2298, 2302])).
% 1.64/1.89 tff(2310,plain,(b(s(s(s(elem!1))), s(z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(2311,plain,
% 1.64/1.89 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2310, 82, 61, 3, 81])).
% 1.64/1.89 tff(2312,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1267, 155, 125, 2, 3, 145])).
% 1.64/1.89 tff(2313,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(2314,plain,
% 1.64/1.89 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2313, 494, 3, 2251])).
% 1.64/1.89 tff(2315,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[58, 2314, 2311])).
% 1.64/1.89 tff(2316,plain,(b(s(s(s(elem!1))), s(z)) | (~r(s(z), s(s(z)))) | (~b(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(2317,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2316, 61, 3, 81])).
% 1.64/1.89 tff(2318,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(z, s(z))) | (~b(s(s(s(elem!1))), 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(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(2319,plain,
% 1.64/1.89 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(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(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(2320,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(s(elem!1))))) | (~b(s(z), s(s(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(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2319])).
% 1.64/1.89 tff(2321,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(s(elem!1))))) | (~b(s(z), s(s(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(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[2320, 2318])).
% 1.64/1.89 tff(2322,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(s(elem!1))))) | (~b(s(z), s(s(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)))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(2323,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(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[2322, 2321])).
% 1.64/1.89 tff(2324,plain,
% 1.64/1.89 (~b(s(s(s(elem!1))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2323, 97, 2317, 2239, 61])).
% 1.64/1.89 tff(2325,plain,
% 1.64/1.89 (r(s(s(s(elem!1))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[246, 2324])).
% 1.64/1.89 tff(2326,plain,
% 1.64/1.89 (~b(z, s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1257, 97, 2317, 2239, 61])).
% 1.64/1.89 tff(2327,plain,
% 1.64/1.89 (r(z, s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[590, 2326])).
% 1.64/1.89 tff(2328,plain,
% 1.64/1.89 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[735, 155, 2327, 2325, 2047])).
% 1.64/1.89 tff(2329,plain,
% 1.64/1.89 (b(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[143, 2328])).
% 1.64/1.89 tff(2330,plain,
% 1.64/1.89 (~b(s(s(s(z))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2278, 97, 2239, 61, 2056, 1331, 2329])).
% 1.64/1.89 tff(2331,plain,
% 1.64/1.89 (r(s(s(s(z))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[402, 2330])).
% 1.64/1.89 tff(2332,plain,
% 1.64/1.89 (~r(s(z), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2191, 2331, 2056, 2047, 2251, 1331, 81])).
% 1.64/1.89 tff(2333,plain,
% 1.64/1.89 (b(s(z), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[253, 2332])).
% 1.64/1.89 tff(2334,plain,
% 1.64/1.89 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1710, 2333, 2239, 2317])).
% 1.64/1.89 tff(2335,plain,
% 1.64/1.89 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1674, 155, 2327, 2325, 2331])).
% 1.64/1.89 tff(2336,plain,
% 1.64/1.89 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1678, 53, 2335, 2334])).
% 1.64/1.89 tff(2337,plain,
% 1.64/1.89 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2336])).
% 1.64/1.89 tff(2338,plain,
% 1.64/1.89 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[2337])).
% 1.64/1.89 tff(2339,plain,
% 1.64/1.89 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1775, 2335, 2239, 2317, 2333])).
% 1.64/1.89 tff(2340,plain,
% 1.64/1.89 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2336])).
% 1.64/1.89 tff(2341,plain,
% 1.64/1.89 (s(s(z)) = s(s(elem!1))),
% 1.64/1.89 inference(transitivity,[status(thm)],[73, 2340, 19])).
% 1.64/1.89 tff(2342,plain,
% 1.64/1.89 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2341])).
% 1.64/1.89 tff(2343,plain,
% 1.64/1.89 (s(z) = s(elem!1)),
% 1.64/1.89 inference(transitivity,[status(thm)],[24, 2342, 29])).
% 1.64/1.89 tff(2344,plain,
% 1.64/1.89 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2343])).
% 1.64/1.89 tff(2345,plain,
% 1.64/1.89 (z = elem!1),
% 1.64/1.89 inference(transitivity,[status(thm)],[1443, 2344, 85])).
% 1.64/1.89 tff(2346,plain,
% 1.64/1.89 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2345])).
% 1.64/1.89 tff(2347,plain,
% 1.64/1.89 (r(elem!1, s(s(s(elem!1))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[2327, 2346])).
% 1.64/1.89 tff(2348,plain,
% 1.64/1.89 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[2340])).
% 1.64/1.89 tff(2349,plain,
% 1.64/1.89 (s(s(elem!1)) = s(s(z))),
% 1.64/1.89 inference(transitivity,[status(thm)],[167, 2348, 72])).
% 1.64/1.89 tff(2350,plain,
% 1.64/1.89 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2349])).
% 1.64/1.89 tff(2351,plain,
% 1.64/1.89 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.64/1.89 inference(symmetry,[status(thm)],[2350])).
% 1.64/1.89 tff(2352,plain,
% 1.64/1.89 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2351])).
% 1.64/1.89 tff(2353,plain,
% 1.64/1.89 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[43, 2352])).
% 1.64/1.89 tff(2354,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2349])).
% 1.64/1.89 tff(2355,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.89 inference(symmetry,[status(thm)],[2354])).
% 1.64/1.89 tff(2356,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1995, 2336, 1331])).
% 1.64/1.89 tff(2357,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[2356, 2355])).
% 1.64/1.89 tff(2358,plain,
% 1.64/1.89 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2345])).
% 1.64/1.89 tff(2359,plain,
% 1.64/1.89 (r(s(s(s(elem!1))), elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[2325, 2358])).
% 1.64/1.89 tff(2360,plain,
% 1.64/1.89 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2341])).
% 1.64/1.89 tff(2361,plain,
% 1.64/1.89 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.64/1.89 inference(transitivity,[status(thm)],[2360, 1428])).
% 1.64/1.89 tff(2362,plain,
% 1.64/1.89 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2361])).
% 1.64/1.89 tff(2363,plain,
% 1.64/1.89 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[331, 2362])).
% 1.64/1.89 tff(2364,plain,
% 1.64/1.89 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[523, 2339])).
% 1.64/1.89 tff(2365,plain,
% 1.64/1.89 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1808, 2364, 2317, 2327, 2325, 2239, 61])).
% 1.64/1.89 tff(2366,plain,
% 1.64/1.89 (r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[511, 2365])).
% 1.64/1.89 tff(2367,plain,
% 1.64/1.89 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2341, 2343])).
% 1.64/1.89 tff(2368,plain,
% 1.64/1.89 (r(s(s(elem!1)), s(elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[2251, 2367])).
% 1.64/1.89 tff(2369,plain,
% 1.64/1.89 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2343])).
% 1.64/1.89 tff(2370,plain,
% 1.64/1.89 (r(s(elem!1), s(s(z)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[3, 2369])).
% 1.64/1.89 tff(2371,plain,
% 1.64/1.89 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1816, 2370, 2368, 2336, 2366])).
% 1.64/1.89 tff(2372,plain,
% 1.64/1.89 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1484, 2371, 2363])).
% 1.64/1.89 tff(2373,plain,
% 1.64/1.89 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1586, 2372, 2359, 2357, 2353, 2347, 2345])).
% 1.64/1.89 tff(2374,plain,
% 1.64/1.89 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[486, 2373, 2339])).
% 1.64/1.89 tff(2375,plain,
% 1.64/1.89 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[2374, 2338])).
% 1.64/1.89 tff(2376,plain,
% 1.64/1.89 (elem!1 = z),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1888, 2345])).
% 1.64/1.89 tff(2377,plain,
% 1.64/1.89 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2349])).
% 1.64/1.89 tff(2378,plain,
% 1.64/1.89 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[2377])).
% 1.64/1.89 tff(2379,plain,
% 1.64/1.89 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[2329, 2378])).
% 1.64/1.89 tff(2380,plain,
% 1.64/1.89 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2341])).
% 1.64/1.89 tff(2381,plain,
% 1.64/1.89 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 1.64/1.89 inference(symmetry,[status(thm)],[2380])).
% 1.64/1.89 tff(2382,plain,
% 1.64/1.89 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2345])).
% 1.64/1.89 tff(2383,plain,
% 1.64/1.89 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 1.64/1.89 inference(transitivity,[status(thm)],[2382, 2381])).
% 1.64/1.89 tff(2384,plain,
% 1.64/1.89 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2341])).
% 1.64/1.89 tff(2385,plain,
% 1.64/1.89 (b(z, s(s(elem!1)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[2056, 2384])).
% 1.64/1.89 tff(2386,plain,
% 1.64/1.89 (b(elem!1, s(s(z)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[2385, 2383])).
% 1.64/1.89 tff(2387,plain,
% 1.64/1.89 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1537])).
% 1.64/1.89 tff(2388,plain,
% 1.64/1.89 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.64/1.89 inference(symmetry,[status(thm)],[2387])).
% 1.64/1.89 tff(2389,assumption,(b(elem!1, s(s(z)))), introduced(assumption)).
% 1.64/1.89 tff(2390,plain,
% 1.64/1.89 (b(elem!1, s(s(elem!1)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[2389, 2388])).
% 1.64/1.89 tff(2391,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.89 tff(2392,assumption,(b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.64/1.89 tff(2393,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(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(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(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(2394,plain,
% 1.64/1.89 (((~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(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(2395,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(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(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2394])).
% 1.64/1.89 tff(2396,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(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(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[2395, 2393])).
% 1.64/1.89 tff(2397,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(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(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(2398,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[2397, 2396])).
% 1.64/1.89 tff(2399,plain,
% 1.64/1.89 (~b(elem!1, s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2398, 97, 1545, 2392, 2391])).
% 1.64/1.89 tff(2400,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2399, 2390])).
% 1.64/1.89 tff(2401,plain,((~b(elem!1, s(s(z)))) | (~(z = elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(2402,plain,
% 1.64/1.89 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2401, 2372, 2345, 2386, 2379])).
% 1.64/1.89 tff(2403,plain,
% 1.64/1.89 (b(elem!1, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1972])).
% 1.64/1.89 tff(2404,plain,
% 1.64/1.89 (b(z, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[2403])).
% 1.64/1.89 tff(2405,plain,
% 1.64/1.89 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[372, 2404])).
% 1.64/1.89 tff(2406,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1925, 2405])).
% 1.64/1.89 tff(2407,plain,((~b(z, s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(elem!1))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(2408,plain,
% 1.64/1.89 (~b(z, s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2407, 2402, 2376])).
% 1.64/1.89 tff(2409,plain,
% 1.64/1.89 (r(z, s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1093, 2408])).
% 1.64/1.89 tff(2410,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(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(2411,plain,
% 1.64/1.89 (((~b(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(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(2412,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(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2411])).
% 1.64/1.89 tff(2413,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(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[2412, 2410])).
% 1.64/1.89 tff(2414,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(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(2415,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(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[2414, 2413])).
% 1.64/1.89 tff(2416,plain,
% 1.64/1.89 (~b(z, s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2415, 97, 2056, 1331, 2329])).
% 1.64/1.90 tff(2417,plain,
% 1.64/1.90 (r(z, s(s(s(z))))),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[1318, 2416])).
% 1.64/1.90 tff(2418,plain,
% 1.64/1.90 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.64/1.90 inference(symmetry,[status(thm)],[2342])).
% 1.64/1.90 tff(2419,plain,
% 1.64/1.90 (s(elem!1) = s(z)),
% 1.64/1.90 inference(transitivity,[status(thm)],[30, 2418, 23])).
% 1.64/1.90 tff(2420,plain,
% 1.64/1.90 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 1.64/1.90 inference(monotonicity,[status(thm)],[2419])).
% 1.64/1.90 tff(2421,plain,
% 1.64/1.90 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.90 inference(symmetry,[status(thm)],[2420])).
% 1.64/1.90 tff(2422,plain,
% 1.64/1.90 (b(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.90 inference(modus_ponens,[status(thm)],[2317, 2421])).
% 1.64/1.90 tff(2423,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.64/1.90 tff(2424,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(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(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.90 inference(rewrite,[status(thm)],[])).
% 1.64/1.90 tff(2425,plain,
% 1.64/1.90 (((~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(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(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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.90 inference(rewrite,[status(thm)],[])).
% 1.64/1.90 tff(2426,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(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.64/1.90 inference(monotonicity,[status(thm)],[2425])).
% 1.64/1.90 tff(2427,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(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.90 inference(transitivity,[status(thm)],[2426, 2424])).
% 1.64/1.90 tff(2428,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(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(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)))))),
% 1.64/1.90 inference(quant_inst,[status(thm)],[])).
% 1.64/1.90 tff(2429,plain,
% 1.64/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[2428, 2427])).
% 1.74/1.90 tff(2430,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2429, 97, 1545, 805, 2391, 2423])).
% 1.74/1.90 tff(2431,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(2432,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)],[2431, 2372, 2379, 2422])).
% 1.74/1.90 tff(2433,plain,
% 1.74/1.90 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[821, 2432, 2364])).
% 1.74/1.90 tff(2434,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(s(elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1976])).
% 1.74/1.90 tff(2435,plain,
% 1.74/1.90 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[2434])).
% 1.74/1.90 tff(2436,plain,
% 1.74/1.90 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[823, 2435])).
% 1.74/1.90 tff(2437,assumption,(~r(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 1.74/1.90 tff(2438,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2437, 2436])).
% 1.74/1.90 tff(2439,plain,(r(s(s(s(s(elem!1)))), s(s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(2440,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)],[2439, 2433, 2376])).
% 1.74/1.90 tff(2441,assumption,(r(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.74/1.90 tff(2442,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(2443,plain,
% 1.74/1.90 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(2444,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[2443])).
% 1.74/1.90 tff(2445,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[2444, 2442])).
% 1.74/1.90 tff(2446,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(2447,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[2446, 2445])).
% 1.74/1.90 tff(2448,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2447, 155, 463, 1300, 2441, 387])).
% 1.74/1.90 tff(2449,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(2450,plain,
% 1.74/1.90 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2449, 2440, 2417, 2409])).
% 1.74/1.90 tff(2451,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2450, 2375])).
% 1.74/1.90 tff(2452,plain,((~b(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~b(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(2453,plain,
% 1.74/1.90 (~b(s(s(s(z))), s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2452, 61, 3, 81])).
% 1.74/1.90 tff(2454,plain,
% 1.74/1.90 (r(s(s(s(z))), s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[421, 2453])).
% 1.74/1.90 tff(2455,plain,
% 1.74/1.90 (~r(s(z), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2294, 155, 81, 2047, 3, 1960])).
% 1.74/1.90 tff(2456,plain,
% 1.74/1.90 (b(s(z), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[253, 2455])).
% 1.74/1.90 tff(2457,plain,
% 1.74/1.90 (~r(s(s(s(z))), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1656, 155, 2251, 3, 1960])).
% 1.74/1.90 tff(2458,plain,
% 1.74/1.90 (b(s(s(s(z))), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1358, 2457])).
% 1.74/1.90 tff(2459,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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(2460,plain,
% 1.74/1.90 (((~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(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(2461,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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[2460])).
% 1.74/1.90 tff(2462,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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[2461, 2459])).
% 1.74/1.90 tff(2463,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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(2464,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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[2463, 2462])).
% 1.74/1.90 tff(2465,plain,
% 1.74/1.90 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2464, 97, 1139, 2458, 2456])).
% 1.74/1.90 tff(2466,assumption,(~(s(s(s(elem!1))) = s(s(s(z))))), introduced(assumption)).
% 1.74/1.90 tff(2467,plain,
% 1.74/1.90 (((~![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)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(2468,plain,
% 1.74/1.90 ((~![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)))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(2469,plain,
% 1.74/1.90 ((~![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))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[2468, 2467])).
% 1.74/1.90 tff(2470,plain,
% 1.74/1.90 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2469, 53, 2466, 2465])).
% 1.74/1.90 tff(2471,plain,
% 1.74/1.90 (~b(s(s(s(z))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1664, 97, 61, 2458, 2456])).
% 1.74/1.90 tff(2472,plain,
% 1.74/1.90 (r(s(s(s(z))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[402, 2471])).
% 1.74/1.90 tff(2473,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(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(2474,plain,
% 1.74/1.90 (((~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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(2475,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(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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[2474])).
% 1.74/1.90 tff(2476,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(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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[2475, 2473])).
% 1.74/1.90 tff(2477,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(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))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(2478,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(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[2477, 2476])).
% 1.74/1.90 tff(2479,plain,
% 1.74/1.90 (~b(z, s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2478, 97, 61, 2458, 2456])).
% 1.74/1.90 tff(2480,plain,
% 1.74/1.90 (r(z, s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1318, 2479])).
% 1.74/1.90 tff(2481,plain,
% 1.74/1.90 (~b(s(s(s(elem!1))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2323, 97, 1139, 2239, 61])).
% 1.74/1.90 tff(2482,plain,
% 1.74/1.90 (r(s(s(s(elem!1))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[246, 2481])).
% 1.74/1.90 tff(2483,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(2484,plain,
% 1.74/1.90 (((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(2485,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[2484])).
% 1.74/1.90 tff(2486,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[2485, 2483])).
% 1.74/1.90 tff(2487,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(2488,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[2487, 2486])).
% 1.74/1.90 tff(2489,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2488, 155, 2482, 2480, 2472, 2470])).
% 1.74/1.90 tff(2490,plain,((~r(s(s(s(z))), s(s(z)))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(2491,plain,
% 1.74/1.90 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2490, 2454, 61, 2317, 3, 81])).
% 1.74/1.90 tff(2492,plain,
% 1.74/1.90 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[2491])).
% 1.74/1.90 tff(2493,plain,
% 1.74/1.90 (~r(s(z), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2294, 155, 81, 2047, 3, 2454])).
% 1.74/1.90 tff(2494,plain,
% 1.74/1.90 (b(s(z), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[253, 2493])).
% 1.74/1.90 tff(2495,plain,
% 1.74/1.90 (~r(s(s(s(z))), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1656, 155, 2251, 3, 2454])).
% 1.74/1.90 tff(2496,plain,
% 1.74/1.90 (b(s(s(s(z))), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1358, 2495])).
% 1.74/1.90 tff(2497,plain,
% 1.74/1.90 (~b(s(s(s(z))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1664, 97, 61, 2496, 2494])).
% 1.74/1.90 tff(2498,plain,
% 1.74/1.90 (r(s(s(s(z))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[402, 2497])).
% 1.74/1.90 tff(2499,plain,
% 1.74/1.90 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1674, 155, 2327, 2325, 2498])).
% 1.74/1.90 tff(2500,plain,
% 1.74/1.90 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1775, 2499, 2239, 2317, 2494])).
% 1.74/1.90 tff(2501,plain,
% 1.74/1.90 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[2491])).
% 1.74/1.90 tff(2502,plain,
% 1.74/1.90 (s(s(elem!1)) = s(s(z))),
% 1.74/1.90 inference(transitivity,[status(thm)],[167, 2501, 72])).
% 1.74/1.90 tff(2503,plain,
% 1.74/1.90 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[2502])).
% 1.74/1.90 tff(2504,plain,
% 1.74/1.90 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.90 inference(symmetry,[status(thm)],[2503])).
% 1.74/1.90 tff(2505,plain,
% 1.74/1.90 (~b(s(s(s(elem!1))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2323, 97, 1139, 193, 61])).
% 1.74/1.90 tff(2506,plain,
% 1.74/1.90 (r(s(s(s(elem!1))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[246, 2505])).
% 1.74/1.90 tff(2507,plain,
% 1.74/1.90 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[1414])).
% 1.74/1.90 tff(2508,assumption,(s(s(s(elem!1))) = s(s(s(z)))), introduced(assumption)).
% 1.74/1.90 tff(2509,plain,
% 1.74/1.90 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.74/1.90 inference(symmetry,[status(thm)],[2508])).
% 1.74/1.90 tff(2510,plain,
% 1.74/1.90 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[2509])).
% 1.74/1.90 tff(2511,plain,
% 1.74/1.90 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[2510, 1414])).
% 1.74/1.90 tff(2512,plain,
% 1.74/1.90 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[2511, 2507])).
% 1.74/1.90 tff(2513,plain,
% 1.74/1.90 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[2512])).
% 1.74/1.90 tff(2514,plain,
% 1.74/1.90 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[286, 2513])).
% 1.74/1.90 tff(2515,plain,
% 1.74/1.90 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1808, 2514, 1139, 570, 2506, 193, 61])).
% 1.74/1.90 tff(2516,plain,
% 1.74/1.90 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[2508])).
% 1.74/1.90 tff(2517,plain,
% 1.74/1.90 (s(s(elem!1)) = s(s(z))),
% 1.74/1.90 inference(transitivity,[status(thm)],[167, 2516, 72])).
% 1.74/1.90 tff(2518,plain,
% 1.74/1.90 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(elem!1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[2517])).
% 1.74/1.90 tff(2519,plain,
% 1.74/1.90 (r(s(s(z)), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.74/1.90 inference(symmetry,[status(thm)],[2518])).
% 1.74/1.90 tff(2520,plain,
% 1.74/1.90 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[2517])).
% 1.74/1.90 tff(2521,plain,
% 1.74/1.90 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.74/1.90 inference(symmetry,[status(thm)],[2520])).
% 1.74/1.90 tff(2522,plain,
% 1.74/1.90 (s(z) = s(elem!1)),
% 1.74/1.90 inference(transitivity,[status(thm)],[24, 2521, 29])).
% 1.74/1.90 tff(2523,plain,
% 1.74/1.90 (r(s(s(z)), s(z)) <=> r(s(s(z)), s(elem!1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[2522])).
% 1.74/1.90 tff(2524,plain,
% 1.74/1.90 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.74/1.90 inference(transitivity,[status(thm)],[2523, 2519])).
% 1.74/1.90 tff(2525,plain,
% 1.74/1.90 (r(s(s(elem!1)), s(elem!1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[2, 2524])).
% 1.74/1.90 tff(2526,plain,
% 1.74/1.90 (s(elem!1) = s(z)),
% 1.74/1.90 inference(transitivity,[status(thm)],[30, 2520, 23])).
% 1.74/1.90 tff(2527,plain,
% 1.74/1.90 (r(s(elem!1), s(s(z))) <=> r(s(z), s(s(z)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[2526])).
% 1.74/1.91 tff(2528,plain,
% 1.74/1.91 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 1.74/1.91 inference(symmetry,[status(thm)],[2527])).
% 1.74/1.91 tff(2529,plain,
% 1.74/1.91 (r(s(elem!1), s(s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[3, 2528])).
% 1.74/1.91 tff(2530,plain,
% 1.74/1.91 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[2517])).
% 1.74/1.91 tff(2531,plain,
% 1.74/1.91 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.91 inference(symmetry,[status(thm)],[2530])).
% 1.74/1.91 tff(2532,plain,
% 1.74/1.91 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1170, 2531])).
% 1.74/1.91 tff(2533,plain,
% 1.74/1.91 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1816, 2532, 2529, 2509, 2525])).
% 1.74/1.91 tff(2534,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[511, 2533, 2515])).
% 1.74/1.91 tff(2535,plain,((~(s(s(s(elem!1))) = s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(2536,plain,
% 1.74/1.91 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2535, 2491, 2327, 2239, 61, 3, 2251, 2317])).
% 1.74/1.91 tff(2537,plain,
% 1.74/1.91 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[452, 2536])).
% 1.74/1.91 tff(2538,plain,
% 1.74/1.91 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[2537, 2504])).
% 1.74/1.91 tff(2539,plain,
% 1.74/1.91 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[2502])).
% 1.74/1.91 tff(2540,plain,
% 1.74/1.91 (s(elem!1) = s(z)),
% 1.74/1.91 inference(transitivity,[status(thm)],[30, 2539, 23])).
% 1.74/1.91 tff(2541,plain,
% 1.74/1.91 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[2540])).
% 1.74/1.91 tff(2542,plain,
% 1.74/1.91 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.74/1.91 inference(symmetry,[status(thm)],[2541])).
% 1.74/1.91 tff(2543,plain,
% 1.74/1.91 (z = elem!1),
% 1.74/1.91 inference(transitivity,[status(thm)],[1443, 2542, 85])).
% 1.74/1.91 tff(2544,plain,
% 1.74/1.91 (elem!1 = z),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1888, 2543])).
% 1.74/1.91 tff(2545,plain,
% 1.74/1.91 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[2502, 2491])).
% 1.74/1.91 tff(2546,plain,
% 1.74/1.91 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.91 inference(symmetry,[status(thm)],[2545])).
% 1.74/1.91 tff(2547,plain,
% 1.74/1.91 (~b(z, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2478, 97, 61, 2496, 2494])).
% 1.74/1.91 tff(2548,plain,
% 1.74/1.91 (r(z, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1318, 2547])).
% 1.74/1.91 tff(2549,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(2550,plain,
% 1.74/1.91 (((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(2551,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[2550])).
% 1.74/1.91 tff(2552,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[2551, 2549])).
% 1.74/1.91 tff(2553,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(2554,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[2553, 2552])).
% 1.74/1.91 tff(2555,plain,
% 1.74/1.91 (~r(s(s(z)), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2554, 155, 2047, 2548, 2498])).
% 1.74/1.91 tff(2556,plain,
% 1.74/1.91 (b(s(s(z)), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[437, 2555])).
% 1.74/1.91 tff(2557,plain,
% 1.74/1.91 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[2556, 2546])).
% 1.74/1.91 tff(2558,plain,
% 1.74/1.91 (elem!1 = z),
% 1.74/1.91 inference(transitivity,[status(thm)],[1450, 2541, 17])).
% 1.74/1.91 tff(2559,plain,
% 1.74/1.91 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[2558])).
% 1.74/1.91 tff(2560,plain,
% 1.74/1.91 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.74/1.91 inference(symmetry,[status(thm)],[2559])).
% 1.74/1.91 tff(2561,plain,
% 1.74/1.91 (b(elem!1, s(s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[2056, 2560])).
% 1.74/1.91 tff(2562,plain,
% 1.74/1.91 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2401, 2538, 2543, 2561, 2557])).
% 1.74/1.91 tff(2563,plain,
% 1.74/1.91 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2407, 2562, 2544])).
% 1.74/1.91 tff(2564,plain,
% 1.74/1.91 (r(z, s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1093, 2563])).
% 1.74/1.91 tff(2565,plain,
% 1.74/1.91 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2153, 2564, 81, 2047, 2251])).
% 1.74/1.91 tff(2566,plain,
% 1.74/1.91 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[336, 2565])).
% 1.74/1.91 tff(2567,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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), 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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(2568,plain,
% 1.74/1.91 (((~b(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(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(2569,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(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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[2568])).
% 1.74/1.91 tff(2570,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(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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[2569, 2567])).
% 1.74/1.91 tff(2571,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(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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(2572,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[2571, 2570])).
% 1.74/1.91 tff(2573,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2572, 97, 1545, 473, 339, 127])).
% 1.74/1.91 tff(2574,plain,((~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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(2575,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)],[2574, 2566, 2329, 2538])).
% 1.74/1.91 tff(2576,plain,
% 1.74/1.91 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[486, 2575, 2500])).
% 1.74/1.91 tff(2577,plain,
% 1.74/1.91 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[2576, 2492])).
% 1.74/1.91 tff(2578,plain,
% 1.74/1.91 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[523, 2500])).
% 1.74/1.91 tff(2579,plain,
% 1.74/1.91 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[2491, 2540])).
% 1.74/1.91 tff(2580,plain,
% 1.74/1.91 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.91 inference(symmetry,[status(thm)],[2579])).
% 1.74/1.91 tff(2581,plain,
% 1.74/1.91 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[2496, 2580])).
% 1.74/1.91 tff(2582,plain,
% 1.74/1.91 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2431, 2538, 2557, 2581])).
% 1.74/1.91 tff(2583,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)],[821, 2582, 2578])).
% 1.74/1.91 tff(2584,plain,
% 1.74/1.91 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2439, 2583, 2544])).
% 1.74/1.91 tff(2585,plain,
% 1.74/1.91 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2449, 2584, 2548, 2564])).
% 1.74/1.91 tff(2586,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2585, 2577])).
% 1.74/1.91 tff(2587,plain,((~b(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(2588,plain,
% 1.74/1.91 (~r(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2587, 3, 61])).
% 1.74/1.91 tff(2589,plain,
% 1.74/1.91 (b(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[568, 2588])).
% 1.74/1.91 tff(2590,assumption,(~b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.74/1.91 tff(2591,plain,
% 1.74/1.91 (r(s(s(s(z))), s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[421, 2590])).
% 1.74/1.91 tff(2592,plain,
% 1.74/1.91 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.74/1.91 inference(commutativity,[status(thm)],[])).
% 1.74/1.91 tff(2593,plain,
% 1.74/1.91 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.74/1.91 inference(symmetry,[status(thm)],[2592])).
% 1.74/1.91 tff(2594,plain,
% 1.74/1.91 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(z))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[2593])).
% 1.74/1.91 tff(2595,plain,
% 1.74/1.91 (~(s(s(z)) = s(s(s(s(z)))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[80, 2594])).
% 1.74/1.91 tff(2596,plain,
% 1.74/1.91 (r(s(s(s(elem!1))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[246, 239])).
% 1.74/1.91 tff(2597,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.74/1.91 tff(2598,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(z), 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(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(2599,plain,
% 1.74/1.91 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(2600,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(z), z)) | (~b(s(z), 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(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[2599])).
% 1.74/1.91 tff(2601,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(z), z)) | (~b(s(z), 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(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[2600, 2598])).
% 1.74/1.91 tff(2602,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(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(2603,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(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[2602, 2601])).
% 1.74/1.91 tff(2604,plain,
% 1.74/1.91 (~b(z, s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2603, 97, 550, 61, 87])).
% 1.74/1.91 tff(2605,plain,
% 1.74/1.91 (r(z, s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[222, 2604])).
% 1.74/1.91 tff(2606,plain,
% 1.74/1.91 (~r(z, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1969, 2605, 1961, 1960])).
% 1.74/1.91 tff(2607,plain,
% 1.74/1.91 (b(z, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1318, 2606])).
% 1.74/1.91 tff(2608,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(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(2609,plain,
% 1.74/1.91 (((~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(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(2610,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(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(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[2609])).
% 1.74/1.91 tff(2611,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(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(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[2610, 2608])).
% 1.74/1.91 tff(2612,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(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))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(2613,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[2612, 2611])).
% 1.74/1.91 tff(2614,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2613, 97, 61, 86, 1330, 1216])).
% 1.74/1.91 tff(2615,plain,((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(2616,plain,
% 1.74/1.91 (~b(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2615, 2607, 61, 86])).
% 1.74/1.91 tff(2617,plain,
% 1.74/1.91 (r(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[402, 2616])).
% 1.74/1.91 tff(2618,plain,
% 1.74/1.91 (~b(s(s(z)), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[105, 86, 61, 87])).
% 1.74/1.91 tff(2619,plain,
% 1.74/1.91 (r(s(s(z)), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[625, 2618])).
% 1.74/1.91 tff(2620,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(2621,plain,
% 1.74/1.91 (((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(2622,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[2621])).
% 1.74/1.91 tff(2623,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[2622, 2620])).
% 1.74/1.91 tff(2624,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(2625,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[2624, 2623])).
% 1.74/1.91 tff(2626,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2625, 155, 2605, 2619, 1960, 2617])).
% 1.74/1.91 tff(2627,plain,((~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(2628,plain,
% 1.74/1.91 (~b(s(z), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2627, 87, 61, 1961, 550, 2591])).
% 1.74/1.91 tff(2629,plain,
% 1.74/1.91 (r(s(z), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[253, 2628])).
% 1.74/1.91 tff(2630,assumption,(r(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.74/1.91 tff(2631,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(2632,plain,
% 1.74/1.91 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(2633,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[2632])).
% 1.74/1.91 tff(2634,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[2633, 2631])).
% 1.74/1.91 tff(2635,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(2636,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[2635, 2634])).
% 1.74/1.91 tff(2637,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2636, 155, 125, 338, 2597, 2630])).
% 1.74/1.92 tff(2638,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(2639,plain,
% 1.74/1.92 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2638, 338, 2597, 494])).
% 1.74/1.92 tff(2640,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1376, 155, 3, 338, 1961, 1960])).
% 1.74/1.92 tff(2641,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(2642,plain,
% 1.74/1.92 (~r(s(z), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2641, 338, 2591, 1961])).
% 1.74/1.92 tff(2643,plain,
% 1.74/1.92 (b(s(z), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[548, 2642])).
% 1.74/1.92 tff(2644,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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(2645,plain,
% 1.74/1.92 (((~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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(2646,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(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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[2645])).
% 1.74/1.92 tff(2647,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(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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 1.74/1.92 inference(transitivity,[status(thm)],[2646, 2644])).
% 1.74/1.92 tff(2648,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(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)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(2649,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[2648, 2647])).
% 1.74/1.92 tff(2650,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2649, 97, 61, 83, 87, 535])).
% 1.74/1.92 tff(2651,plain,((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(2652,plain,
% 1.74/1.92 (~b(s(s(z)), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2651, 2643, 87, 61])).
% 1.74/1.92 tff(2653,plain,
% 1.74/1.92 (r(s(s(z)), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[625, 2652])).
% 1.74/1.92 tff(2654,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(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(2655,plain,
% 1.74/1.92 (((~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(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(2656,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(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~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(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[2655])).
% 1.74/1.92 tff(2657,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(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~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(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[2656, 2654])).
% 1.74/1.92 tff(2658,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(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(2659,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[2658, 2657])).
% 1.74/1.92 tff(2660,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2659, 97, 61, 204, 535, 127])).
% 1.74/1.92 tff(2661,plain,((~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(2662,plain,
% 1.74/1.92 (~b(z, s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2661, 2643, 61, 127])).
% 1.74/1.92 tff(2663,plain,
% 1.74/1.92 (r(z, s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[222, 2662])).
% 1.74/1.92 tff(2664,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(2665,plain,
% 1.74/1.92 (((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(2666,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[2665])).
% 1.74/1.92 tff(2667,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[2666, 2664])).
% 1.74/1.92 tff(2668,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(2669,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[2668, 2667])).
% 1.74/1.92 tff(2670,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2669, 155, 226, 288, 645, 145])).
% 1.74/1.92 tff(2671,plain,((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(2672,plain,
% 1.74/1.92 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2671, 2663, 288, 2653])).
% 1.74/1.92 tff(2673,plain,
% 1.74/1.92 (b(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[58, 2672])).
% 1.74/1.92 tff(2674,plain,
% 1.74/1.92 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 1.74/1.92 inference(symmetry,[status(thm)],[1992])).
% 1.74/1.92 tff(2675,plain,
% 1.74/1.92 (b(s(s(s(z))), s(s(z)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[60, 2674])).
% 1.74/1.92 tff(2676,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2590, 2675])).
% 1.74/1.92 tff(2677,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | b(s(s(s(z))), s(s(z))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(2678,plain,
% 1.74/1.92 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2677, 2673, 2590])).
% 1.74/1.92 tff(2679,plain,
% 1.74/1.92 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.74/1.92 inference(commutativity,[status(thm)],[])).
% 1.74/1.92 tff(2680,plain,
% 1.74/1.92 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[2508, 2679])).
% 1.74/1.92 tff(2681,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1, 2680])).
% 1.74/1.92 tff(2682,plain,((~(s(s(s(elem!1))) = s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(2683,plain,
% 1.74/1.92 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2682, 2678])).
% 1.74/1.92 tff(2684,assumption,(~b(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.74/1.92 tff(2685,assumption,(~r(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.74/1.92 tff(2686,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2469, 53, 2685, 2466, 2684])).
% 1.74/1.92 tff(2687,plain,(b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))) | (s(s(s(elem!1))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(2688,plain,
% 1.74/1.92 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2687, 2683, 2639])).
% 1.74/1.92 tff(2689,plain,
% 1.74/1.92 (((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(2690,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[2689])).
% 1.74/1.92 tff(2691,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[2690, 2620])).
% 1.74/1.92 tff(2692,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(2693,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[2692, 2691])).
% 1.74/1.92 tff(2694,plain,
% 1.74/1.92 (~r(s(s(s(z))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2693, 155, 2663, 2653, 2591])).
% 1.74/1.92 tff(2695,plain,
% 1.74/1.92 (b(s(s(s(z))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[402, 2694])).
% 1.74/1.92 tff(2696,plain,
% 1.74/1.92 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[459, 155, 387, 1961, 1960])).
% 1.74/1.92 tff(2697,plain,
% 1.74/1.92 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[452, 2696])).
% 1.74/1.92 tff(2698,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(2699,plain,
% 1.74/1.92 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(2700,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[2699])).
% 1.74/1.92 tff(2701,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[2700, 2698])).
% 1.74/1.92 tff(2702,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(2703,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[2702, 2701])).
% 1.74/1.92 tff(2704,plain,
% 1.74/1.92 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2703, 155, 387, 338, 2597])).
% 1.74/1.92 tff(2705,plain,
% 1.74/1.92 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[511, 2704])).
% 1.74/1.92 tff(2706,plain,
% 1.74/1.92 (~r(s(z), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2641, 338, 1960, 1961])).
% 1.74/1.92 tff(2707,plain,
% 1.74/1.92 (b(s(z), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[548, 2706])).
% 1.74/1.92 tff(2708,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(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(2709,plain,
% 1.74/1.92 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(2710,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(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, 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(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[2709])).
% 1.74/1.92 tff(2711,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(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, 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(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[2710, 2708])).
% 1.74/1.92 tff(2712,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(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(2713,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[2712, 2711])).
% 1.74/1.92 tff(2714,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2713, 97, 550, 61, 513, 876])).
% 1.74/1.92 tff(2715,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(2716,plain,
% 1.74/1.92 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2715, 2705, 550, 61])).
% 1.74/1.92 tff(2717,plain,
% 1.74/1.92 (r(s(s(s(s(elem!1)))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[842, 2716])).
% 1.74/1.92 tff(2718,assumption,(~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.74/1.92 tff(2719,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)],[486, 519, 2718])).
% 1.74/1.92 tff(2720,plain,
% 1.74/1.92 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[543, 513, 535, 61])).
% 1.74/1.93 tff(2721,plain,
% 1.74/1.93 (r(z, s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1093, 2720])).
% 1.74/1.93 tff(2722,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1872, 2721, 2719, 288, 824])).
% 1.74/1.93 tff(2723,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(2724,plain,
% 1.74/1.93 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2723, 2717, 2707, 61, 288, 2705, 82])).
% 1.74/1.93 tff(2725,plain,
% 1.74/1.93 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[340])).
% 1.74/1.93 tff(2726,plain,
% 1.74/1.93 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.93 inference(symmetry,[status(thm)],[2725])).
% 1.74/1.93 tff(2727,plain,
% 1.74/1.93 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[387, 2726])).
% 1.74/1.93 tff(2728,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2685, 2727])).
% 1.74/1.93 tff(2729,plain,((~(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(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(2730,plain,
% 1.74/1.93 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2729, 387, 2639])).
% 1.74/1.93 tff(2731,plain,
% 1.74/1.93 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[523, 2730])).
% 1.74/1.93 tff(2732,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)],[832, 2717, 570, 288])).
% 1.74/1.93 tff(2733,plain,
% 1.74/1.93 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[821, 2732, 2731])).
% 1.74/1.93 tff(2734,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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(2735,plain,
% 1.74/1.93 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(2736,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(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), 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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[2735])).
% 1.74/1.93 tff(2737,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(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), 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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[2736, 2734])).
% 1.74/1.93 tff(2738,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(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(2739,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[2738, 2737])).
% 1.74/1.93 tff(2740,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2739, 97, 473, 805, 441, 127])).
% 1.74/1.93 tff(2741,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(2742,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2741, 2733, 2724, 127, 2697])).
% 1.74/1.93 tff(2743,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), z)) | b(s(s(s(elem!1))), s(z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(2744,plain,
% 1.74/1.93 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2743, 338, 61, 288, 82, 570, 550, 1961, 2591, 127, 2597])).
% 1.74/1.93 tff(2745,assumption,(~b(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 1.74/1.93 tff(2746,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[384, 53, 2437, 2745, 286])).
% 1.74/1.93 tff(2747,plain,(r(s(s(s(s(elem!1)))), s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(2748,plain,
% 1.74/1.93 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2747, 2744])).
% 1.74/1.93 tff(2749,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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(2750,plain,
% 1.74/1.93 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(2751,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(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(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))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[2750])).
% 1.74/1.93 tff(2752,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(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(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))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[2751, 2749])).
% 1.74/1.93 tff(2753,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(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(2754,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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[2753, 2752])).
% 1.74/1.93 tff(2755,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)],[2754, 97, 2748, 2695, 2688])).
% 1.74/1.93 tff(2756,plain,
% 1.74/1.93 (~r(z, s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1969, 2663, 1961, 2591])).
% 1.74/1.93 tff(2757,plain,
% 1.74/1.93 (b(z, s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1318, 2756])).
% 1.74/1.93 tff(2758,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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(2759,plain,
% 1.74/1.93 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), 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)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(2760,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(z))), z)) | (~b(s(s(s(z))), 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)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[2759])).
% 1.74/1.93 tff(2761,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(z))), z)) | (~b(s(s(s(z))), 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)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.74/1.93 inference(transitivity,[status(thm)],[2760, 2758])).
% 1.74/1.93 tff(2762,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(z))), z)) | (~b(s(s(s(z))), 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)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(2763,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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[2762, 2761])).
% 1.74/1.93 tff(2764,plain,
% 1.74/1.93 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2763, 97, 2748, 2757, 2695])).
% 1.74/1.93 tff(2765,plain,
% 1.74/1.93 (r(z, s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1093, 2764])).
% 1.74/1.93 tff(2766,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(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(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(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(2767,plain,
% 1.74/1.93 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(2768,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(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, 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(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[2767])).
% 1.74/1.93 tff(2769,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(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, 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(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.74/1.93 inference(transitivity,[status(thm)],[2768, 2766])).
% 1.74/1.93 tff(2770,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(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(2771,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(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[2770, 2769])).
% 1.74/1.93 tff(2772,plain,
% 1.74/1.93 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2771, 97, 550, 61, 2748, 2757, 2695])).
% 1.74/1.93 tff(2773,plain,
% 1.74/1.93 (r(s(s(s(s(elem!1)))), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[842, 2772])).
% 1.74/1.93 tff(2774,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)],[1872, 2773, 288, 2765])).
% 1.74/1.93 tff(2775,plain,
% 1.74/1.93 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[486, 2774, 2755])).
% 1.74/1.93 tff(2776,plain,
% 1.74/1.93 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[349, 2775])).
% 1.74/1.93 tff(2777,plain,
% 1.74/1.93 (s(s(s(s(elem!1)))) = elem!1),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1734, 2776])).
% 1.74/1.93 tff(2778,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.74/1.93 inference(monotonicity,[status(thm)],[2777])).
% 1.74/1.93 tff(2779,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(symmetry,[status(thm)],[2778])).
% 1.74/1.93 tff(2780,assumption,(s(s(s(s(z)))) = elem!1), introduced(assumption)).
% 1.74/1.93 tff(2781,plain,
% 1.74/1.93 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[2780, 1736])).
% 1.74/1.93 tff(2782,plain,
% 1.74/1.93 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[2781])).
% 1.74/1.93 tff(2783,plain,
% 1.74/1.93 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 1.74/1.93 inference(symmetry,[status(thm)],[2782])).
% 1.74/1.93 tff(2784,plain,
% 1.74/1.93 (s(s(s(s(elem!1)))) = s(s(s(z)))),
% 1.74/1.93 inference(transitivity,[status(thm)],[345, 271, 2783, 63])).
% 1.74/1.93 tff(2785,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[286, 2784])).
% 1.74/1.93 tff(2786,plain,((~(s(s(s(s(z)))) = elem!1)) | (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(2787,plain,
% 1.74/1.93 (~(s(s(s(s(z)))) = elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2786, 2775])).
% 1.74/1.93 tff(2788,plain,
% 1.74/1.93 (r(s(s(s(s(z)))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.74/1.93 inference(monotonicity,[status(thm)],[2777])).
% 1.74/1.93 tff(2789,plain,
% 1.74/1.93 ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(s(z)))), elem!1))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[2788])).
% 1.74/1.93 tff(2790,assumption,(s(s(s(s(z)))) = s(z)), introduced(assumption)).
% 1.74/1.93 tff(2791,plain,
% 1.74/1.93 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[2790])).
% 1.74/1.93 tff(2792,plain,
% 1.74/1.93 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.74/1.93 inference(symmetry,[status(thm)],[63])).
% 1.74/1.93 tff(2793,plain,
% 1.74/1.93 (s(s(s(z))) = z),
% 1.74/1.93 inference(transitivity,[status(thm)],[2792, 2791, 17])).
% 1.74/1.93 tff(2794,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[398, 2793])).
% 1.74/1.93 tff(2795,plain,(~(s(s(s(s(z)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(2796,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.74/1.93 tff(2797,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(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)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(2798,plain,
% 1.74/1.93 (((~b(z, s(z))) | (~b(z, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(2799,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(z, s(z))) | (~b(z, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[2798])).
% 1.74/1.93 tff(2800,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(z, s(z))) | (~b(z, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/1.93 inference(transitivity,[status(thm)],[2799, 2797])).
% 1.74/1.93 tff(2801,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(z, s(z))) | (~b(z, 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))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(2802,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(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[2801, 2800])).
% 1.74/1.93 tff(2803,plain,
% 1.74/1.93 (~b(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2802, 97, 550, 61, 2796])).
% 1.74/1.93 tff(2804,plain,
% 1.74/1.93 (((~![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)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(2805,plain,
% 1.74/1.93 ((~![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)))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(2806,plain,
% 1.74/1.93 ((~![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))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[2805, 2804])).
% 1.74/1.93 tff(2807,plain,
% 1.74/1.93 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2806, 53])).
% 1.74/1.93 tff(2808,plain,
% 1.74/1.93 (r(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2807, 2803, 2795])).
% 1.74/1.93 tff(2809,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(z, s(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(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(2810,plain,
% 1.74/1.93 (((~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(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(2811,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(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(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[2810])).
% 1.74/1.93 tff(2812,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(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(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[2811, 2809])).
% 1.74/1.94 tff(2813,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(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)))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(2814,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[2813, 2812])).
% 1.74/1.94 tff(2815,plain,
% 1.74/1.94 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2814, 97, 61, 1216, 2796])).
% 1.74/1.94 tff(2816,plain,
% 1.74/1.94 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 1.74/1.94 inference(commutativity,[status(thm)],[])).
% 1.74/1.94 tff(2817,plain,
% 1.74/1.94 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(z))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[2816])).
% 1.74/1.94 tff(2818,assumption,(s(s(s(s(z)))) = s(s(s(z)))), introduced(assumption)).
% 1.74/1.94 tff(2819,plain,
% 1.74/1.94 (s(s(s(z))) = s(s(s(s(z))))),
% 1.74/1.94 inference(symmetry,[status(thm)],[2818])).
% 1.74/1.94 tff(2820,plain,
% 1.74/1.94 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[2819])).
% 1.74/1.94 tff(2821,plain,
% 1.74/1.94 (s(s(z)) = s(s(s(z)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[73, 2820, 63])).
% 1.74/1.94 tff(2822,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[432, 2821])).
% 1.74/1.94 tff(2823,plain,(~(s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(2824,plain,
% 1.74/1.94 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[2823, 2817])).
% 1.74/1.94 tff(2825,plain,
% 1.74/1.94 (((~![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))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(2826,plain,
% 1.74/1.94 ((~![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))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(2827,plain,
% 1.74/1.94 ((~![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)))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[2826, 2825])).
% 1.74/1.94 tff(2828,plain,
% 1.74/1.94 ((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)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2827, 53])).
% 1.74/1.94 tff(2829,plain,
% 1.74/1.94 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2828, 2824])).
% 1.74/1.94 tff(2830,plain,
% 1.74/1.94 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2829, 2815])).
% 1.74/1.94 tff(2831,plain,
% 1.74/1.94 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 1.74/1.94 inference(commutativity,[status(thm)],[])).
% 1.74/1.94 tff(2832,plain,
% 1.74/1.94 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(z) = s(s(s(s(z))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[2831])).
% 1.74/1.94 tff(2833,plain,
% 1.74/1.94 (~(s(z) = s(s(s(s(z)))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[2795, 2832])).
% 1.74/1.94 tff(2834,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(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)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(2835,plain,
% 1.74/1.94 (((~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)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(2836,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(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))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[2835])).
% 1.74/1.94 tff(2837,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(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)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[2836, 2834])).
% 1.74/1.94 tff(2838,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(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)))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(2839,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(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[2838, 2837])).
% 1.74/1.94 tff(2840,plain,
% 1.74/1.94 (~b(s(z), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2839, 97, 550, 61, 2796])).
% 1.74/1.94 tff(2841,plain,
% 1.74/1.94 (((~![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))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(2842,plain,
% 1.74/1.94 ((~![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))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(2843,plain,
% 1.74/1.94 ((~![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)))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[2842, 2841])).
% 1.74/1.94 tff(2844,plain,
% 1.74/1.94 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2843, 53])).
% 1.74/1.94 tff(2845,plain,
% 1.74/1.94 (r(s(z), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2844, 2840, 2833])).
% 1.74/1.94 tff(2846,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(2847,plain,
% 1.74/1.94 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(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)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(2848,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[2847])).
% 1.74/1.94 tff(2849,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[2848, 2846])).
% 1.74/1.94 tff(2850,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(2851,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[2850, 2849])).
% 1.74/1.94 tff(2852,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2851, 155, 2597, 2845, 2830, 2808])).
% 1.74/1.94 tff(2853,plain,((~b(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(2854,plain,
% 1.74/1.94 (~b(s(s(s(s(z)))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2853, 2695, 61, 2597, 550])).
% 1.74/1.94 tff(2855,plain,
% 1.74/1.94 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(2856,plain,
% 1.74/1.94 (~(s(s(s(s(z)))) = z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2855, 38])).
% 1.74/1.94 tff(2857,plain,
% 1.74/1.94 (((~![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))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(2858,plain,
% 1.74/1.94 ((~![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))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(2859,plain,
% 1.74/1.94 ((~![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)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[2858, 2857])).
% 1.74/1.94 tff(2860,plain,
% 1.74/1.94 (b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2859, 53, 2856])).
% 1.74/1.94 tff(2861,plain,
% 1.74/1.94 (r(s(s(s(s(z)))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2860, 2854])).
% 1.74/1.94 tff(2862,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(2863,plain,
% 1.74/1.94 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(2864,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[2863])).
% 1.74/1.94 tff(2865,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[2864, 2862])).
% 1.74/1.94 tff(2866,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(2867,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[2866, 2865])).
% 1.74/1.94 tff(2868,plain,
% 1.74/1.94 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2867, 155, 2765, 2773, 2861])).
% 1.74/1.94 tff(2869,plain,
% 1.74/1.94 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[2868, 2789])).
% 1.74/1.94 tff(2870,plain,
% 1.74/1.94 (((~![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))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(2871,plain,
% 1.74/1.94 ((~![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))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(2872,plain,
% 1.74/1.94 ((~![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)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[2871, 2870])).
% 1.74/1.94 tff(2873,plain,
% 1.74/1.94 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2872, 53])).
% 1.74/1.94 tff(2874,plain,
% 1.74/1.94 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2873, 2869, 2787])).
% 1.74/1.94 tff(2875,plain,
% 1.74/1.94 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[2874, 2779])).
% 1.74/1.94 tff(2876,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(2877,plain,
% 1.74/1.94 (((~r(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)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(2878,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[2877])).
% 1.74/1.94 tff(2879,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[2878, 2876])).
% 1.74/1.94 tff(2880,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))) | (~r(s(s(s(s(z)))), z)))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(2881,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[2880, 2879])).
% 1.74/1.94 tff(2882,plain,
% 1.74/1.94 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2881, 155, 2663, 2653, 2861])).
% 1.74/1.94 tff(2883,plain,
% 1.74/1.94 (((~![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))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(2884,plain,
% 1.74/1.94 ((~![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))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(2885,plain,
% 1.74/1.94 ((~![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)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[2884, 2883])).
% 1.74/1.94 tff(2886,plain,
% 1.74/1.94 ((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)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2885, 53])).
% 1.74/1.94 tff(2887,plain,
% 1.74/1.94 (b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2886, 2882, 80])).
% 1.74/1.94 tff(2888,plain,
% 1.74/1.94 (~b(s(s(z)), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2651, 87, 61, 535])).
% 1.74/1.94 tff(2889,plain,
% 1.74/1.94 (r(s(s(z)), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[625, 2888])).
% 1.74/1.94 tff(2890,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(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(2891,plain,
% 1.74/1.94 (((~b(s(z), s(s(z)))) | (~b(s(z), 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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(2892,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(z), s(s(z)))) | (~b(s(z), 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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[2891])).
% 1.74/1.95 tff(2893,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(s(z)))) | (~b(s(z), 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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[2892, 2890])).
% 1.74/1.95 tff(2894,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(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(2895,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, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[2894, 2893])).
% 1.74/1.95 tff(2896,plain,
% 1.74/1.95 (~b(z, s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2895, 97, 61, 87, 535])).
% 1.74/1.95 tff(2897,plain,
% 1.74/1.95 (r(z, s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[222, 2896])).
% 1.74/1.95 tff(2898,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2899,plain,
% 1.74/1.95 (((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2900,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[2899])).
% 1.74/1.95 tff(2901,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[2900, 2898])).
% 1.74/1.95 tff(2902,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(2903,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[2902, 2901])).
% 1.74/1.95 tff(2904,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2903, 155, 2897, 824, 2889, 1170])).
% 1.74/1.95 tff(2905,plain,((~b(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(2906,plain,
% 1.74/1.95 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2905, 2773, 2643, 61, 87])).
% 1.74/1.95 tff(2907,plain,
% 1.74/1.95 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[452, 2906])).
% 1.74/1.95 tff(2908,plain,
% 1.74/1.95 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[2775])).
% 1.74/1.95 tff(2909,plain,
% 1.74/1.95 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[127, 2908])).
% 1.74/1.95 tff(2910,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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~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(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2911,plain,
% 1.74/1.95 (((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2912,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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[2911])).
% 1.74/1.95 tff(2913,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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[2912, 2910])).
% 1.74/1.95 tff(2914,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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(2915,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[2914, 2913])).
% 1.74/1.95 tff(2916,plain,
% 1.74/1.95 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2915, 97, 2909, 2907, 2887])).
% 1.74/1.95 tff(2917,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2916, 2875])).
% 1.74/1.95 tff(2918,plain,((~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), z)) | b(s(s(s(elem!1))), s(z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(2919,plain,
% 1.74/1.95 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2918, 2629, 2597, 550, 61, 87, 288, 82, 570, 1961, 2590])).
% 1.74/1.95 tff(2920,plain,
% 1.74/1.95 (r(s(s(z)), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[143, 2919])).
% 1.74/1.95 tff(2921,plain,
% 1.74/1.95 (~r(s(z), s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2641, 2629, 2591, 1961])).
% 1.74/1.95 tff(2922,plain,
% 1.74/1.95 (b(s(z), s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[548, 2921])).
% 1.74/1.95 tff(2923,plain,
% 1.74/1.95 (~b(s(s(z)), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2651, 2922, 87, 61])).
% 1.74/1.95 tff(2924,plain,
% 1.74/1.95 (r(s(s(z)), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[625, 2923])).
% 1.74/1.95 tff(2925,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[735, 155, 570, 288, 2924, 2920])).
% 1.74/1.95 tff(2926,plain,((~b(s(s(z)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | b(s(s(s(elem!1))), s(z)) | (~r(s(s(z)), s(s(s(z))))) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(2927,plain,
% 1.74/1.95 (~b(s(s(z)), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2926, 570, 288, 61, 2597, 550, 82, 1961, 2590])).
% 1.74/1.95 tff(2928,plain,
% 1.74/1.95 (r(s(s(z)), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[122, 2927])).
% 1.74/1.95 tff(2929,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1656, 155, 2, 3, 2597, 1960])).
% 1.74/1.95 tff(2930,plain,((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(2931,plain,
% 1.74/1.95 (~r(s(z), s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2930, 2928, 2597, 2591])).
% 1.74/1.95 tff(2932,plain,
% 1.74/1.95 (b(s(z), s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[548, 2931])).
% 1.74/1.95 tff(2933,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2934,plain,
% 1.74/1.95 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2935,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[2934])).
% 1.74/1.95 tff(2936,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[2935, 2933])).
% 1.74/1.95 tff(2937,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(2938,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[2937, 2936])).
% 1.74/1.95 tff(2939,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2938, 155, 2, 338, 1961, 2597])).
% 1.74/1.95 tff(2940,plain,((~r(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)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(2941,plain,
% 1.74/1.95 (~r(s(z), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2940, 2928, 1961, 2597])).
% 1.74/1.95 tff(2942,plain,
% 1.74/1.95 (b(s(z), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[253, 2941])).
% 1.74/1.95 tff(2943,plain,
% 1.74/1.95 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2253, 645, 125, 570, 2])).
% 1.74/1.95 tff(2944,plain,
% 1.74/1.95 (b(s(s(z)), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[143, 2943])).
% 1.74/1.95 tff(2945,plain,
% 1.74/1.95 (~b(z, s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2661, 2944, 61, 535])).
% 1.74/1.95 tff(2946,plain,
% 1.74/1.95 (r(z, s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[222, 2945])).
% 1.74/1.95 tff(2947,plain,
% 1.74/1.95 (~r(z, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1969, 2946, 1961, 1960])).
% 1.74/1.95 tff(2948,plain,
% 1.74/1.95 (b(z, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1318, 2947])).
% 1.74/1.95 tff(2949,plain,
% 1.74/1.95 (~b(s(s(s(z))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2615, 2948, 61, 86])).
% 1.74/1.95 tff(2950,plain,
% 1.74/1.95 (r(s(s(s(z))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[402, 2949])).
% 1.74/1.95 tff(2951,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2693, 155, 2946, 645, 1960, 2950])).
% 1.74/1.95 tff(2952,plain,((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(2953,plain,
% 1.74/1.95 (~r(s(s(z)), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2952, 2942, 61, 2591, 1961, 2932, 494, 570, 2928])).
% 1.74/1.95 tff(2954,plain,
% 1.74/1.95 (b(s(s(z)), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[625, 2953])).
% 1.74/1.95 tff(2955,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, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), 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(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2956,plain,
% 1.74/1.95 (((~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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2957,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)), 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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[2956])).
% 1.74/1.95 tff(2958,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)), 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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[2957, 2955])).
% 1.74/1.95 tff(2959,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)), 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))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(2960,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[2959, 2958])).
% 1.74/1.95 tff(2961,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2960, 97, 61, 204, 83, 535])).
% 1.74/1.95 tff(2962,plain,((~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(2963,plain,
% 1.74/1.95 (~b(z, s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2962, 2954, 61, 2932])).
% 1.74/1.95 tff(2964,plain,
% 1.74/1.95 (r(z, s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[222, 2963])).
% 1.74/1.95 tff(2965,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), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2966,plain,
% 1.74/1.95 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2967,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, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), 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(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z)))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[2966])).
% 1.74/1.95 tff(2968,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, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), 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(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[2967, 2965])).
% 1.74/1.95 tff(2969,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, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(2970,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[2969, 2968])).
% 1.74/1.95 tff(2971,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2970, 97, 550, 83, 535, 1330])).
% 1.74/1.95 tff(2972,plain,((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(2973,plain,
% 1.74/1.95 (~b(z, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2972, 2954, 550, 2932])).
% 1.74/1.95 tff(2974,plain,
% 1.74/1.95 (r(z, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1318, 2973])).
% 1.74/1.95 tff(2975,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1969, 2974, 2964, 1961, 2591])).
% 1.74/1.95 tff(2976,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), z)) | b(s(s(s(elem!1))), s(z)) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(2977,plain,
% 1.74/1.95 (~r(z, s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2976, 2597, 550, 61, 1961, 288, 82, 2590])).
% 1.74/1.95 tff(2978,plain,
% 1.74/1.95 (b(z, s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[590, 2977])).
% 1.74/1.95 tff(2979,plain,
% 1.74/1.95 (~r(s(z), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2641, 3, 1960, 1961])).
% 1.74/1.95 tff(2980,plain,
% 1.74/1.95 (b(s(z), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[253, 2979])).
% 1.74/1.95 tff(2981,plain,
% 1.74/1.95 (~r(s(s(z)), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2930, 3, 2597, 1960])).
% 1.74/1.95 tff(2982,plain,
% 1.74/1.95 (b(s(s(z)), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[122, 2981])).
% 1.74/1.95 tff(2983,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2627, 2982, 2980, 61, 1961, 550, 1960])).
% 1.74/1.95 tff(2984,plain,((~r(s(z), s(s(z)))) | (~b(z, s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(z), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(2985,plain,
% 1.74/1.95 (~r(s(z), s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2984, 2597, 1961, 550, 2591, 61])).
% 1.74/1.95 tff(2986,plain,
% 1.74/1.95 (b(s(z), s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[548, 2985])).
% 1.74/1.95 tff(2987,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), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2988,plain,
% 1.74/1.95 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2989,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, s(z))) | (~b(z, 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(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[2988])).
% 1.74/1.95 tff(2990,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, s(z))) | (~b(z, 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(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.74/1.95 inference(transitivity,[status(thm)],[2989, 2987])).
% 1.74/1.95 tff(2991,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, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(2992,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), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[2991, 2990])).
% 1.74/1.96 tff(2993,plain,
% 1.74/1.96 (~b(s(s(z)), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2992, 97, 550, 61, 83])).
% 1.74/1.96 tff(2994,plain,
% 1.74/1.96 (r(s(s(z)), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[122, 2993])).
% 1.74/1.96 tff(2995,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), z)) | (~b(z, s(z))) | (~b(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(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(2996,plain,
% 1.74/1.96 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(2997,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(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), 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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2996])).
% 1.74/1.96 tff(2998,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(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), 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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 1.74/1.96 inference(transitivity,[status(thm)],[2997, 2995])).
% 1.74/1.96 tff(2999,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(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(3000,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[2999, 2998])).
% 1.74/1.96 tff(3001,plain,
% 1.74/1.96 (~b(s(z), s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3000, 97, 550, 61, 83])).
% 1.74/1.96 tff(3002,plain,
% 1.74/1.96 (r(s(z), s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[548, 3001])).
% 1.74/1.96 tff(3003,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2930, 3002, 2994, 2597, 1960])).
% 1.74/1.96 tff(3004,plain,((~b(s(s(z)), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(3005,plain,
% 1.74/1.96 (~b(s(s(z)), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3004, 2597, 2591, 550, 61])).
% 1.74/1.96 tff(3006,plain,
% 1.74/1.96 (r(s(s(z)), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[625, 3005])).
% 1.74/1.96 tff(3007,plain,
% 1.74/1.96 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2671, 226, 288, 645])).
% 1.74/1.96 tff(3008,plain,
% 1.74/1.96 (b(z, s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[590, 585])).
% 1.74/1.96 tff(3009,plain,
% 1.74/1.96 (r(s(z), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[181, 176])).
% 1.74/1.96 tff(3010,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(3011,plain,
% 1.74/1.96 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(3012,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[3011])).
% 1.74/1.96 tff(3013,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[3012, 3010])).
% 1.74/1.96 tff(3014,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(3015,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[3014, 3013])).
% 1.74/1.96 tff(3016,plain,
% 1.74/1.96 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3015, 155, 125, 3009, 2597])).
% 1.74/1.96 tff(3017,plain,
% 1.74/1.96 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(elem!1)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[340])).
% 1.74/1.96 tff(3018,plain,
% 1.74/1.96 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(elem!1))))),
% 1.74/1.96 inference(symmetry,[status(thm)],[3017])).
% 1.74/1.96 tff(3019,plain,
% 1.74/1.96 (r(z, s(s(s(elem!1))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[463, 3018])).
% 1.74/1.96 tff(3020,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[585, 3019])).
% 1.74/1.96 tff(3021,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | r(z, s(s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(3022,plain,
% 1.74/1.96 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3021, 463, 585])).
% 1.74/1.96 tff(3023,plain,
% 1.74/1.96 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[486, 3022, 2718])).
% 1.74/1.96 tff(3024,plain,
% 1.74/1.96 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[503, 495, 125, 488])).
% 1.74/1.96 tff(3025,plain,
% 1.74/1.96 (b(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[280, 3024])).
% 1.74/1.96 tff(3026,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(3027,plain,
% 1.74/1.96 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(3028,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[3027])).
% 1.74/1.96 tff(3029,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[3028, 3026])).
% 1.74/1.96 tff(3030,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(3031,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[3030, 3029])).
% 1.74/1.96 tff(3032,plain,
% 1.74/1.96 ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3031, 155, 488, 2, 495])).
% 1.74/1.96 tff(3033,plain,
% 1.74/1.96 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3032, 309])).
% 1.74/1.96 tff(3034,plain,
% 1.74/1.96 (b(s(s(z)), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[141, 53, 42, 3033])).
% 1.74/1.96 tff(3035,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(3036,plain,
% 1.74/1.96 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(3037,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[3036])).
% 1.74/1.96 tff(3038,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[3037, 3035])).
% 1.74/1.96 tff(3039,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(3040,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[3039, 3038])).
% 1.74/1.96 tff(3041,plain,
% 1.74/1.96 ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3040, 155, 463, 2, 495])).
% 1.74/1.96 tff(3042,plain,
% 1.74/1.96 (~r(s(s(z)), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3041, 309])).
% 1.74/1.96 tff(3043,plain,
% 1.74/1.96 (b(s(s(z)), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[625, 3042])).
% 1.74/1.96 tff(3044,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[985, 97, 126, 124, 3043, 3034])).
% 1.74/1.96 tff(3045,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(3046,plain,
% 1.74/1.96 (~r(s(s(z)), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3045, 495, 124, 488, 309, 126, 463])).
% 1.74/1.96 tff(3047,plain,
% 1.74/1.96 (b(s(s(z)), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[122, 3046])).
% 1.74/1.96 tff(3048,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), z)) | (~b(z, s(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(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(3049,plain,
% 1.74/1.96 (((~b(z, s(z))) | (~b(z, 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(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(3050,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(z))) | (~b(z, 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(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[3049])).
% 1.74/1.96 tff(3051,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(z))) | (~b(z, 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(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[3050, 3048])).
% 1.74/1.96 tff(3052,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(z))) | (~b(z, 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)))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(3053,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[3052, 3051])).
% 1.74/1.96 tff(3054,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3053, 97, 550, 61, 255, 876])).
% 1.74/1.96 tff(3055,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(3056,plain,
% 1.74/1.96 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3055, 3025, 550, 61])).
% 1.74/1.96 tff(3057,plain,
% 1.74/1.96 (r(s(s(s(s(elem!1)))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[842, 3056])).
% 1.74/1.96 tff(3058,plain,
% 1.74/1.96 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2905, 3057, 535, 61, 3047])).
% 1.74/1.96 tff(3059,plain,
% 1.74/1.96 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[452, 3058])).
% 1.74/1.96 tff(3060,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(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(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(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(3061,plain,
% 1.74/1.96 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(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(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(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(3062,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(s(s(z))))) | (~b(s(s(z)), s(s(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(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(s(s(z)))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[3061])).
% 1.74/1.96 tff(3063,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(s(s(z))))) | (~b(s(s(z)), s(s(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(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(s(s(z))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[3062, 3060])).
% 1.74/1.97 tff(3064,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(s(s(z))))) | (~b(s(s(z)), s(s(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)))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(3065,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[3064, 3063])).
% 1.74/1.97 tff(3066,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3065, 97, 255, 441, 535, 1361])).
% 1.74/1.97 tff(3067,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(3068,plain,
% 1.74/1.97 (~b(s(s(z)), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3067, 3059, 535, 3025])).
% 1.74/1.97 tff(3069,plain,
% 1.74/1.97 (r(s(s(z)), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[437, 3068])).
% 1.74/1.97 tff(3070,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(3071,plain,
% 1.74/1.97 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(3072,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3071])).
% 1.74/1.97 tff(3073,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[3072, 3070])).
% 1.74/1.97 tff(3074,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(3075,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[3074, 3073])).
% 1.74/1.97 tff(3076,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3075, 155, 463, 309, 645, 1961, 386])).
% 1.74/1.97 tff(3077,plain,((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(3078,plain,
% 1.74/1.97 (~r(s(s(s(z))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3077, 3069, 645, 309, 463])).
% 1.74/1.97 tff(3079,plain,
% 1.74/1.97 (b(s(s(s(z))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[402, 3078])).
% 1.74/1.97 tff(3080,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(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(3081,plain,
% 1.74/1.97 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), 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(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(3082,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(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3081])).
% 1.74/1.97 tff(3083,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(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[3082, 3080])).
% 1.74/1.97 tff(3084,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(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), 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))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(3085,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[3084, 3083])).
% 1.74/1.97 tff(3086,plain,
% 1.74/1.97 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3085, 97, 61, 126, 60, 3047, 3079])).
% 1.74/1.97 tff(3087,assumption,(~b(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.97 tff(3088,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1678, 53, 1, 1749, 3087])).
% 1.74/1.97 tff(3089,plain,(b(s(s(s(z))), s(s(s(elem!1)))) | (s(s(s(z))) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(3090,plain,
% 1.74/1.97 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3089, 3086, 1749])).
% 1.74/1.97 tff(3091,plain,
% 1.74/1.97 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3090])).
% 1.74/1.97 tff(3092,plain,
% 1.74/1.97 (s(s(z)) = s(s(elem!1))),
% 1.74/1.97 inference(transitivity,[status(thm)],[73, 3091, 19])).
% 1.74/1.97 tff(3093,plain,
% 1.74/1.97 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3092])).
% 1.74/1.97 tff(3094,plain,
% 1.74/1.97 (s(z) = s(elem!1)),
% 1.74/1.97 inference(transitivity,[status(thm)],[24, 3093, 29])).
% 1.74/1.97 tff(3095,plain,
% 1.74/1.97 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3094])).
% 1.74/1.97 tff(3096,plain,
% 1.74/1.97 (z = elem!1),
% 1.74/1.97 inference(transitivity,[status(thm)],[1443, 3095, 85])).
% 1.74/1.97 tff(3097,plain,
% 1.74/1.97 (r(z, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3096])).
% 1.74/1.97 tff(3098,plain,
% 1.74/1.97 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[463, 3097])).
% 1.74/1.97 tff(3099,plain,
% 1.74/1.97 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3096])).
% 1.74/1.97 tff(3100,plain,
% 1.74/1.97 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3092])).
% 1.74/1.97 tff(3101,plain,
% 1.74/1.97 (r(s(s(elem!1)), z)),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[645, 3100])).
% 1.74/1.97 tff(3102,plain,
% 1.74/1.97 (r(s(s(elem!1)), elem!1)),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[3101, 3099])).
% 1.74/1.97 tff(3103,plain,
% 1.74/1.97 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.97 inference(monotonicity,[status(thm)],[1444])).
% 1.74/1.97 tff(3104,plain,
% 1.74/1.97 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[824, 3103])).
% 1.74/1.97 tff(3105,assumption,(~r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.74/1.97 tff(3106,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3105, 3104])).
% 1.74/1.97 tff(3107,plain,(r(s(s(s(s(elem!1)))), elem!1) | (~r(s(s(s(s(elem!1)))), z)) | (~(s(s(s(z))) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(3108,plain,
% 1.74/1.97 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3107, 3090, 3057])).
% 1.74/1.97 tff(3109,plain,
% 1.74/1.97 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3092])).
% 1.74/1.97 tff(3110,plain,
% 1.74/1.97 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[309, 3109])).
% 1.74/1.97 tff(3111,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(3112,plain,
% 1.74/1.97 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(3113,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3112])).
% 1.74/1.97 tff(3114,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[3113, 3111])).
% 1.74/1.97 tff(3115,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(3116,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[3115, 3114])).
% 1.74/1.97 tff(3117,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3116, 155, 3110, 3108, 3102, 3098])).
% 1.74/1.97 tff(3118,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(3119,plain,
% 1.74/1.97 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3118, 463, 645, 309, 1749, 61, 126, 60, 535, 550, 3008, 3023, 125])).
% 1.74/1.97 tff(3120,plain,
% 1.74/1.97 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[511, 3119])).
% 1.74/1.97 tff(3121,plain,
% 1.74/1.97 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2715, 3120, 550, 61])).
% 1.74/1.97 tff(3122,plain,
% 1.74/1.97 (r(s(s(s(s(elem!1)))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[842, 3121])).
% 1.74/1.97 tff(3123,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(3124,plain,
% 1.74/1.97 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(3125,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3124])).
% 1.74/1.97 tff(3126,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.74/1.97 inference(transitivity,[status(thm)],[3125, 3123])).
% 1.74/1.97 tff(3127,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(3128,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[3127, 3126])).
% 1.74/1.97 tff(3129,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3128, 155, 463, 309, 3122, 645])).
% 1.74/1.97 tff(3130,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(3131,plain,
% 1.74/1.97 (~r(z, s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3130, 309, 645, 550, 61, 1749, 126, 59, 535, 125, 2718, 585])).
% 1.74/1.97 tff(3132,plain,
% 1.74/1.97 (b(z, s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1093, 3131])).
% 1.74/1.97 tff(3133,plain,
% 1.74/1.97 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[914, 3132, 126, 3008])).
% 1.74/1.97 tff(3134,plain,
% 1.74/1.97 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[558, 3132, 550, 61])).
% 1.74/1.97 tff(3135,plain,
% 1.74/1.97 (r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[511, 3134])).
% 1.74/1.97 tff(3136,plain,
% 1.74/1.97 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1136, 3135, 125, 3009])).
% 1.74/1.97 tff(3137,plain,
% 1.74/1.97 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[821, 3136, 3133])).
% 1.74/1.97 tff(3138,plain,
% 1.74/1.97 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[523, 3137])).
% 1.74/1.97 tff(3139,plain,
% 1.74/1.97 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[349, 3138])).
% 1.74/1.97 tff(3140,plain,
% 1.74/1.97 (s(s(s(s(elem!1)))) = elem!1),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1734, 3139])).
% 1.74/1.97 tff(3141,plain,
% 1.74/1.97 (~(s(s(s(z))) = elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1742, 3138])).
% 1.74/1.97 tff(3142,plain,
% 1.74/1.97 (elem!1 = s(s(s(s(elem!1))))),
% 1.74/1.97 inference(symmetry,[status(thm)],[3140])).
% 1.74/1.97 tff(3143,plain,
% 1.74/1.97 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3142])).
% 1.74/1.97 tff(3144,plain,
% 1.74/1.97 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), elem!1)),
% 1.74/1.97 inference(symmetry,[status(thm)],[3143])).
% 1.74/1.97 tff(3145,plain,
% 1.74/1.97 ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(z))), elem!1))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3144])).
% 1.74/1.97 tff(3146,plain,
% 1.74/1.97 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3138])).
% 1.74/1.97 tff(3147,plain,
% 1.74/1.97 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3146])).
% 1.74/1.97 tff(3148,plain,
% 1.74/1.97 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[1749, 3147])).
% 1.74/1.97 tff(3149,plain,
% 1.74/1.97 (~r(s(s(s(z))), elem!1)),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[3148, 3145])).
% 1.74/1.97 tff(3150,plain,
% 1.74/1.97 (b(s(s(s(z))), elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1755, 3149, 3141])).
% 1.74/1.97 tff(3151,plain,
% 1.74/1.97 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1764, 3150, 3140])).
% 1.74/1.97 tff(3152,plain,
% 1.74/1.97 (b(s(z), s(s(s(elem!1))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[255, 1243])).
% 1.74/1.97 tff(3153,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[176, 3152])).
% 1.74/1.97 tff(3154,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | b(s(z), s(s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(3155,plain,
% 1.74/1.97 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3154, 3138, 176])).
% 1.74/1.97 tff(3156,plain,
% 1.74/1.97 (r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[280, 3155])).
% 1.74/1.97 tff(3157,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(3158,plain,
% 1.74/1.97 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(3159,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3158])).
% 1.74/1.97 tff(3160,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[3159, 3157])).
% 1.74/1.97 tff(3161,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(3162,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[3161, 3160])).
% 1.74/1.97 tff(3163,plain,
% 1.74/1.97 (~r(s(s(z)), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3162, 155, 3156, 309, 3135])).
% 1.74/1.97 tff(3164,plain,
% 1.74/1.97 (b(s(s(z)), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[122, 3163])).
% 1.74/1.97 tff(3165,plain,
% 1.74/1.97 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[340])).
% 1.74/1.97 tff(3166,plain,
% 1.74/1.97 ((~r(s(s(s(elem!1))), s(s(z)))) <=> (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3165])).
% 1.74/1.97 tff(3167,plain,
% 1.74/1.97 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[4, 3166])).
% 1.74/1.97 tff(3168,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1170, 3167])).
% 1.74/1.98 tff(3169,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | r(s(s(s(elem!1))), s(s(z))) | (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(3170,plain,
% 1.74/1.98 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3169, 3138, 4])).
% 1.74/1.98 tff(3171,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[452, 3170])).
% 1.74/1.98 tff(3172,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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(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(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(3173,plain,
% 1.74/1.98 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(3174,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(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[3173])).
% 1.74/1.98 tff(3175,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(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[3174, 3172])).
% 1.74/1.98 tff(3176,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(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(3177,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[3176, 3175])).
% 1.74/1.98 tff(3178,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3177, 97, 3171, 3164, 1331, 3151])).
% 1.74/1.98 tff(3179,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | r(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(z))) | b(s(z), s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(z)))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(3180,plain,
% 1.74/1.98 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3179, 2718, 3016, 4, 176, 125, 126, 550, 61, 645, 535, 1331, 585])).
% 1.74/1.98 tff(3181,plain,
% 1.74/1.98 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[336, 3180])).
% 1.74/1.98 tff(3182,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(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(3183,plain,
% 1.74/1.98 (((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(3184,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(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[3183])).
% 1.74/1.98 tff(3185,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(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[3184, 3182])).
% 1.74/1.98 tff(3186,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(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(3187,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(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[3186, 3185])).
% 1.74/1.98 tff(3188,plain,
% 1.74/1.98 (~b(s(z), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3187, 97, 3181, 535, 1331])).
% 1.74/1.98 tff(3189,plain,
% 1.74/1.98 (r(s(z), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[253, 3188])).
% 1.74/1.98 tff(3190,plain,
% 1.74/1.98 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2636, 155, 125, 3189, 2597])).
% 1.74/1.98 tff(3191,plain,
% 1.74/1.98 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3169, 340, 4])).
% 1.74/1.98 tff(3192,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[452, 3191])).
% 1.74/1.98 tff(3193,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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(3194,plain,
% 1.74/1.98 (((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(3195,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(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[3194])).
% 1.74/1.98 tff(3196,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(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[3195, 3193])).
% 1.74/1.98 tff(3197,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(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(3198,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[3197, 3196])).
% 1.74/1.98 tff(3199,plain,
% 1.74/1.98 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3198, 97, 339, 3192, 1331])).
% 1.74/1.98 tff(3200,plain,
% 1.74/1.98 ((~r(s(s(s(elem!1))), s(s(s(z))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2725])).
% 1.74/1.98 tff(3201,plain,
% 1.74/1.98 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2685, 3200])).
% 1.74/1.98 tff(3202,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[384, 53, 3201, 3199, 286])).
% 1.74/1.98 tff(3203,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(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)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(3204,plain,
% 1.74/1.98 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3203, 3181, 1331, 3190, 4])).
% 1.74/1.98 tff(3205,plain,
% 1.74/1.98 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[486, 3204, 2718])).
% 1.74/1.98 tff(3206,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(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(3207,plain,
% 1.74/1.98 (((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(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(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(3208,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(s(s(elem!1)))))) | (~b(s(s(z)), s(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(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(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[3207])).
% 1.74/1.98 tff(3209,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(s(s(elem!1)))))) | (~b(s(s(z)), s(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(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(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[3208, 3206])).
% 1.74/1.98 tff(3210,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(s(s(elem!1)))))) | (~b(s(s(z)), s(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(elem!1))), s(s(s(z))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(3211,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(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[3210, 3209])).
% 1.74/1.98 tff(3212,plain,
% 1.74/1.98 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3211, 97, 3181, 59, 1331])).
% 1.74/1.98 tff(3213,plain,
% 1.74/1.98 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2687, 3212, 3190])).
% 1.74/1.98 tff(3214,plain,
% 1.74/1.98 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2508])).
% 1.74/1.98 tff(3215,plain,
% 1.74/1.98 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[3214])).
% 1.74/1.98 tff(3216,plain,
% 1.74/1.98 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[3215])).
% 1.74/1.98 tff(3217,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.74/1.98 inference(symmetry,[status(thm)],[3216])).
% 1.74/1.98 tff(3218,plain,
% 1.74/1.98 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[513, 3217])).
% 1.74/1.98 tff(3219,plain,
% 1.74/1.98 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[3215])).
% 1.74/1.98 tff(3220,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.98 inference(symmetry,[status(thm)],[3219])).
% 1.74/1.98 tff(3221,plain,
% 1.74/1.98 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[3215])).
% 1.74/1.98 tff(3222,plain,
% 1.74/1.98 ((~r(s(s(s(s(z)))), s(s(z)))) <=> (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[3221])).
% 1.74/1.98 tff(3223,plain,
% 1.74/1.98 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[3215])).
% 1.74/1.98 tff(3224,plain,
% 1.74/1.98 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(z)))), z)),
% 1.74/1.98 inference(symmetry,[status(thm)],[3223])).
% 1.74/1.98 tff(3225,plain,
% 1.74/1.98 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2715, 513, 550, 61])).
% 1.74/1.98 tff(3226,plain,
% 1.74/1.98 (r(s(s(s(s(elem!1)))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[842, 3225])).
% 1.74/1.98 tff(3227,plain,
% 1.74/1.98 (r(s(s(s(s(z)))), z)),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[3226, 3224])).
% 1.74/1.98 tff(3228,plain,
% 1.74/1.98 ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2881, 155, 226, 645])).
% 1.74/1.98 tff(3229,plain,
% 1.74/1.98 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3228, 3227])).
% 1.74/1.98 tff(3230,plain,
% 1.74/1.98 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[3229, 3222])).
% 1.74/1.98 tff(3231,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[452, 3230])).
% 1.74/1.98 tff(3232,plain,
% 1.74/1.98 (b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[3231, 3220])).
% 1.74/1.98 tff(3233,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), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(3234,plain,
% 1.74/1.98 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(3235,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), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[3234])).
% 1.74/1.98 tff(3236,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), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[3235, 3233])).
% 1.74/1.98 tff(3237,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), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(3238,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[3237, 3236])).
% 1.74/1.98 tff(3239,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3238, 97, 550, 339, 513, 87])).
% 1.74/1.98 tff(3240,plain,((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(3241,plain,
% 1.74/1.98 (~b(s(s(z)), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3240, 513, 550, 339])).
% 1.74/1.98 tff(3242,plain,
% 1.74/1.98 (r(s(s(z)), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[122, 3241])).
% 1.74/1.98 tff(3243,plain,
% 1.74/1.98 (~r(s(s(z)), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2938, 155, 3242, 338, 2597])).
% 1.74/1.98 tff(3244,plain,
% 1.74/1.98 (b(s(s(z)), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[437, 3243])).
% 1.74/1.98 tff(3245,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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(3246,plain,
% 1.74/1.98 (((~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(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(3247,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(s(z))))) | (~b(s(s(z)), s(s(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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[3246])).
% 1.74/1.98 tff(3248,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(s(z))))) | (~b(s(s(z)), s(s(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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[3247, 3245])).
% 1.74/1.98 tff(3249,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(s(z))))) | (~b(s(s(z)), s(s(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))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(3250,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[3249, 3248])).
% 1.74/1.98 tff(3251,plain,
% 1.74/1.98 (~b(s(s(s(s(z)))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3250, 97, 535, 3244, 3232])).
% 1.74/1.98 tff(3252,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3251, 3218])).
% 1.74/1.98 tff(3253,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~(s(s(s(elem!1))) = s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(3254,plain,
% 1.74/1.99 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3253, 3213, 535, 226, 645, 3189, 2597, 550, 3181, 61])).
% 1.74/1.99 tff(3255,plain,
% 1.74/1.99 (r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[511, 3254])).
% 1.74/1.99 tff(3256,plain,
% 1.74/1.99 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[503, 3255, 125, 3205])).
% 1.74/1.99 tff(3257,plain,
% 1.74/1.99 (b(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[280, 3256])).
% 1.74/1.99 tff(3258,plain,
% 1.74/1.99 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3055, 3257, 550, 61])).
% 1.74/1.99 tff(3259,plain,
% 1.74/1.99 (r(s(s(s(s(elem!1)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[842, 3258])).
% 1.74/1.99 tff(3260,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), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(3261,plain,
% 1.74/1.99 (((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(3262,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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[3261])).
% 1.74/1.99 tff(3263,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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[3262, 3260])).
% 1.74/1.99 tff(3264,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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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)))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(3265,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[3264, 3263])).
% 1.74/1.99 tff(3266,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3265, 97, 255, 339, 441, 535])).
% 1.74/1.99 tff(3267,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(3268,plain,
% 1.74/1.99 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3267, 3257, 535, 3181])).
% 1.74/1.99 tff(3269,plain,
% 1.74/1.99 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[452, 3268])).
% 1.74/1.99 tff(3270,plain,
% 1.74/1.99 (~b(s(s(z)), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2905, 3269, 535, 61, 3259])).
% 1.74/1.99 tff(3271,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(3272,plain,
% 1.74/1.99 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(3273,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[3272])).
% 1.74/1.99 tff(3274,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[3273, 3271])).
% 1.74/1.99 tff(3275,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(3276,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[3275, 3274])).
% 1.74/1.99 tff(3277,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3276, 155, 226, 824, 1170, 2, 495])).
% 1.74/1.99 tff(3278,plain,((~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(3279,plain,
% 1.74/1.99 (~r(s(s(z)), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3278, 3269, 226, 3255, 3259])).
% 1.74/1.99 tff(3280,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[122, 3279, 3270])).
% 1.74/1.99 tff(3281,plain,(b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | r(s(s(s(elem!1))), s(s(z))) | b(s(z), s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(3282,plain,
% 1.74/1.99 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3281, 2597, 535, 61, 550, 125, 645, 226, 1331, 4, 176, 126, 585])).
% 1.74/1.99 tff(3283,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(s(elem!1))))) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(3284,plain,
% 1.74/1.99 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(3285,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(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[3284])).
% 1.74/1.99 tff(3286,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(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.99 inference(transitivity,[status(thm)],[3285, 3283])).
% 1.74/1.99 tff(3287,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(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(3288,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[3287, 3286])).
% 1.74/1.99 tff(3289,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3288, 97, 126, 124, 473, 876])).
% 1.74/1.99 tff(3290,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(3291,plain,
% 1.74/1.99 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3290, 3282, 3008, 126])).
% 1.74/1.99 tff(3292,plain,
% 1.74/1.99 (r(s(s(s(s(elem!1)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[842, 3291])).
% 1.74/1.99 tff(3293,plain,
% 1.74/1.99 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3290, 473, 3008, 126])).
% 1.74/1.99 tff(3294,plain,
% 1.74/1.99 (r(s(s(s(s(elem!1)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[842, 3293])).
% 1.74/1.99 tff(3295,plain,
% 1.74/1.99 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1136, 495, 125, 225])).
% 1.74/1.99 tff(3296,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))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(3297,plain,
% 1.74/1.99 (((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(3298,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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[3297])).
% 1.74/1.99 tff(3299,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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[3298, 3296])).
% 1.74/1.99 tff(3300,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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(3301,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[3300, 3299])).
% 1.74/1.99 tff(3302,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3301, 97, 126, 372, 473, 441])).
% 1.74/1.99 tff(3303,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(3304,plain,
% 1.74/1.99 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3303, 441, 126, 473])).
% 1.74/1.99 tff(3305,plain,
% 1.74/1.99 (r(z, s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1093, 3304])).
% 1.74/1.99 tff(3306,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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(3307,plain,
% 1.74/1.99 (((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(3308,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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[3307])).
% 1.74/1.99 tff(3309,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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[3308, 3306])).
% 1.74/1.99 tff(3310,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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(3311,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[3310, 3309])).
% 1.74/1.99 tff(3312,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3311, 97, 473, 339, 60, 441])).
% 1.74/1.99 tff(3313,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(3314,plain,
% 1.74/1.99 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3313, 441, 60, 473])).
% 1.74/1.99 tff(3315,plain,
% 1.74/1.99 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[336, 3314])).
% 1.74/1.99 tff(3316,plain,
% 1.74/1.99 (r(z, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[1444])).
% 1.74/1.99 tff(3317,plain,
% 1.74/1.99 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[463, 3316])).
% 1.74/1.99 tff(3318,plain,
% 1.74/1.99 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[1444])).
% 1.74/1.99 tff(3319,plain,
% 1.74/1.99 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[1399])).
% 1.74/1.99 tff(3320,plain,
% 1.74/1.99 (r(s(s(elem!1)), z)),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[645, 3319])).
% 1.74/2.00 tff(3321,plain,
% 1.74/2.00 (r(s(s(elem!1)), elem!1)),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[3320, 3318])).
% 1.74/2.00 tff(3322,plain,
% 1.74/2.00 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3107, 1393, 824])).
% 1.74/2.00 tff(3323,plain,
% 1.74/2.00 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[1399])).
% 1.74/2.00 tff(3324,plain,
% 1.74/2.00 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[309, 3323])).
% 1.74/2.00 tff(3325,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3116, 155, 3324, 3322, 3321, 3317])).
% 1.74/2.00 tff(3326,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(3327,plain,
% 1.74/2.00 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3326, 3315, 645, 3305, 3294])).
% 1.74/2.00 tff(3328,plain,
% 1.74/2.00 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3089, 3327, 1749])).
% 1.74/2.00 tff(3329,plain,
% 1.74/2.00 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3021, 3305, 585])).
% 1.74/2.00 tff(3330,plain,
% 1.74/2.00 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[523, 3329])).
% 1.74/2.00 tff(3331,plain,
% 1.74/2.00 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[821, 3330, 815])).
% 1.74/2.00 tff(3332,plain,
% 1.74/2.00 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2741, 3331, 473, 441])).
% 1.74/2.00 tff(3333,plain,
% 1.74/2.00 (r(s(s(z)), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[143, 3332])).
% 1.74/2.00 tff(3334,plain,
% 1.74/2.00 (~r(s(s(z)), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1273, 3333, 125, 225])).
% 1.74/2.00 tff(3335,plain,
% 1.74/2.00 (b(s(s(z)), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[122, 3334])).
% 1.74/2.00 tff(3336,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(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(3337,plain,
% 1.74/2.00 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), 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))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(3338,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(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[3337])).
% 1.74/2.00 tff(3339,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(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[3338, 3336])).
% 1.74/2.00 tff(3340,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(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(3341,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[3340, 3339])).
% 1.74/2.00 tff(3342,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3341, 97, 60, 3335, 1331, 3328])).
% 1.74/2.00 tff(3343,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~r(s(s(z)), z)) | r(z, s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(3344,plain,
% 1.74/2.00 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3343, 3295, 1331, 125, 225, 473, 60, 1749, 645, 585, 126])).
% 1.74/2.00 tff(3345,plain,
% 1.74/2.00 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[452, 3344])).
% 1.74/2.00 tff(3346,plain,
% 1.74/2.00 (~b(s(s(z)), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2905, 3345, 535, 61, 3294])).
% 1.74/2.00 tff(3347,plain,
% 1.74/2.00 (~r(s(s(z)), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3278, 3345, 226, 495, 3294])).
% 1.74/2.00 tff(3348,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[122, 3347, 3346])).
% 1.74/2.00 tff(3349,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~r(s(s(z)), z)) | r(z, s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(3350,plain,
% 1.74/2.00 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3349, 3282, 535, 61, 1331, 125, 3009, 226, 59, 3016, 645, 585, 126])).
% 1.74/2.00 tff(3351,plain,
% 1.74/2.00 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[511, 3350])).
% 1.74/2.00 tff(3352,plain,
% 1.74/2.00 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[701, 3351, 3008, 3282])).
% 1.74/2.00 tff(3353,plain,
% 1.74/2.00 (r(z, s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1093, 3352])).
% 1.74/2.00 tff(3354,plain,
% 1.74/2.00 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[753, 3351, 59, 3282])).
% 1.74/2.00 tff(3355,plain,
% 1.74/2.00 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[336, 3354])).
% 1.74/2.00 tff(3356,plain,
% 1.74/2.00 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3326, 3355, 645, 3353, 3292])).
% 1.74/2.00 tff(3357,plain,
% 1.74/2.00 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3089, 3356, 3016])).
% 1.74/2.00 tff(3358,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(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(3359,plain,
% 1.74/2.00 (((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(3360,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))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[3359])).
% 1.74/2.00 tff(3361,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))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[3360, 3358])).
% 1.74/2.00 tff(3362,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))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(3363,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(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[3362, 3361])).
% 1.74/2.00 tff(3364,plain,
% 1.74/2.00 (~b(s(s(s(z))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3363, 97, 550, 61, 126, 3008, 3357])).
% 1.74/2.00 tff(3365,plain,
% 1.74/2.00 (r(s(s(s(z))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[402, 3364])).
% 1.74/2.00 tff(3366,plain,
% 1.74/2.00 (~r(s(s(z)), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3077, 3365, 645, 3353, 3355])).
% 1.74/2.00 tff(3367,plain,
% 1.74/2.00 (b(s(s(z)), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[437, 3366])).
% 1.74/2.00 tff(3368,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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(3369,plain,
% 1.74/2.00 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(3370,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(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[3369])).
% 1.74/2.00 tff(3371,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(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[3370, 3368])).
% 1.74/2.00 tff(3372,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(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(3373,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[3372, 3371])).
% 1.74/2.00 tff(3374,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3373, 97, 59, 3367, 1331, 3357])).
% 1.74/2.00 tff(3375,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | r(z, s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(z))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(3376,plain,
% 1.74/2.00 (~r(s(s(s(z))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3375, 1331, 645, 550, 61, 126, 535, 125, 226, 585, 4, 176])).
% 1.74/2.00 tff(3377,plain,
% 1.74/2.00 (b(s(s(s(z))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1358, 3376])).
% 1.74/2.00 tff(3378,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), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(3379,plain,
% 1.74/2.00 (((~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(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(3380,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), 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(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[3379])).
% 1.74/2.00 tff(3381,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), 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(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.74/2.00 inference(transitivity,[status(thm)],[3380, 3378])).
% 1.74/2.00 tff(3382,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), 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)))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(3383,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), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[3382, 3381])).
% 1.74/2.00 tff(3384,plain,
% 1.74/2.00 (~b(s(s(s(z))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3383, 97, 550, 61, 3377])).
% 1.74/2.00 tff(3385,plain,
% 1.74/2.00 (r(s(s(s(z))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[402, 3384])).
% 1.74/2.00 tff(3386,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), 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(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(3387,plain,
% 1.74/2.00 (((~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(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(3388,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), 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(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[3387])).
% 1.74/2.00 tff(3389,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), 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(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[3388, 3386])).
% 1.74/2.00 tff(3390,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), 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))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(3391,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), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[3390, 3389])).
% 1.74/2.00 tff(3392,plain,
% 1.74/2.00 (~b(z, s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3391, 97, 550, 61, 3377])).
% 1.74/2.00 tff(3393,plain,
% 1.74/2.00 (r(z, s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1318, 3392])).
% 1.74/2.00 tff(3394,plain,
% 1.74/2.00 (~r(s(s(z)), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2554, 155, 645, 3393, 3385])).
% 1.74/2.00 tff(3395,plain,
% 1.74/2.00 (b(s(s(z)), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[437, 3394])).
% 1.74/2.00 tff(3396,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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(3397,plain,
% 1.74/2.01 (((~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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(3398,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[3397])).
% 1.74/2.01 tff(3399,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[3398, 3396])).
% 1.74/2.01 tff(3400,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(3401,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[3400, 3399])).
% 1.74/2.01 tff(3402,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3401, 97, 535, 3395, 3377, 1331])).
% 1.74/2.01 tff(3403,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | r(z, s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(z))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(3404,plain,
% 1.74/2.01 (~b(s(s(s(z))), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3403, 126, 645, 550, 61, 535, 125, 226, 585, 4, 176])).
% 1.74/2.01 tff(3405,plain,
% 1.74/2.01 (r(s(s(s(z))), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[421, 3404])).
% 1.74/2.01 tff(3406,plain,
% 1.74/2.01 (~r(s(s(s(z))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2693, 155, 226, 645, 3405])).
% 1.74/2.01 tff(3407,plain,
% 1.74/2.01 (b(s(s(s(z))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[402, 3406])).
% 1.74/2.01 tff(3408,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $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(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(3409,plain,
% 1.74/2.01 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(3410,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $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(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[3409])).
% 1.74/2.01 tff(3411,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $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(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[3410, 3408])).
% 1.74/2.01 tff(3412,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $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(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(3413,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[3412, 3411])).
% 1.74/2.01 tff(3414,plain,
% 1.74/2.01 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3413, 97, 61, 126, 3407])).
% 1.74/2.01 tff(3415,plain,
% 1.74/2.01 (((~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(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(3416,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[3415])).
% 1.74/2.01 tff(3417,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.74/2.01 inference(transitivity,[status(thm)],[3416, 3378])).
% 1.74/2.01 tff(3418,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $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))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(3419,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[3418, 3417])).
% 1.74/2.01 tff(3420,plain,
% 1.74/2.01 (~b(s(s(s(z))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3419, 97, 550, 61, 3407])).
% 1.74/2.01 tff(3421,plain,
% 1.74/2.01 (r(s(s(s(z))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1358, 3420])).
% 1.74/2.01 tff(3422,plain,
% 1.74/2.01 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3015, 155, 125, 3009, 3421])).
% 1.74/2.01 tff(3423,plain,
% 1.74/2.01 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3089, 3422, 3414])).
% 1.74/2.01 tff(3424,plain,
% 1.74/2.01 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[3423])).
% 1.74/2.01 tff(3425,plain,
% 1.74/2.01 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 1.74/2.01 inference(symmetry,[status(thm)],[3424])).
% 1.74/2.01 tff(3426,plain,
% 1.74/2.01 (b(s(s(s(z))), s(s(z)))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[59, 3425])).
% 1.74/2.01 tff(3427,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3404, 3426])).
% 1.74/2.01 tff(3428,plain,((~b(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(z)))) | r(z, s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(z))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(3429,plain,
% 1.74/2.01 (~b(s(s(s(elem!1))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3428, 61, 494, 550, 226, 645, 535, 585, 4, 176])).
% 1.74/2.01 tff(3430,plain,
% 1.74/2.01 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.74/2.01 inference(monotonicity,[status(thm)],[340])).
% 1.74/2.01 tff(3431,plain,
% 1.74/2.01 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(elem!1))), z)),
% 1.74/2.01 inference(symmetry,[status(thm)],[3430])).
% 1.74/2.01 tff(3432,plain,
% 1.74/2.01 (b(s(s(s(elem!1))), z)),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[876, 3431])).
% 1.74/2.01 tff(3433,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[239, 3432])).
% 1.74/2.01 tff(3434,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), z) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(3435,plain,
% 1.74/2.01 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3434, 876, 239])).
% 1.74/2.01 tff(3436,plain,
% 1.74/2.01 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[523, 3435])).
% 1.74/2.01 tff(3437,plain,
% 1.74/2.01 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2715, 876, 550, 61])).
% 1.74/2.01 tff(3438,plain,
% 1.74/2.01 (r(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[511, 3437])).
% 1.74/2.01 tff(3439,plain,
% 1.74/2.01 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1136, 3438, 125, 225])).
% 1.74/2.01 tff(3440,plain,
% 1.74/2.01 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[821, 3439, 3436])).
% 1.74/2.01 tff(3441,plain,
% 1.74/2.01 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3055, 876, 550, 61])).
% 1.74/2.01 tff(3442,plain,
% 1.74/2.01 (r(s(z), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[280, 3441])).
% 1.74/2.01 tff(3443,plain,
% 1.74/2.01 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[503, 3442, 125, 3438])).
% 1.74/2.01 tff(3444,plain,
% 1.74/2.01 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[486, 3443, 3435])).
% 1.74/2.01 tff(3445,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(3446,plain,
% 1.74/2.01 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(3447,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[3446])).
% 1.74/2.01 tff(3448,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/2.01 inference(transitivity,[status(thm)],[3447, 3445])).
% 1.74/2.01 tff(3449,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(3450,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[3449, 3448])).
% 1.74/2.01 tff(3451,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3450, 97, 124, 3444, 3440, 876])).
% 1.74/2.01 tff(3452,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(3453,plain,
% 1.74/2.01 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3452, 61, 494, 3009, 550, 3008, 3429])).
% 1.74/2.01 tff(3454,plain,
% 1.74/2.01 (r(s(s(s(s(elem!1)))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[842, 3453])).
% 1.74/2.01 tff(3455,plain,
% 1.74/2.01 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2903, 155, 226, 3454, 645])).
% 1.74/2.01 tff(3456,plain,
% 1.74/2.01 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[452, 3455])).
% 1.74/2.01 tff(3457,plain,
% 1.74/2.01 (r(s(s(s(elem!1))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[246, 3429])).
% 1.74/2.01 tff(3458,plain,
% 1.74/2.01 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2723, 2718, 824, 288, 535, 61, 82])).
% 1.74/2.01 tff(3459,plain,
% 1.74/2.01 (r(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[511, 3458])).
% 1.74/2.01 tff(3460,plain,
% 1.74/2.01 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2903, 155, 226, 824, 645])).
% 1.74/2.01 tff(3461,plain,
% 1.74/2.01 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[452, 3460])).
% 1.74/2.01 tff(3462,plain,
% 1.74/2.01 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1872, 463, 288, 824])).
% 1.74/2.01 tff(3463,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[486, 3462, 3022, 2718])).
% 1.74/2.01 tff(3464,plain,((~r(z, s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(3465,plain,
% 1.74/2.01 (~r(z, s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3464, 2718, 288, 824, 585])).
% 1.74/2.01 tff(3466,plain,
% 1.74/2.01 (b(z, s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1093, 3465])).
% 1.74/2.01 tff(3467,plain,
% 1.74/2.01 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1494, 3466, 61, 3461])).
% 1.74/2.01 tff(3468,plain,
% 1.74/2.01 (r(s(z), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[280, 3467])).
% 1.74/2.01 tff(3469,plain,
% 1.74/2.01 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[503, 3468, 494, 3459])).
% 1.74/2.01 tff(3470,plain,
% 1.74/2.01 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[486, 3469, 2718])).
% 1.74/2.01 tff(3471,plain,
% 1.74/2.01 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[349, 3470])).
% 1.74/2.01 tff(3472,plain,
% 1.74/2.01 (s(s(s(s(elem!1)))) = elem!1),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1734, 3471])).
% 1.74/2.01 tff(3473,plain,
% 1.74/2.01 (elem!1 = s(s(s(s(elem!1))))),
% 1.74/2.01 inference(symmetry,[status(thm)],[3472])).
% 1.74/2.01 tff(3474,plain,
% 1.74/2.01 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[3473])).
% 1.74/2.01 tff(3475,plain,
% 1.74/2.01 (~(s(s(s(z))) = elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1742, 3470])).
% 1.74/2.01 tff(3476,plain,
% 1.74/2.01 (~b(s(s(s(z))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3419, 97, 550, 61, 1216])).
% 1.74/2.01 tff(3477,plain,
% 1.74/2.01 (r(s(s(s(z))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1358, 3476])).
% 1.74/2.01 tff(3478,plain,
% 1.74/2.01 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2225, 1216, 2208, 372, 441, 1757])).
% 1.74/2.01 tff(3479,plain,
% 1.74/2.01 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1494, 372, 61, 441])).
% 1.74/2.01 tff(3480,plain,
% 1.74/2.01 (r(s(z), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[280, 3479])).
% 1.74/2.01 tff(3481,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(3482,plain,
% 1.74/2.01 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(3483,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[3482])).
% 1.74/2.01 tff(3484,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[3483, 3481])).
% 1.74/2.01 tff(3485,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(3486,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[3485, 3484])).
% 1.74/2.01 tff(3487,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3486, 155, 3480, 3478, 495, 3477])).
% 1.74/2.01 tff(3488,plain,((~b(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (s(s(s(z))) = elem!1) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(3489,plain,
% 1.74/2.01 (~b(s(s(s(z))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3488, 3459, 550, 61, 3475, 3466, 3461, 3472])).
% 1.74/2.01 tff(3490,plain,
% 1.74/2.01 (r(s(s(s(z))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[402, 3489])).
% 1.74/2.01 tff(3491,plain,
% 1.74/2.01 (~r(s(s(s(z))), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2625, 155, 226, 645, 3490])).
% 1.74/2.01 tff(3492,plain,
% 1.74/2.01 (b(s(s(s(z))), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[421, 3491])).
% 1.74/2.01 tff(3493,plain,
% 1.74/2.01 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3177, 97, 441, 87, 1331])).
% 1.74/2.01 tff(3494,plain,
% 1.74/2.01 (~b(s(s(s(z))), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1764, 3493, 1757])).
% 1.74/2.01 tff(3495,plain,
% 1.74/2.01 (r(s(s(s(z))), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1755, 3494, 2208])).
% 1.74/2.01 tff(3496,plain,
% 1.74/2.01 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[3495, 2211])).
% 1.74/2.01 tff(3497,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(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(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(3498,plain,
% 1.74/2.01 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), 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(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(3499,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(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(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[3498])).
% 1.74/2.01 tff(3500,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(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(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[3499, 3497])).
% 1.74/2.02 tff(3501,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(3502,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[3501, 3500])).
% 1.74/2.02 tff(3503,plain,
% 1.74/2.02 (~b(s(s(s(z))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3502, 97, 87, 535, 1331])).
% 1.74/2.02 tff(3504,plain,
% 1.74/2.02 (r(s(s(s(z))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1358, 3503])).
% 1.74/2.02 tff(3505,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(3506,plain,
% 1.74/2.02 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(3507,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[3506])).
% 1.74/2.02 tff(3508,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[3507, 3505])).
% 1.74/2.02 tff(3509,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(3510,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[3509, 3508])).
% 1.74/2.02 tff(3511,plain,
% 1.74/2.02 ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3510, 155, 287, 824, 386])).
% 1.74/2.02 tff(3512,plain,
% 1.74/2.02 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3511, 3504])).
% 1.74/2.02 tff(3513,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3512, 3496])).
% 1.74/2.02 tff(3514,plain,((~b(s(s(z)), s(z))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (s(s(s(z))) = elem!1) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(3515,plain,
% 1.74/2.02 (~b(s(s(z)), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3514, 3472, 3468, 824, 3490, 3475, 535, 3492, 3461])).
% 1.74/2.02 tff(3516,plain,
% 1.74/2.02 (r(s(s(z)), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[122, 3515])).
% 1.74/2.02 tff(3517,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(3518,plain,
% 1.74/2.02 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(3519,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[3518])).
% 1.74/2.02 tff(3520,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.74/2.02 inference(transitivity,[status(thm)],[3519, 3517])).
% 1.74/2.02 tff(3521,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(3522,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[3521, 3520])).
% 1.74/2.02 tff(3523,plain,
% 1.74/2.02 ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3522, 155, 3468, 824, 645])).
% 1.74/2.02 tff(3524,plain,
% 1.74/2.02 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3523, 3516])).
% 1.74/2.02 tff(3525,plain,
% 1.74/2.02 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[336, 3524])).
% 1.74/2.02 tff(3526,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(3527,plain,
% 1.74/2.02 (((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(3528,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[3527])).
% 1.74/2.02 tff(3529,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[3528, 3526])).
% 1.74/2.02 tff(3530,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(3531,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[3530, 3529])).
% 1.74/2.02 tff(3532,plain,
% 1.74/2.02 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3531, 97, 3525, 3461, 3492])).
% 1.74/2.02 tff(3533,plain,
% 1.74/2.02 (~b(s(s(s(z))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1764, 3532, 3472])).
% 1.74/2.02 tff(3534,plain,
% 1.74/2.02 (r(s(s(s(z))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1755, 3533, 3475])).
% 1.74/2.02 tff(3535,plain,
% 1.74/2.02 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[3534, 3474])).
% 1.74/2.02 tff(3536,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(3537,plain,
% 1.74/2.02 (((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(3538,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[3537])).
% 1.74/2.02 tff(3539,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[3538, 3536])).
% 1.74/2.02 tff(3540,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(3541,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[3540, 3539])).
% 1.74/2.02 tff(3542,plain,
% 1.74/2.02 (~b(s(s(s(z))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3541, 97, 3525, 535, 3492])).
% 1.74/2.02 tff(3543,plain,
% 1.74/2.02 (r(s(s(s(z))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1358, 3542])).
% 1.74/2.02 tff(3544,plain,
% 1.74/2.02 ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3510, 155, 3468, 824, 3490])).
% 1.74/2.02 tff(3545,plain,
% 1.74/2.02 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3544, 3543])).
% 1.74/2.02 tff(3546,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3545, 3535])).
% 1.74/2.02 tff(3547,plain,(b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), z)) | r(z, s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(3548,plain,
% 1.74/2.02 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3547, 3454, 535, 645, 226, 550, 61, 3457, 585, 82])).
% 1.74/2.02 tff(3549,plain,
% 1.74/2.02 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3313, 3548, 59, 3456])).
% 1.74/2.02 tff(3550,plain,
% 1.74/2.02 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[336, 3549])).
% 1.74/2.02 tff(3551,plain,
% 1.74/2.02 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1190, 3548, 3008, 3456])).
% 1.74/2.02 tff(3552,plain,
% 1.74/2.02 (r(z, s(s(s(s(elem!1)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1093, 3551])).
% 1.74/2.02 tff(3553,plain,
% 1.74/2.02 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(3554,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[3553])).
% 1.74/2.02 tff(3555,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.74/2.02 inference(transitivity,[status(thm)],[3554, 3123])).
% 1.74/2.02 tff(3556,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(3557,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[3556, 3555])).
% 1.74/2.02 tff(3558,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3557, 155, 3552, 3550, 3454, 645])).
% 1.74/2.02 tff(3559,plain,((~b(z, s(z))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~b(s(z), z)) | r(z, s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(s(z))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(3560,plain,
% 1.74/2.02 (~b(z, s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3559, 176, 535, 226, 550, 585, 82, 4, 645])).
% 1.74/2.02 tff(3561,plain,
% 1.74/2.02 (r(z, s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[723, 3560])).
% 1.74/2.02 tff(3562,plain,
% 1.74/2.02 (~r(s(s(s(z))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2693, 155, 226, 645, 2591])).
% 1.74/2.02 tff(3563,plain,
% 1.74/2.02 (b(s(s(s(z))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[402, 3562])).
% 1.74/2.02 tff(3564,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(3565,plain,
% 1.74/2.02 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(3566,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[3565])).
% 1.74/2.02 tff(3567,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.87/2.03 inference(transitivity,[status(thm)],[3566, 3564])).
% 1.87/2.03 tff(3568,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(3569,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[3568, 3567])).
% 1.87/2.03 tff(3570,plain,
% 1.87/2.03 (~b(s(s(s(z))), s(z))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[3569, 97, 550, 124, 3563])).
% 1.87/2.03 tff(3571,plain,
% 1.87/2.03 (r(s(s(s(z))), s(z))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1358, 3570])).
% 1.87/2.03 tff(3572,plain,
% 1.87/2.03 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[3015, 155, 125, 225, 3571])).
% 1.87/2.03 tff(3573,plain,
% 1.87/2.03 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[2677, 2590, 60])).
% 1.87/2.03 tff(3574,plain,
% 1.87/2.03 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[3089, 3573, 3572])).
% 1.87/2.03 tff(3575,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(3576,plain,
% 1.87/2.03 (((~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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(3577,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[3576])).
% 1.87/2.03 tff(3578,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[3577, 3575])).
% 1.87/2.03 tff(3579,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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)))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(3580,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[3579, 3578])).
% 1.87/2.03 tff(3581,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[3580, 97, 124, 60, 3563, 3574])).
% 1.87/2.03 tff(3582,plain,(b(s(s(s(z))), s(s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(3583,plain,
% 1.87/2.03 (b(s(s(s(z))), s(s(z)))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[3582, 3009, 59, 494, 3008, 550, 226, 645])).
% 1.87/2.03 tff(3584,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[3401, 97, 535, 1361, 1360, 1331])).
% 1.87/2.03 tff(3585,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(3586,plain,
% 1.87/2.03 (~b(s(s(z)), s(s(s(z))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[3585, 1360, 535, 1331])).
% 1.87/2.03 tff(3587,plain,
% 1.87/2.03 (r(s(s(z)), s(s(s(z))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[437, 3586])).
% 1.87/2.03 tff(3588,plain,
% 1.87/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(3589,plain,
% 1.87/2.03 (((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(3590,plain,
% 1.87/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[3589])).
% 1.87/2.03 tff(3591,plain,
% 1.87/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[3590, 3588])).
% 1.87/2.03 tff(3592,plain,
% 1.87/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(3593,plain,
% 1.87/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[3592, 3591])).
% 1.87/2.03 tff(3594,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[3593, 155, 729, 645, 2, 1961, 386])).
% 1.87/2.03 tff(3595,plain,((~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(3596,plain,
% 1.87/2.03 (~r(s(s(s(z))), z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[3595, 2, 645, 729, 1961])).
% 1.87/2.03 tff(3597,plain,
% 1.87/2.03 (b(s(s(s(z))), z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[402, 3596])).
% 1.87/2.03 tff(3598,plain,
% 1.87/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(3599,plain,
% 1.87/2.03 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(3600,plain,
% 1.87/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[3599])).
% 1.87/2.03 tff(3601,plain,
% 1.87/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[3600, 3598])).
% 1.87/2.03 tff(3602,plain,
% 1.87/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(3603,plain,
% 1.87/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[3602, 3601])).
% 1.87/2.03 tff(3604,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[3603, 155, 729, 645, 2, 338, 1961])).
% 1.87/2.03 tff(3605,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(3606,plain,
% 1.87/2.03 (~r(s(z), s(s(s(z))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[3605, 2, 729, 645, 1961])).
% 1.87/2.03 tff(3607,plain,
% 1.87/2.03 (b(s(z), s(s(s(z))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[253, 3606])).
% 1.87/2.03 tff(3608,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(3609,plain,
% 1.87/2.03 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(3610,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[3609])).
% 1.87/2.03 tff(3611,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.87/2.03 inference(transitivity,[status(thm)],[3610, 3608])).
% 1.87/2.03 tff(3612,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(3613,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[3612, 3611])).
% 1.87/2.03 tff(3614,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[3613, 97, 550, 124, 3607, 3597])).
% 1.87/2.03 tff(3615,plain,((~r(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(3616,plain,
% 1.87/2.03 (~r(s(s(z)), s(z))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[3615, 3587, 124, 729, 645, 550])).
% 1.87/2.03 tff(3617,plain,
% 1.87/2.03 (b(s(s(z)), s(z))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[122, 3616])).
% 1.87/2.03 tff(3618,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(3619,plain,
% 1.87/2.03 (((~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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(3620,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[3619])).
% 1.87/2.03 tff(3621,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[3620, 3618])).
% 1.87/2.03 tff(3622,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $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)))))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(3623,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[3622, 3621])).
% 1.87/2.03 tff(3624,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[3623, 97, 550, 3617, 1360, 1331])).
% 1.87/2.03 tff(3625,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(3626,plain,
% 1.87/2.03 (~b(s(s(s(z))), s(z))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[3625, 3583, 550, 3008, 3561, 645, 535])).
% 1.87/2.03 tff(3627,plain,
% 1.87/2.03 (r(s(s(s(z))), s(z))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1358, 3626])).
% 1.87/2.03 tff(3628,plain,
% 1.87/2.03 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[3015, 155, 494, 3009, 3627])).
% 1.87/2.03 tff(3629,plain,
% 1.87/2.03 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[3169, 1170, 4])).
% 1.87/2.03 tff(3630,plain,
% 1.87/2.03 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[486, 3629, 2718])).
% 1.87/2.03 tff(3631,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(3632,plain,
% 1.87/2.03 (((~b(z, s(s(s(elem!1))))) | (~b(z, 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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(3633,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[3632])).
% 1.87/2.03 tff(3634,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[3633, 3631])).
% 1.87/2.03 tff(3635,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(3636,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[3635, 3634])).
% 1.87/2.04 tff(3637,plain,
% 1.87/2.04 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3636, 97, 550, 124, 876])).
% 1.87/2.04 tff(3638,plain,
% 1.87/2.04 (r(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[511, 3637])).
% 1.87/2.04 tff(3639,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(3640,plain,
% 1.87/2.04 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(3641,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[3640])).
% 1.87/2.04 tff(3642,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.87/2.04 inference(transitivity,[status(thm)],[3641, 3639])).
% 1.87/2.04 tff(3643,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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)))))))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(3644,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[3643, 3642])).
% 1.87/2.04 tff(3645,plain,
% 1.87/2.04 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3644, 97, 550, 124, 876])).
% 1.87/2.04 tff(3646,plain,
% 1.87/2.04 (r(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[280, 3645])).
% 1.87/2.04 tff(3647,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[503, 3646, 3638, 125, 488])).
% 1.87/2.04 tff(3648,plain,((~b(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(3649,plain,
% 1.87/2.04 (~b(s(s(s(s(elem!1)))), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3648, 3630, 125, 550, 124])).
% 1.87/2.04 tff(3650,plain,
% 1.87/2.04 (r(s(s(s(s(elem!1)))), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[842, 3649])).
% 1.87/2.04 tff(3651,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[2903, 155, 226, 3650, 645, 1170])).
% 1.87/2.04 tff(3652,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(3653,plain,
% 1.87/2.04 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3652, 2718, 645, 494, 550, 3008, 226, 4])).
% 1.87/2.04 tff(3654,plain,
% 1.87/2.04 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[452, 3653])).
% 1.87/2.04 tff(3655,plain,
% 1.87/2.04 (b(s(s(s(z))), s(s(z)))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3582, 3009, 60, 494, 3008, 550, 226, 645])).
% 1.87/2.04 tff(3656,plain,
% 1.87/2.04 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[486, 472, 2718])).
% 1.87/2.04 tff(3657,plain,
% 1.87/2.04 (~b(s(s(z)), s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3067, 255, 535, 441])).
% 1.87/2.04 tff(3658,plain,
% 1.87/2.04 (r(s(s(z)), s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[437, 3657])).
% 1.87/2.04 tff(3659,plain,
% 1.87/2.04 (~r(s(s(z)), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3615, 3658, 124, 729, 645, 550])).
% 1.87/2.04 tff(3660,plain,
% 1.87/2.04 (b(s(s(z)), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[122, 3659])).
% 1.87/2.04 tff(3661,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3341, 97, 60, 87, 1331, 1702])).
% 1.87/2.04 tff(3662,plain,((~b(s(s(z)), 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)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(3663,plain,
% 1.87/2.04 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3662, 3660, 1331, 60])).
% 1.87/2.04 tff(3664,plain,
% 1.87/2.04 (~b(s(s(s(z))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3502, 97, 3660, 535, 1331])).
% 1.87/2.04 tff(3665,plain,
% 1.87/2.04 (r(s(s(s(z))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1358, 3664])).
% 1.87/2.04 tff(3666,plain,
% 1.87/2.04 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3015, 155, 125, 225, 3665])).
% 1.87/2.04 tff(3667,plain,
% 1.87/2.04 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3089, 3666, 3663])).
% 1.87/2.04 tff(3668,plain,
% 1.87/2.04 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[3667])).
% 1.87/2.04 tff(3669,plain,
% 1.87/2.04 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.87/2.04 inference(symmetry,[status(thm)],[3668])).
% 1.87/2.04 tff(3670,plain,
% 1.87/2.04 (s(s(elem!1)) = s(s(z))),
% 1.87/2.04 inference(transitivity,[status(thm)],[167, 3669, 72])).
% 1.87/2.04 tff(3671,plain,
% 1.87/2.04 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[3670])).
% 1.87/2.04 tff(3672,plain,
% 1.87/2.04 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.87/2.04 inference(symmetry,[status(thm)],[3671])).
% 1.87/2.04 tff(3673,plain,
% 1.87/2.04 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[3667])).
% 1.87/2.04 tff(3674,plain,
% 1.87/2.04 (r(s(s(z)), s(s(s(elem!1))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[3658, 3673])).
% 1.87/2.04 tff(3675,plain,
% 1.87/2.04 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[3674, 3672])).
% 1.87/2.04 tff(3676,plain,
% 1.87/2.04 (s(s(z)) = s(s(elem!1))),
% 1.87/2.04 inference(transitivity,[status(thm)],[73, 3668, 19])).
% 1.87/2.04 tff(3677,plain,
% 1.87/2.04 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[3676])).
% 1.87/2.04 tff(3678,plain,
% 1.87/2.04 (s(z) = s(elem!1)),
% 1.87/2.04 inference(transitivity,[status(thm)],[24, 3677, 29])).
% 1.87/2.04 tff(3679,plain,
% 1.87/2.04 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[3678])).
% 1.87/2.04 tff(3680,plain,
% 1.87/2.04 (z = elem!1),
% 1.87/2.04 inference(transitivity,[status(thm)],[1443, 3679, 85])).
% 1.87/2.04 tff(3681,plain,
% 1.87/2.04 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.87/2.04 inference(monotonicity,[status(thm)],[3680])).
% 1.87/2.04 tff(3682,plain,
% 1.87/2.04 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 1.87/2.04 inference(monotonicity,[status(thm)],[3676])).
% 1.87/2.04 tff(3683,plain,
% 1.87/2.04 (r(s(s(elem!1)), z)),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[645, 3682])).
% 1.87/2.04 tff(3684,plain,
% 1.87/2.04 (r(s(s(elem!1)), elem!1)),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[3683, 3681])).
% 1.87/2.04 tff(3685,plain,
% 1.87/2.04 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3107, 3667, 824])).
% 1.87/2.04 tff(3686,plain,
% 1.87/2.04 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[3676])).
% 1.87/2.04 tff(3687,plain,
% 1.87/2.04 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3267, 255, 535, 441])).
% 1.87/2.04 tff(3688,plain,
% 1.87/2.04 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[336, 3687])).
% 1.87/2.04 tff(3689,plain,
% 1.87/2.04 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[3688, 3686])).
% 1.87/2.04 tff(3690,plain,
% 1.87/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), 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)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), 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)), s(s(s(elem!1))))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(3691,plain,
% 1.87/2.04 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(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)), s(s(s(elem!1))))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(3692,plain,
% 1.87/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), 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)), s(s(s(elem!1)))))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[3691])).
% 1.87/2.04 tff(3693,plain,
% 1.87/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), 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)), s(s(s(elem!1))))))),
% 1.87/2.04 inference(transitivity,[status(thm)],[3692, 3690])).
% 1.87/2.04 tff(3694,plain,
% 1.87/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(3695,plain,
% 1.87/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[3694, 3693])).
% 1.87/2.04 tff(3696,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3695, 155, 3689, 488, 3685, 3684, 3675])).
% 1.87/2.04 tff(3697,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(3698,plain,
% 1.87/2.04 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3697, 3656, 645, 824, 125, 225, 535, 1331, 60, 124, 729, 550, 441])).
% 1.87/2.04 tff(3699,plain,
% 1.87/2.04 (r(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[280, 3698])).
% 1.87/2.04 tff(3700,plain,
% 1.87/2.04 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[503, 3699, 125, 3656])).
% 1.87/2.04 tff(3701,plain,
% 1.87/2.04 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[523, 472])).
% 1.87/2.04 tff(3702,plain,
% 1.87/2.04 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[987, 3699, 125, 729, 124, 372, 3656, 3701])).
% 1.87/2.04 tff(3703,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[511, 3702, 3700])).
% 1.87/2.04 tff(3704,plain,((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(3705,plain,
% 1.87/2.04 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3704, 372, 729, 124, 494, 645, 824, 3009, 535, 1331, 60, 550, 441, 2718])).
% 1.87/2.04 tff(3706,plain,
% 1.87/2.04 (~(s(s(s(z))) = elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1742, 3705])).
% 1.87/2.04 tff(3707,plain,
% 1.87/2.04 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[349, 3705])).
% 1.87/2.04 tff(3708,plain,
% 1.87/2.04 (s(s(s(s(elem!1)))) = elem!1),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1734, 3707])).
% 1.87/2.04 tff(3709,plain,
% 1.87/2.04 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[518, 3705, 82])).
% 1.87/2.04 tff(3710,plain,
% 1.87/2.04 (r(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[511, 3709])).
% 1.87/2.04 tff(3711,plain,
% 1.87/2.04 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3154, 3705, 176])).
% 1.87/2.04 tff(3712,plain,
% 1.87/2.04 (r(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[280, 3711])).
% 1.87/2.04 tff(3713,plain,
% 1.87/2.04 (~b(s(s(s(z))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3541, 97, 339, 535, 1331])).
% 1.87/2.04 tff(3714,plain,
% 1.87/2.04 (r(s(s(s(z))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1358, 3713])).
% 1.87/2.04 tff(3715,plain,
% 1.87/2.04 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3531, 97, 339, 441, 1331])).
% 1.87/2.04 tff(3716,plain,
% 1.87/2.04 (~b(s(s(s(z))), elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1764, 3715, 1757])).
% 1.87/2.04 tff(3717,plain,
% 1.87/2.04 (r(s(s(s(z))), elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1755, 3716, 2208])).
% 1.87/2.04 tff(3718,plain,
% 1.87/2.04 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[3717, 2211])).
% 1.87/2.04 tff(3719,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3486, 155, 287, 3718, 495, 3714])).
% 1.87/2.04 tff(3720,plain,((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(s(s(z))) = elem!1) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(3721,plain,
% 1.87/2.04 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3720, 3712, 3710, 3708, 3706, 535, 1331, 441])).
% 1.87/2.04 tff(3722,plain,
% 1.87/2.04 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[336, 3721])).
% 1.87/2.04 tff(3723,plain,
% 1.87/2.04 ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3522, 155, 3712, 824, 645])).
% 1.87/2.04 tff(3724,plain,
% 1.87/2.04 (~r(s(s(z)), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3723, 3722])).
% 1.87/2.04 tff(3725,plain,
% 1.87/2.04 (b(s(s(z)), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[122, 3724])).
% 1.87/2.04 tff(3726,plain,
% 1.87/2.04 (~b(s(s(s(z))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3502, 97, 3725, 535, 1331])).
% 1.87/2.04 tff(3727,plain,
% 1.87/2.04 (r(s(s(s(z))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1358, 3726])).
% 1.87/2.04 tff(3728,plain,
% 1.87/2.04 (~r(s(s(s(z))), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3514, 3725, 3712, 824, 3708, 3706, 535, 1331, 441])).
% 1.87/2.04 tff(3729,plain,
% 1.87/2.04 (b(s(s(s(z))), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[402, 3728])).
% 1.87/2.04 tff(3730,plain,
% 1.87/2.04 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[2225, 3729, 3706, 372, 441, 3708])).
% 1.87/2.04 tff(3731,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3486, 155, 3712, 3730, 3710, 3727])).
% 1.87/2.04 tff(3732,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | b(s(z), s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(z)) | (~r(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), z)) | b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(3733,plain,
% 1.87/2.04 (~b(z, s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3732, 824, 3655, 441, 535, 645, 176, 82, 729, 3008, 60, 550, 2718])).
% 1.87/2.04 tff(3734,plain,
% 1.87/2.04 (r(z, s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1093, 3733])).
% 1.87/2.04 tff(3735,plain,
% 1.87/2.04 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3021, 3734, 585])).
% 1.87/2.04 tff(3736,plain,
% 1.87/2.04 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[486, 3735, 2718])).
% 1.87/2.04 tff(3737,plain,
% 1.87/2.04 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3697, 3736, 645, 824, 494, 3009, 535, 3655, 60, 3008, 729, 550, 441])).
% 1.87/2.04 tff(3738,plain,
% 1.87/2.04 (r(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[280, 3737])).
% 1.87/2.04 tff(3739,plain,
% 1.87/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(3740,plain,
% 1.87/2.04 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(3741,plain,
% 1.87/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[3740])).
% 1.87/2.04 tff(3742,plain,
% 1.87/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 1.87/2.04 inference(transitivity,[status(thm)],[3741, 3739])).
% 1.87/2.04 tff(3743,plain,
% 1.87/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(3744,plain,
% 1.87/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[3743, 3742])).
% 1.87/2.04 tff(3745,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3744, 155, 729, 287, 463, 226, 2])).
% 1.87/2.04 tff(3746,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(3747,plain,
% 1.87/2.04 (~r(s(s(z)), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3746, 3738, 226, 729, 3734])).
% 1.87/2.04 tff(3748,plain,
% 1.87/2.04 (b(s(s(z)), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[122, 3747])).
% 1.87/2.04 tff(3749,plain,
% 1.87/2.04 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[523, 3735])).
% 1.87/2.04 tff(3750,plain,
% 1.87/2.04 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[924, 3738, 3009, 3736])).
% 1.87/2.04 tff(3751,plain,
% 1.87/2.04 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[821, 3750, 3749])).
% 1.87/2.04 tff(3752,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(3753,plain,
% 1.87/2.04 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(3754,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[3753])).
% 1.87/2.04 tff(3755,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.87/2.04 inference(transitivity,[status(thm)],[3754, 3752])).
% 1.87/2.04 tff(3756,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(3757,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[3756, 3755])).
% 1.87/2.04 tff(3758,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3757, 97, 3751, 60, 441, 3748])).
% 1.87/2.04 tff(3759,plain,((~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(z, s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(3760,plain,
% 1.87/2.04 (~r(s(s(s(s(elem!1)))), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3759, 3654, 59, 226, 3561, 645, 535, 550, 2718, 585, 176, 82])).
% 1.87/2.04 tff(3761,plain,
% 1.87/2.04 (b(s(s(s(s(elem!1)))), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[842, 3760])).
% 1.87/2.04 tff(3762,plain,
% 1.87/2.04 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3648, 3761, 494, 550, 3008])).
% 1.87/2.04 tff(3763,plain,
% 1.87/2.04 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[486, 3762, 2718])).
% 1.87/2.04 tff(3764,plain,
% 1.87/2.04 (~(s(s(s(z))) = elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1742, 3763])).
% 1.87/2.04 tff(3765,plain,
% 1.87/2.04 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[349, 3763])).
% 1.87/2.04 tff(3766,plain,
% 1.87/2.04 (s(s(s(s(elem!1)))) = elem!1),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1734, 3765])).
% 1.87/2.04 tff(3767,plain,
% 1.87/2.04 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3154, 3763, 176])).
% 1.87/2.04 tff(3768,plain,
% 1.87/2.04 (r(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[280, 3767])).
% 1.87/2.04 tff(3769,plain,
% 1.87/2.04 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[518, 3763, 82])).
% 1.87/2.04 tff(3770,plain,
% 1.87/2.04 (r(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[511, 3769])).
% 1.87/2.04 tff(3771,plain,
% 1.87/2.04 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3720, 3770, 3768, 3766, 3764, 535, 3583, 3654])).
% 1.87/2.04 tff(3772,plain,
% 1.87/2.04 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[336, 3771])).
% 1.87/2.04 tff(3773,plain,
% 1.87/2.04 (~r(s(s(z)), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[761, 155, 3561, 3768, 3772, 645])).
% 1.87/2.04 tff(3774,plain,
% 1.87/2.04 (b(s(s(z)), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[122, 3773])).
% 1.87/2.04 tff(3775,plain,
% 1.87/2.04 (~b(s(s(s(z))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3502, 97, 3774, 535, 3583])).
% 1.87/2.04 tff(3776,plain,
% 1.87/2.04 (r(s(s(s(z))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1358, 3775])).
% 1.87/2.04 tff(3777,plain,
% 1.87/2.04 (elem!1 = s(s(s(s(elem!1))))),
% 1.87/2.04 inference(symmetry,[status(thm)],[3766])).
% 1.87/2.04 tff(3778,plain,
% 1.87/2.04 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[3777])).
% 1.87/2.04 tff(3779,plain,
% 1.87/2.04 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[3177, 97, 3654, 3774, 3583])).
% 1.87/2.04 tff(3780,plain,
% 1.87/2.04 (~b(s(s(s(z))), elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1764, 3779, 3766])).
% 1.87/2.04 tff(3781,plain,
% 1.87/2.04 (r(s(s(s(z))), elem!1)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1755, 3780, 3764])).
% 1.87/2.04 tff(3782,plain,
% 1.87/2.04 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[3781, 3778])).
% 1.87/2.04 tff(3783,plain,
% 1.87/2.04 ($false),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3486, 155, 3768, 3782, 3770, 3776])).
% 1.87/2.05 tff(3784,plain,(b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), z)) | b(s(z), s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(z)) | (~b(s(z), z)) | (~r(z, s(s(z)))) | r(z, s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.05 tff(3785,plain,
% 1.87/2.05 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3784, 176, 645, 535, 82, 550, 226, 585, 4])).
% 1.87/2.05 tff(3786,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(3787,plain,
% 1.87/2.05 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(3788,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[3787])).
% 1.87/2.05 tff(3789,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.87/2.05 inference(transitivity,[status(thm)],[3788, 3786])).
% 1.87/2.05 tff(3790,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(3791,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[3790, 3789])).
% 1.87/2.05 tff(3792,plain,
% 1.87/2.05 ($false),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3791, 97, 124, 372, 473, 876])).
% 1.87/2.05 tff(3793,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.05 tff(3794,plain,
% 1.87/2.05 (~b(z, s(s(s(s(elem!1)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3793, 876, 124, 473])).
% 1.87/2.05 tff(3795,plain,
% 1.87/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(3796,plain,
% 1.87/2.05 (((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(3797,plain,
% 1.87/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[3796])).
% 1.87/2.05 tff(3798,plain,
% 1.87/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[3797, 3795])).
% 1.87/2.05 tff(3799,plain,
% 1.87/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(3800,plain,
% 1.87/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[3799, 3798])).
% 1.87/2.05 tff(3801,plain,
% 1.87/2.05 ($false),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3800, 155, 729, 287, 463, 226, 1170])).
% 1.87/2.05 tff(3802,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.05 tff(3803,plain,
% 1.87/2.05 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3802, 463, 226, 729, 1170])).
% 1.87/2.05 tff(3804,plain,
% 1.87/2.05 (b(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[280, 3803])).
% 1.87/2.05 tff(3805,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), s(s(s(s(elem!1)))))) | (~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), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(3806,plain,
% 1.87/2.05 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(3807,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[3806])).
% 1.87/2.05 tff(3808,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[3807, 3805])).
% 1.87/2.05 tff(3809,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(3810,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[3809, 3808])).
% 1.87/2.05 tff(3811,plain,
% 1.87/2.05 ($false),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3810, 97, 255, 339, 876, 535])).
% 1.87/2.05 tff(3812,plain,((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.05 tff(3813,plain,
% 1.87/2.05 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3812, 3804, 535, 876])).
% 1.87/2.05 tff(3814,plain,
% 1.87/2.05 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[336, 3813])).
% 1.87/2.05 tff(3815,plain,
% 1.87/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(3816,plain,
% 1.87/2.05 (((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(3817,plain,
% 1.87/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[3816])).
% 1.87/2.05 tff(3818,plain,
% 1.87/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[3817, 3815])).
% 1.87/2.05 tff(3819,plain,
% 1.87/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(3820,plain,
% 1.87/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[3819, 3818])).
% 1.87/2.05 tff(3821,plain,
% 1.87/2.05 ($false),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3820, 155, 463, 3814, 226, 1170])).
% 1.87/2.05 tff(3822,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.05 tff(3823,plain,
% 1.87/2.05 (~r(z, s(s(s(s(elem!1)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3822, 876, 1170, 535, 226, 729])).
% 1.87/2.05 tff(3824,plain,
% 1.87/2.05 ($false),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[1093, 3823, 3794])).
% 1.87/2.05 tff(3825,plain,((~b(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.05 tff(3826,plain,
% 1.87/2.05 (~b(s(s(s(s(elem!1)))), z)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3825, 1170, 535, 226, 729, 124, 473])).
% 1.87/2.05 tff(3827,plain,
% 1.87/2.05 (r(s(s(s(s(elem!1)))), z)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[842, 3826])).
% 1.87/2.05 tff(3828,plain,
% 1.87/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(3829,plain,
% 1.87/2.05 (((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(3830,plain,
% 1.87/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[3829])).
% 1.87/2.05 tff(3831,plain,
% 1.87/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[3830, 3828])).
% 1.87/2.05 tff(3832,plain,
% 1.87/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(3833,plain,
% 1.87/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[3832, 3831])).
% 1.87/2.05 tff(3834,plain,
% 1.87/2.05 ($false),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3833, 155, 729, 824, 645, 1170, 495])).
% 1.87/2.05 tff(3835,plain,((~r(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.05 tff(3836,plain,
% 1.87/2.05 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[3835, 3827, 729, 645, 1170])).
% 1.87/2.05 tff(3837,plain,
% 1.87/2.05 (b(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[511, 3836])).
% 1.87/2.05 tff(3838,plain,
% 1.87/2.05 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[753, 3837, 60, 473])).
% 1.87/2.05 tff(3839,plain,
% 1.87/2.05 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[336, 3838])).
% 1.87/2.05 tff(3840,plain,
% 1.87/2.05 (~b(z, s(s(s(s(elem!1)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[701, 3837, 124, 473])).
% 1.87/2.05 tff(3841,plain,
% 1.87/2.05 (r(z, s(s(s(s(elem!1)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[1093, 3840])).
% 1.87/2.05 tff(3842,plain,
% 1.87/2.05 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[1444, 1399])).
% 1.87/2.05 tff(3843,plain,
% 1.87/2.05 (r(elem!1, s(s(elem!1)))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[226, 3842])).
% 1.87/2.05 tff(3844,plain,
% 1.87/2.05 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[1822, 1393, 1170])).
% 1.87/2.05 tff(3845,plain,
% 1.87/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(3846,plain,
% 1.87/2.05 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, 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)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(3847,plain,
% 1.87/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[3846])).
% 1.87/2.05 tff(3848,plain,
% 1.87/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[3847, 3845])).
% 1.87/2.06 tff(3849,plain,
% 1.87/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(3850,plain,
% 1.87/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[3849, 3848])).
% 1.87/2.06 tff(3851,plain,
% 1.87/2.06 ($false),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3850, 155, 3844, 3324, 3843, 3317])).
% 1.87/2.06 tff(3852,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.06 tff(3853,plain,
% 1.87/2.06 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3852, 3841, 226, 1170, 3839])).
% 1.87/2.06 tff(3854,plain,
% 1.87/2.06 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3089, 3853, 1749])).
% 1.87/2.06 tff(3855,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(3856,plain,
% 1.87/2.06 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(3857,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[3856])).
% 1.87/2.06 tff(3858,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[3857, 3855])).
% 1.87/2.06 tff(3859,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(3860,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[3859, 3858])).
% 1.87/2.06 tff(3861,plain,
% 1.87/2.06 ($false),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3860, 97, 124, 473, 1216, 1702])).
% 1.87/2.06 tff(3862,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.06 tff(3863,plain,
% 1.87/2.06 (~b(s(s(s(z))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3862, 3854, 473, 124])).
% 1.87/2.06 tff(3864,plain,
% 1.87/2.06 (r(s(s(s(z))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[402, 3863])).
% 1.87/2.06 tff(3865,plain,
% 1.87/2.06 (~r(s(s(z)), s(s(s(z))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3077, 3864, 645, 3841, 3839])).
% 1.87/2.06 tff(3866,plain,
% 1.87/2.06 (b(s(s(z)), s(s(s(z))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[437, 3865])).
% 1.87/2.06 tff(3867,plain,
% 1.87/2.06 ($false),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3373, 97, 60, 3866, 1331, 3854])).
% 1.87/2.06 tff(3868,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(z, s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.06 tff(3869,plain,
% 1.87/2.06 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3868, 3583, 59, 645, 3785, 3008, 3628, 226, 3561, 535])).
% 1.87/2.06 tff(3870,plain,
% 1.87/2.06 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[452, 3869])).
% 1.87/2.06 tff(3871,plain,
% 1.87/2.06 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3313, 3870, 59, 3785])).
% 1.87/2.06 tff(3872,plain,
% 1.87/2.06 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[336, 3871])).
% 1.87/2.06 tff(3873,plain,
% 1.87/2.06 (~b(z, s(s(s(s(elem!1)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[1190, 3870, 3008, 3785])).
% 1.87/2.06 tff(3874,plain,
% 1.87/2.06 (r(z, s(s(s(s(elem!1)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[1093, 3873])).
% 1.87/2.06 tff(3875,plain,
% 1.87/2.06 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3868, 1331, 60, 645, 473, 124, 1749, 226, 729, 535])).
% 1.87/2.06 tff(3876,plain,
% 1.87/2.06 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[452, 3875])).
% 1.87/2.06 tff(3877,plain,
% 1.87/2.06 (~b(z, s(s(s(s(elem!1)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[1190, 3876, 124, 473])).
% 1.87/2.06 tff(3878,plain,
% 1.87/2.06 (r(z, s(s(s(s(elem!1)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[1093, 3877])).
% 1.87/2.06 tff(3879,plain,
% 1.87/2.06 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3313, 3876, 60, 473])).
% 1.87/2.06 tff(3880,plain,
% 1.87/2.06 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[336, 3879])).
% 1.87/2.06 tff(3881,plain,
% 1.87/2.06 (~b(s(s(s(elem!1))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3290, 876, 124, 473])).
% 1.87/2.06 tff(3882,plain,
% 1.87/2.06 (~r(s(s(z)), s(z))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3615, 1961, 124, 729, 645, 550])).
% 1.87/2.06 tff(3883,plain,
% 1.87/2.06 (b(s(s(z)), s(z))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[122, 3882])).
% 1.87/2.06 tff(3884,plain,
% 1.87/2.06 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3662, 3883, 1331, 60])).
% 1.87/2.06 tff(3885,plain,
% 1.87/2.06 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3089, 3884, 1749])).
% 1.87/2.06 tff(3886,plain,
% 1.87/2.06 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 1.87/2.06 inference(monotonicity,[status(thm)],[3885])).
% 1.87/2.06 tff(3887,plain,
% 1.87/2.06 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 1.87/2.06 inference(symmetry,[status(thm)],[3886])).
% 1.87/2.06 tff(3888,plain,
% 1.87/2.06 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(s(s(z))), z))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[3887])).
% 1.87/2.06 tff(3889,plain,
% 1.87/2.06 (~b(s(s(s(z))), z)),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[239, 3888])).
% 1.87/2.06 tff(3890,plain,
% 1.87/2.06 (~r(s(s(s(z))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3077, 1961, 645, 463, 309])).
% 1.87/2.06 tff(3891,plain,
% 1.87/2.06 (b(s(s(s(z))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[402, 3890])).
% 1.87/2.06 tff(3892,plain,
% 1.87/2.06 ($false),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3891, 3889])).
% 1.87/2.06 tff(3893,plain,((~r(s(s(z)), s(s(s(z))))) | b(s(s(s(elem!1))), z) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.06 tff(3894,plain,
% 1.87/2.06 (~r(s(s(z)), s(s(s(z))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3893, 3881, 1749, 1331, 60, 645, 3878, 3880, 124, 729, 550])).
% 1.87/2.06 tff(3895,plain,
% 1.87/2.06 (b(s(s(z)), s(s(s(z))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[437, 3894])).
% 1.87/2.06 tff(3896,plain,
% 1.87/2.06 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3067, 3895, 535, 3876])).
% 1.87/2.06 tff(3897,plain,
% 1.87/2.06 (r(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[280, 3896])).
% 1.87/2.06 tff(3898,plain,
% 1.87/2.06 (~r(s(s(z)), s(z))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3746, 3897, 226, 729, 3878])).
% 1.87/2.06 tff(3899,plain,
% 1.87/2.06 (b(s(s(z)), s(z))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[122, 3898])).
% 1.87/2.06 tff(3900,plain,
% 1.87/2.06 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3662, 3899, 1331, 60])).
% 1.87/2.06 tff(3901,plain,
% 1.87/2.06 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3089, 3900, 1749])).
% 1.87/2.06 tff(3902,plain,
% 1.87/2.06 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[3901])).
% 1.87/2.06 tff(3903,plain,
% 1.87/2.06 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.87/2.06 inference(symmetry,[status(thm)],[3902])).
% 1.87/2.06 tff(3904,plain,
% 1.87/2.06 (s(s(elem!1)) = s(s(z))),
% 1.87/2.06 inference(transitivity,[status(thm)],[167, 3903, 72])).
% 1.87/2.06 tff(3905,plain,
% 1.87/2.06 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[3904])).
% 1.87/2.06 tff(3906,plain,
% 1.87/2.06 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.87/2.06 inference(symmetry,[status(thm)],[3905])).
% 1.87/2.06 tff(3907,plain,
% 1.87/2.06 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[3901])).
% 1.87/2.06 tff(3908,plain,
% 1.87/2.06 (b(s(s(z)), s(s(s(elem!1))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[3895, 3907])).
% 1.87/2.06 tff(3909,plain,
% 1.87/2.06 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[3908, 3906])).
% 1.87/2.06 tff(3910,plain,
% 1.87/2.06 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[3904])).
% 1.87/2.06 tff(3911,plain,
% 1.87/2.06 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.87/2.06 inference(symmetry,[status(thm)],[3910])).
% 1.87/2.06 tff(3912,plain,
% 1.87/2.06 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[60, 3911])).
% 1.87/2.06 tff(3913,plain,
% 1.87/2.06 (s(s(z)) = s(s(elem!1))),
% 1.87/2.06 inference(transitivity,[status(thm)],[73, 3902, 19])).
% 1.87/2.06 tff(3914,plain,
% 1.87/2.06 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[3913])).
% 1.87/2.06 tff(3915,plain,
% 1.87/2.06 (s(z) = s(elem!1)),
% 1.87/2.06 inference(transitivity,[status(thm)],[24, 3914, 29])).
% 1.87/2.06 tff(3916,plain,
% 1.87/2.06 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[3915])).
% 1.87/2.06 tff(3917,plain,
% 1.87/2.06 (z = elem!1),
% 1.87/2.06 inference(transitivity,[status(thm)],[1443, 3916, 85])).
% 1.87/2.06 tff(3918,plain,
% 1.87/2.06 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.87/2.06 inference(monotonicity,[status(thm)],[3917])).
% 1.87/2.06 tff(3919,plain,
% 1.87/2.06 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[876, 3918])).
% 1.87/2.06 tff(3920,plain,
% 1.87/2.06 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[3917])).
% 1.87/2.06 tff(3921,plain,
% 1.87/2.06 (b(elem!1, s(s(s(elem!1))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[124, 3920])).
% 1.87/2.06 tff(3922,plain,
% 1.87/2.06 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[3913])).
% 1.87/2.06 tff(3923,plain,
% 1.87/2.06 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[3876, 3922])).
% 1.87/2.06 tff(3924,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), 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)))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(3925,plain,
% 1.87/2.06 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(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)))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(3926,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(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)))), 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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(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))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[3925])).
% 1.87/2.06 tff(3927,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(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)))), 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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(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)))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[3926, 3924])).
% 1.87/2.06 tff(3928,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(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)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(3929,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[3928, 3927])).
% 1.87/2.06 tff(3930,plain,
% 1.87/2.06 ($false),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3929, 97, 3923, 3921, 473, 3919, 3912, 3909])).
% 1.87/2.06 tff(3931,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.06 tff(3932,plain,
% 1.87/2.06 (~b(s(s(s(s(elem!1)))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3931, 3785, 3008, 59, 3628, 3583, 226, 3561, 535, 645, 550])).
% 1.87/2.06 tff(3933,plain,
% 1.87/2.06 (r(s(s(s(s(elem!1)))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[842, 3932])).
% 1.87/2.06 tff(3934,plain,
% 1.87/2.06 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3326, 3933, 645, 3872, 3874])).
% 1.87/2.06 tff(3935,plain,
% 1.87/2.06 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3089, 3934, 3628])).
% 1.87/2.06 tff(3936,plain,
% 1.87/2.06 (~b(s(s(s(z))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3862, 3935, 3785, 3008])).
% 1.87/2.06 tff(3937,plain,
% 1.87/2.06 (r(s(s(s(z))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[402, 3936])).
% 1.87/2.06 tff(3938,plain,
% 1.87/2.06 (~r(s(s(z)), s(s(s(z))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3077, 3937, 645, 3874, 3872])).
% 1.87/2.06 tff(3939,plain,
% 1.87/2.06 (b(s(s(z)), s(s(s(z))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[437, 3938])).
% 1.87/2.06 tff(3940,plain,
% 1.87/2.06 (~b(s(s(z)), s(z))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3662, 3935, 3583, 59])).
% 1.87/2.06 tff(3941,plain,
% 1.87/2.06 (r(s(s(z)), s(z))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[122, 3940])).
% 1.87/2.06 tff(3942,plain,
% 1.87/2.06 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3746, 3941, 226, 3561, 3874])).
% 1.87/2.06 tff(3943,plain,
% 1.87/2.06 (b(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[280, 3942])).
% 1.87/2.06 tff(3944,plain,
% 1.87/2.06 ($false),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3067, 3943, 3939, 535, 3870])).
% 1.87/2.06 tff(3945,plain,(b(s(z), s(s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(z), z)) | b(s(s(s(elem!1))), s(z)) | r(z, s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.06 tff(3946,plain,
% 1.87/2.06 (b(s(z), s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3945, 4, 226, 645, 550, 82, 585, 535])).
% 1.87/2.06 tff(3947,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(3948,plain,
% 1.87/2.06 (((~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(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(3949,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[3948])).
% 1.87/2.06 tff(3950,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[3949, 3947])).
% 1.87/2.06 tff(3951,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(3952,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[3951, 3950])).
% 1.87/2.06 tff(3953,plain,
% 1.87/2.06 ($false),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3952, 97, 3946, 550, 3008, 59])).
% 1.87/2.06 tff(3954,plain,(r(s(s(s(elem!1))), s(s(z))) | (~b(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | b(s(s(s(elem!1))), s(z)) | r(z, s(s(s(elem!1)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.06 tff(3955,plain,
% 1.87/2.06 ($false),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3954, 3007, 226, 82, 550, 585, 645, 535])).
% 1.87/2.06 tff(3956,plain,((~r(z, s(s(z)))) | b(s(s(s(elem!1))), s(z)) | (~b(s(z), z)) | r(z, s(s(s(elem!1)))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.06 tff(3957,plain,
% 1.87/2.06 (~r(z, s(s(z)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3956, 2977, 550, 82, 3006, 2986, 288])).
% 1.87/2.06 tff(3958,plain,
% 1.87/2.06 (b(z, s(s(z)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[222, 3957])).
% 1.87/2.06 tff(3959,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), s(z))) | (~b(s(z), s(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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(3960,plain,
% 1.87/2.06 (((~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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(3961,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[3960])).
% 1.87/2.06 tff(3962,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[3961, 3959])).
% 1.87/2.06 tff(3963,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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)))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(3964,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[3963, 3962])).
% 1.87/2.06 tff(3965,plain,
% 1.87/2.06 ($false),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3964, 97, 550, 204, 87, 535])).
% 1.87/2.06 tff(3966,plain,((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.06 tff(3967,plain,
% 1.87/2.06 (~b(s(s(z)), s(z))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3966, 3958, 550, 2986])).
% 1.87/2.06 tff(3968,plain,
% 1.87/2.06 (r(s(s(z)), s(z))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[122, 3967])).
% 1.87/2.06 tff(3969,plain,
% 1.87/2.06 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[2661, 3958, 61, 2986])).
% 1.87/2.06 tff(3970,plain,
% 1.87/2.06 (r(s(s(z)), s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[143, 3969])).
% 1.87/2.06 tff(3971,plain,
% 1.87/2.06 (~r(s(z), s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[1273, 3970, 494, 3968])).
% 1.87/2.06 tff(3972,plain,
% 1.87/2.06 (b(s(z), s(s(s(elem!1))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[181, 3971])).
% 1.87/2.06 tff(3973,plain,
% 1.87/2.06 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[481, 3972, 61, 2978])).
% 1.87/2.06 tff(3974,plain,
% 1.87/2.06 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[201, 3972, 61, 2978])).
% 1.87/2.06 tff(3975,plain,
% 1.87/2.06 (r(s(s(s(elem!1))), s(s(z)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[58, 3974])).
% 1.87/2.06 tff(3976,plain,
% 1.87/2.06 (~b(s(s(s(elem!1))), s(z))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[1147, 61, 535, 3008])).
% 1.87/2.06 tff(3977,plain,
% 1.87/2.06 (r(s(s(s(elem!1))), s(z))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[493, 3976])).
% 1.87/2.06 tff(3978,plain,
% 1.87/2.06 ($false),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[188, 97, 193, 61, 126, 124])).
% 1.87/2.06 tff(3979,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.06 tff(3980,plain,
% 1.87/2.06 (~b(s(s(s(elem!1))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3979, 193, 61, 3008])).
% 1.87/2.06 tff(3981,plain,
% 1.87/2.06 (r(s(s(s(elem!1))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[246, 3980])).
% 1.87/2.06 tff(3982,plain,
% 1.87/2.06 (~r(s(s(z)), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[2671, 226, 288, 145])).
% 1.87/2.06 tff(3983,plain,
% 1.87/2.06 (b(s(s(z)), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[625, 3982])).
% 1.87/2.06 tff(3984,plain,
% 1.87/2.06 (~b(s(s(z)), s(z))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[2651, 3983, 61, 535])).
% 1.87/2.06 tff(3985,plain,
% 1.87/2.06 (r(s(s(z)), s(z))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[121, 3984, 117])).
% 1.87/2.06 tff(3986,plain,
% 1.87/2.06 ($false),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[857, 155, 125, 226, 288, 3985, 145])).
% 1.87/2.06 tff(3987,plain,((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.06 tff(3988,plain,
% 1.87/2.06 (~r(z, s(s(z)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3987, 3981, 61, 3977, 145, 535])).
% 1.87/2.06 tff(3989,plain,
% 1.87/2.06 (b(z, s(s(z)))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[222, 3988])).
% 1.87/2.06 tff(3990,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $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(s(z)))) | (~b(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), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(3991,plain,
% 1.87/2.07 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(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(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(3992,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(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(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[3991])).
% 1.87/2.07 tff(3993,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(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(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.87/2.07 inference(transitivity,[status(thm)],[3992, 3990])).
% 1.87/2.07 tff(3994,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(3995,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[3994, 3993])).
% 1.87/2.07 tff(3996,plain,
% 1.87/2.07 ($false),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[3995, 97, 550, 204, 535, 1361])).
% 1.87/2.07 tff(3997,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.07 tff(3998,plain,
% 1.87/2.07 (~b(s(s(z)), s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[3997, 3989, 535, 550])).
% 1.87/2.07 tff(3999,plain,
% 1.87/2.07 (r(s(s(z)), s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[437, 3998])).
% 1.87/2.07 tff(4000,plain,
% 1.87/2.07 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[481, 193, 3008, 61])).
% 1.87/2.07 tff(4001,plain,
% 1.87/2.07 (~b(s(s(s(s(elem!1)))), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[3055, 550, 255, 61])).
% 1.87/2.07 tff(4002,plain,
% 1.87/2.07 (r(s(s(s(s(elem!1)))), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[842, 4001])).
% 1.87/2.07 tff(4003,plain,
% 1.87/2.07 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2723, 3981, 535, 61, 4002, 4000, 3976])).
% 1.87/2.07 tff(4004,plain,
% 1.87/2.07 (r(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[511, 4003])).
% 1.87/2.07 tff(4005,plain,
% 1.87/2.07 (~r(z, s(s(s(s(elem!1)))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[3464, 3981, 585, 4002, 4000])).
% 1.87/2.07 tff(4006,plain,
% 1.87/2.07 (b(z, s(s(s(s(elem!1)))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1093, 4005])).
% 1.87/2.07 tff(4007,plain,
% 1.87/2.07 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1494, 4006, 61, 255])).
% 1.87/2.07 tff(4008,plain,
% 1.87/2.07 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[452, 4007])).
% 1.87/2.07 tff(4009,plain,
% 1.87/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(4010,plain,
% 1.87/2.07 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~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))))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(4011,plain,
% 1.87/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[4010])).
% 1.87/2.07 tff(4012,plain,
% 1.87/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.87/2.07 inference(transitivity,[status(thm)],[4011, 4009])).
% 1.87/2.07 tff(4013,plain,
% 1.87/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(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)))))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(4014,plain,
% 1.87/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[4013, 4012])).
% 1.87/2.07 tff(4015,plain,
% 1.87/2.07 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[4014, 155, 4008, 4004, 3999, 2597])).
% 1.87/2.07 tff(4016,plain,
% 1.87/2.07 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[384, 53, 4015, 286])).
% 1.87/2.07 tff(4017,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(4018,plain,
% 1.87/2.07 (((~b(s(s(s(s(elem!1)))), 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(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(4019,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[4018])).
% 1.87/2.07 tff(4020,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.87/2.07 inference(transitivity,[status(thm)],[4019, 4017])).
% 1.87/2.07 tff(4021,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(4022,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[4021, 4020])).
% 1.87/2.07 tff(4023,plain,
% 1.87/2.07 ($false),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[4022, 97, 61, 255, 4006, 4016])).
% 1.87/2.07 tff(4024,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | r(z, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.07 tff(4025,plain,
% 1.87/2.07 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[4024, 3975, 2597, 2977, 2986, 550, 61, 3972])).
% 1.87/2.07 tff(4026,plain,
% 1.87/2.07 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1248, 4025, 3972])).
% 1.87/2.07 tff(4027,plain,
% 1.87/2.07 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[486, 4026, 3973])).
% 1.87/2.07 tff(4028,plain,
% 1.87/2.07 (~b(s(s(s(s(elem!1)))), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[3648, 4027, 494, 550, 2978])).
% 1.87/2.07 tff(4029,plain,
% 1.87/2.07 (r(s(s(s(s(elem!1)))), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[842, 4028])).
% 1.87/2.07 tff(4030,plain,
% 1.87/2.07 (r(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[280, 4025])).
% 1.87/2.07 tff(4031,plain,
% 1.87/2.07 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[503, 4027, 494, 4030])).
% 1.87/2.07 tff(4032,plain,
% 1.87/2.07 (b(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[511, 4031])).
% 1.87/2.07 tff(4033,plain,
% 1.87/2.07 ($false),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2723, 4032, 4029, 2986, 61, 288, 3973, 82])).
% 1.87/2.07 tff(4034,plain,((~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), z)) | b(s(s(s(elem!1))), s(z)) | (~b(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.07 tff(4035,plain,
% 1.87/2.07 (~r(s(s(s(z))), s(z))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[4034, 2596, 61, 82, 550, 1961, 2590])).
% 1.87/2.07 tff(4036,plain,
% 1.87/2.07 (b(s(s(s(z))), s(z))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1358, 4035])).
% 1.87/2.07 tff(4037,plain,
% 1.87/2.07 (~b(z, s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[3391, 97, 550, 61, 4036])).
% 1.87/2.07 tff(4038,plain,
% 1.87/2.07 (r(z, s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1318, 4037])).
% 1.87/2.07 tff(4039,plain,
% 1.87/2.07 (~r(z, s(s(z)))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1969, 4038, 1961, 2591])).
% 1.87/2.07 tff(4040,plain,
% 1.87/2.07 (b(z, s(s(z)))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[222, 4039])).
% 1.87/2.07 tff(4041,plain,
% 1.87/2.07 (~b(s(s(s(z))), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[3383, 97, 550, 61, 4036])).
% 1.87/2.07 tff(4042,plain,
% 1.87/2.07 (r(s(s(s(z))), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[402, 4041])).
% 1.87/2.07 tff(4043,plain,
% 1.87/2.07 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(4044,plain,
% 1.87/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[4043])).
% 1.87/2.07 tff(4045,plain,
% 1.87/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.87/2.07 inference(transitivity,[status(thm)],[4044, 2549])).
% 1.87/2.07 tff(4046,plain,
% 1.87/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(4047,plain,
% 1.87/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[4046, 4045])).
% 1.87/2.07 tff(4048,plain,
% 1.87/2.07 (~r(s(s(z)), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[4047, 155, 4038, 1961, 4042])).
% 1.87/2.07 tff(4049,plain,
% 1.87/2.07 (b(s(s(z)), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[625, 4048])).
% 1.87/2.07 tff(4050,plain,
% 1.87/2.07 (~b(s(z), s(s(z)))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2962, 4049, 61, 4040])).
% 1.87/2.07 tff(4051,plain,
% 1.87/2.07 (r(s(z), s(s(z)))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[548, 4050])).
% 1.87/2.07 tff(4052,plain,
% 1.87/2.07 (~r(s(z), s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2641, 4051, 2591, 1961])).
% 1.87/2.07 tff(4053,plain,
% 1.87/2.07 (b(s(z), s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[253, 4052])).
% 1.87/2.07 tff(4054,plain,
% 1.87/2.07 (~b(s(s(z)), s(z))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2627, 4053, 61, 1961, 550, 2591])).
% 1.87/2.07 tff(4055,plain,
% 1.87/2.07 (r(s(s(z)), s(z))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[122, 4054])).
% 1.87/2.07 tff(4056,plain,
% 1.87/2.07 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2313, 4055, 494, 4051])).
% 1.87/2.07 tff(4057,plain,
% 1.87/2.07 (b(s(s(s(elem!1))), s(s(z)))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[58, 4056])).
% 1.87/2.07 tff(4058,plain,
% 1.87/2.07 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2677, 4057, 2590])).
% 1.87/2.07 tff(4059,plain,
% 1.87/2.07 (~b(z, s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[306, 4057, 4049, 4040])).
% 1.87/2.07 tff(4060,plain,
% 1.87/2.07 (r(z, s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[590, 4059])).
% 1.87/2.07 tff(4061,plain,
% 1.87/2.07 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1674, 155, 4060, 2596, 4042])).
% 1.87/2.07 tff(4062,plain,
% 1.87/2.07 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[3089, 4061, 4058])).
% 1.87/2.07 tff(4063,plain,
% 1.87/2.07 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2488, 155, 2596, 4038, 4042])).
% 1.87/2.07 tff(4064,plain,
% 1.87/2.07 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2682, 4058])).
% 1.87/2.07 tff(4065,plain,
% 1.87/2.07 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2687, 4064, 4063])).
% 1.87/2.07 tff(4066,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $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(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(4067,plain,
% 1.87/2.07 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(4068,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(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(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[4067])).
% 1.87/2.07 tff(4069,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(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(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.87/2.07 inference(transitivity,[status(thm)],[4068, 4066])).
% 1.87/2.07 tff(4070,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(4071,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[4070, 4069])).
% 1.87/2.07 tff(4072,plain,
% 1.87/2.07 (~b(s(z), s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[4071, 97, 4036, 4053, 4065])).
% 1.87/2.07 tff(4073,plain,
% 1.87/2.07 (r(s(z), s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[181, 4072])).
% 1.87/2.07 tff(4074,plain,
% 1.87/2.07 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1273, 4073, 494, 4055])).
% 1.87/2.07 tff(4075,plain,
% 1.87/2.07 (b(s(s(z)), s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[143, 4074])).
% 1.87/2.07 tff(4076,plain,
% 1.87/2.07 (~b(s(z), s(s(z)))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2962, 83, 61, 204])).
% 1.87/2.07 tff(4077,plain,
% 1.87/2.07 (r(s(z), s(s(z)))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[548, 4076])).
% 1.87/2.07 tff(4078,plain,
% 1.87/2.07 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2313, 2, 125, 4077])).
% 1.87/2.07 tff(4079,plain,
% 1.87/2.07 (b(s(s(s(elem!1))), s(s(z)))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[58, 4078])).
% 1.87/2.07 tff(4080,plain,
% 1.87/2.07 (~b(z, s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[306, 4079, 83, 204])).
% 1.87/2.07 tff(4081,plain,
% 1.87/2.07 (r(z, s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[590, 4080])).
% 1.87/2.07 tff(4082,plain,
% 1.87/2.07 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[832, 824, 570, 288])).
% 1.87/2.07 tff(4083,plain,
% 1.87/2.07 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[821, 4082, 802])).
% 1.87/2.07 tff(4084,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(4085,plain,
% 1.87/2.07 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(4086,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), 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(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[4085])).
% 1.87/2.07 tff(4087,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), 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(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.07 inference(transitivity,[status(thm)],[4086, 4084])).
% 1.87/2.07 tff(4088,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(4089,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[4088, 4087])).
% 1.87/2.07 tff(4090,plain,
% 1.87/2.07 ($false),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[4089, 97, 805, 60, 371, 1702])).
% 1.87/2.07 tff(4091,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.07 tff(4092,plain,
% 1.87/2.07 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[4091, 4083, 60, 1702])).
% 1.87/2.08 tff(4093,plain,
% 1.87/2.08 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[2747, 4092])).
% 1.87/2.08 tff(4094,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(4095,plain,
% 1.87/2.08 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~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))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(4096,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[4095])).
% 1.87/2.08 tff(4097,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[4096, 4094])).
% 1.87/2.08 tff(4098,plain,
% 1.87/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~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)))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(4099,plain,
% 1.87/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[4098, 4097])).
% 1.87/2.08 tff(4100,plain,
% 1.87/2.08 ($false),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[4099, 155, 824, 4093, 1300, 386])).
% 1.87/2.08 tff(4101,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.08 tff(4102,plain,
% 1.87/2.08 (~r(s(s(s(s(elem!1)))), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[4101, 3701, 386, 4079, 1702, 1300, 4081, 288])).
% 1.87/2.08 tff(4103,plain,
% 1.87/2.08 (b(s(s(s(s(elem!1)))), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[842, 4102])).
% 1.87/2.08 tff(4104,plain,
% 1.87/2.08 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[2715, 4103, 550, 61])).
% 1.87/2.08 tff(4105,plain,
% 1.87/2.08 (r(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[511, 4104])).
% 1.87/2.08 tff(4106,plain,
% 1.87/2.08 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[884, 4103, 83, 204])).
% 1.87/2.08 tff(4107,plain,
% 1.87/2.08 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[452, 4106])).
% 1.87/2.08 tff(4108,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(4109,plain,
% 1.87/2.08 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(4110,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[4109])).
% 1.87/2.08 tff(4111,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[4110, 4108])).
% 1.87/2.08 tff(4112,plain,
% 1.87/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(4113,plain,
% 1.87/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[4112, 4111])).
% 1.87/2.08 tff(4114,plain,
% 1.87/2.08 ($false),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[4113, 155, 125, 823, 1170, 3, 495])).
% 1.87/2.08 tff(4115,plain,((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.08 tff(4116,plain,
% 1.87/2.08 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[4115, 4107, 125, 4077, 4105])).
% 1.87/2.08 tff(4117,plain,
% 1.87/2.08 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[3055, 4103, 550, 61])).
% 1.87/2.08 tff(4118,plain,
% 1.87/2.08 (r(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[280, 4117])).
% 1.87/2.08 tff(4119,plain,
% 1.87/2.08 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[503, 4118, 125, 4105])).
% 1.87/2.08 tff(4120,plain,
% 1.87/2.08 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[821, 3701, 815])).
% 1.87/2.08 tff(4121,plain,
% 1.87/2.08 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[486, 472, 1150])).
% 1.87/2.08 tff(4122,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(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(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(4123,plain,
% 1.87/2.08 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(4124,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[4123])).
% 1.87/2.08 tff(4125,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[4124, 4122])).
% 1.87/2.08 tff(4126,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(4127,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[4126, 4125])).
% 1.87/2.08 tff(4128,plain,
% 1.87/2.08 ($false),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[4127, 97, 4121, 339, 4120, 127])).
% 1.87/2.08 tff(4129,plain,((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.08 tff(4130,plain,
% 1.87/2.08 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[4129, 4119, 127, 472, 4116])).
% 1.87/2.08 tff(4131,plain,
% 1.87/2.08 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[336, 4130])).
% 1.87/2.08 tff(4132,plain,
% 1.87/2.08 ($false),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[3162, 155, 4118, 4131, 2, 4105])).
% 1.87/2.08 tff(4133,plain,((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.08 tff(4134,plain,
% 1.87/2.08 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[4133, 4055, 4075, 494, 550, 61, 4049, 4040, 4042, 4062, 4038, 2596])).
% 1.87/2.08 tff(4135,plain,
% 1.87/2.08 (~b(s(s(s(s(elem!1)))), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[3434, 4134, 239])).
% 1.87/2.08 tff(4136,plain,
% 1.87/2.08 (r(s(s(s(s(elem!1)))), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[842, 4135])).
% 1.87/2.08 tff(4137,plain,
% 1.87/2.08 ((~r(z, s(s(s(s(elem!1)))))) <=> (~r(z, s(s(s(elem!1)))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[3018])).
% 1.87/2.08 tff(4138,assumption,(~r(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.87/2.08 tff(4139,plain,
% 1.87/2.08 (~r(z, s(s(s(elem!1))))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[4138, 4137])).
% 1.87/2.08 tff(4140,plain,
% 1.87/2.08 ($false),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[570, 4139])).
% 1.87/2.08 tff(4141,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.08 tff(4142,plain,
% 1.87/2.08 (r(z, s(s(s(s(elem!1)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[4141, 4134, 4060])).
% 1.87/2.08 tff(4143,plain,
% 1.87/2.08 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[2729, 4134, 4063])).
% 1.87/2.08 tff(4144,plain,
% 1.87/2.08 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[2747, 4143])).
% 1.87/2.08 tff(4145,plain,
% 1.87/2.08 (~(s(s(s(s(z)))) = elem!1)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[2786, 4134])).
% 1.87/2.08 tff(4146,plain,
% 1.87/2.08 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[349, 4134])).
% 1.87/2.08 tff(4147,plain,
% 1.87/2.08 (s(s(s(s(elem!1)))) = elem!1),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[1734, 4146])).
% 1.87/2.08 tff(4148,plain,
% 1.87/2.08 (b(s(s(s(s(z)))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.87/2.08 inference(monotonicity,[status(thm)],[1757])).
% 1.87/2.08 tff(4149,plain,
% 1.87/2.08 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.87/2.08 inference(symmetry,[status(thm)],[4148])).
% 1.87/2.08 tff(4150,assumption,(~(s(s(s(s(z)))) = elem!1)), introduced(assumption)).
% 1.87/2.08 tff(4151,plain,
% 1.87/2.08 (r(s(s(s(s(z)))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.87/2.08 inference(monotonicity,[status(thm)],[1757])).
% 1.87/2.08 tff(4152,plain,
% 1.87/2.08 ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(s(z)))), elem!1))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[4151])).
% 1.87/2.08 tff(4153,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.87/2.08 tff(4154,plain,
% 1.87/2.08 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[2867, 155, 463, 824, 4153])).
% 1.87/2.08 tff(4155,plain,
% 1.87/2.08 (~r(s(s(s(s(z)))), elem!1)),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[4154, 4152])).
% 1.87/2.08 tff(4156,plain,
% 1.87/2.08 (b(s(s(s(s(z)))), elem!1)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[2873, 4155, 4150])).
% 1.87/2.08 tff(4157,plain,
% 1.87/2.08 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[4156, 4149])).
% 1.87/2.08 tff(4158,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(4159,plain,
% 1.87/2.08 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(4160,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[4159])).
% 1.87/2.08 tff(4161,plain,
% 1.87/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.87/2.08 inference(transitivity,[status(thm)],[4160, 4158])).
% 1.87/2.08 tff(4162,plain,
% 1.87/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(4163,plain,
% 1.87/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[4162, 4161])).
% 1.87/2.08 tff(4164,plain,
% 1.87/2.08 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[4163, 155, 1300, 386, 4153])).
% 1.87/2.08 tff(4165,plain,
% 1.87/2.08 (((~![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)))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(4166,plain,
% 1.87/2.08 ((~![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)))))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(4167,plain,
% 1.87/2.08 ((~![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))))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[4166, 4165])).
% 1.87/2.08 tff(4168,plain,
% 1.87/2.08 ((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))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[4167, 53])).
% 1.87/2.08 tff(4169,plain,
% 1.87/2.08 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[4168, 2823])).
% 1.87/2.08 tff(4170,plain,
% 1.87/2.08 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[4169, 4164])).
% 1.87/2.08 tff(4171,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(4172,plain,
% 1.87/2.08 (((~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(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(s(elem!1))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(4173,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[4172])).
% 1.87/2.08 tff(4174,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[4173, 4171])).
% 1.87/2.08 tff(4175,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(s(elem!1)))))))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(4176,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[4175, 4174])).
% 1.87/2.08 tff(4177,plain,
% 1.87/2.08 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[4176, 97, 1360, 371, 4170])).
% 1.87/2.08 tff(4178,plain,
% 1.87/2.08 ($false),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[4177, 4157])).
% 1.87/2.08 tff(4179,plain,((~r(s(s(s(s(z)))), z)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.08 tff(4180,plain,
% 1.87/2.08 (~r(s(s(s(s(z)))), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[4179, 4147, 4145, 4036, 4144, 4038, 4042, 4142, 4136])).
% 1.87/2.08 tff(4181,plain,
% 1.87/2.08 (b(s(s(s(s(z)))), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[2860, 4180])).
% 1.87/2.08 tff(4182,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $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)), 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(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(4183,plain,
% 1.87/2.08 (((~b(z, s(z))) | (~b(z, 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(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(4184,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $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(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(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[4183])).
% 1.87/2.09 tff(4185,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $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(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(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.09 inference(transitivity,[status(thm)],[4184, 4182])).
% 1.87/2.09 tff(4186,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(4187,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $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)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[4186, 4185])).
% 1.87/2.09 tff(4188,plain,
% 1.87/2.09 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[4187, 97, 61, 4049, 4181])).
% 1.87/2.09 tff(4189,plain,
% 1.87/2.09 (((~![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))))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(4190,plain,
% 1.87/2.09 ((~![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))))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(4191,plain,
% 1.87/2.09 ((~![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)))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[4190, 4189])).
% 1.87/2.09 tff(4192,plain,
% 1.87/2.09 ((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)))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[4191, 53])).
% 1.87/2.09 tff(4193,plain,
% 1.87/2.09 (r(s(s(z)), s(s(s(s(z)))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[4192, 4188, 2595])).
% 1.87/2.09 tff(4194,plain,
% 1.87/2.09 (~b(s(s(s(s(z)))), s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[2802, 97, 550, 61, 4181])).
% 1.87/2.09 tff(4195,plain,
% 1.87/2.09 (r(s(s(s(s(z)))), s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[2807, 4194, 2795])).
% 1.87/2.09 tff(4196,plain,
% 1.87/2.09 (~b(s(z), s(s(s(s(z)))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[2839, 97, 550, 61, 4181])).
% 1.87/2.09 tff(4197,plain,
% 1.87/2.09 (r(s(z), s(s(s(s(z)))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[2844, 4196, 2833])).
% 1.87/2.09 tff(4198,plain,
% 1.87/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(4199,plain,
% 1.87/2.09 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(4200,plain,
% 1.87/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[4199])).
% 1.87/2.09 tff(4201,plain,
% 1.87/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.87/2.09 inference(transitivity,[status(thm)],[4200, 4198])).
% 1.87/2.09 tff(4202,plain,
% 1.87/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(4203,plain,
% 1.87/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[4202, 4201])).
% 1.87/2.09 tff(4204,plain,
% 1.87/2.09 ($false),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[4203, 155, 4055, 4197, 4195, 4193])).
% 1.87/2.09 tff(4205,plain,(b(s(s(s(elem!1))), z) | (~b(z, s(z))) | (~b(s(z), z)) | b(s(s(s(z))), s(s(z))) | (~r(s(s(z)), s(s(s(z))))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.09 tff(4206,plain,
% 1.87/2.09 (b(s(s(s(elem!1))), z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[4205, 1961, 550, 2590, 61, 82])).
% 1.87/2.09 tff(4207,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $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(elem!1))), 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(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(4208,plain,
% 1.87/2.09 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(4209,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $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(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), 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(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[4208])).
% 1.87/2.09 tff(4210,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $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(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), 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(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.87/2.09 inference(transitivity,[status(thm)],[4209, 4207])).
% 1.87/2.09 tff(4211,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $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(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(4212,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $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(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[4211, 4210])).
% 1.87/2.09 tff(4213,plain,
% 1.87/2.09 (~b(s(z), s(s(s(elem!1))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[4212, 97, 550, 61, 126])).
% 1.87/2.09 tff(4214,plain,
% 1.87/2.09 (r(s(z), s(s(s(elem!1))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[181, 4213])).
% 1.87/2.09 tff(4215,plain,
% 1.87/2.09 (~b(s(z), s(s(s(z))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[2627, 87, 61, 1961, 550, 1960])).
% 1.87/2.09 tff(4216,plain,
% 1.87/2.09 (r(s(z), s(s(s(z))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[253, 4215])).
% 1.87/2.09 tff(4217,plain,
% 1.87/2.09 (~r(s(z), s(s(z)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[2641, 4216, 1960, 1961])).
% 1.87/2.09 tff(4218,plain,
% 1.87/2.09 (b(s(z), s(s(z)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[548, 4217])).
% 1.87/2.09 tff(4219,plain,
% 1.87/2.09 (~b(s(s(z)), z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[2651, 4218, 87, 61])).
% 1.87/2.09 tff(4220,plain,
% 1.87/2.09 (r(s(s(z)), z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[625, 4219])).
% 1.87/2.09 tff(4221,plain,
% 1.87/2.09 (~b(z, s(s(z)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[3966, 4218, 550, 87])).
% 1.87/2.09 tff(4222,plain,
% 1.87/2.09 (r(z, s(s(z)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[222, 4221])).
% 1.87/2.09 tff(4223,plain,
% 1.87/2.09 (r(s(s(s(elem!1))), s(s(z)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[3954, 4222, 82, 550, 585, 4220, 4218])).
% 1.87/2.09 tff(4224,plain,
% 1.87/2.09 (~r(s(s(s(z))), z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[2693, 155, 4222, 4220, 1960])).
% 1.87/2.09 tff(4225,plain,
% 1.87/2.09 (b(s(s(s(z))), z)),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[402, 4224])).
% 1.87/2.09 tff(4226,plain,
% 1.87/2.09 (~b(s(s(s(z))), s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[3419, 97, 550, 61, 4225])).
% 1.87/2.09 tff(4227,plain,
% 1.87/2.09 (r(s(s(s(z))), s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[1358, 4226])).
% 1.87/2.09 tff(4228,plain,
% 1.87/2.09 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[2682, 1])).
% 1.87/2.09 tff(4229,plain,
% 1.87/2.09 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[2687, 2684, 4228])).
% 1.87/2.09 tff(4230,plain,
% 1.87/2.09 (~r(s(z), s(s(s(z))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[2638, 4229, 2597, 125])).
% 1.87/2.09 tff(4231,plain,
% 1.87/2.09 (b(s(z), s(s(s(z))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[253, 4230])).
% 1.87/2.09 tff(4232,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(4233,plain,
% 1.87/2.09 (((~b(s(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(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(4234,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[4233])).
% 1.87/2.09 tff(4235,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.09 inference(transitivity,[status(thm)],[4234, 4232])).
% 1.87/2.09 tff(4236,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(4237,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[4236, 4235])).
% 1.87/2.09 tff(4238,plain,
% 1.87/2.09 (~b(s(z), s(s(z)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[4237, 97, 1361, 86, 1702])).
% 1.87/2.09 tff(4239,plain,
% 1.87/2.09 (r(s(z), s(s(z)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[548, 4238])).
% 1.87/2.09 tff(4240,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(4241,plain,
% 1.87/2.09 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(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(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(4242,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~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(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[4241])).
% 1.87/2.09 tff(4243,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~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(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.09 inference(transitivity,[status(thm)],[4242, 4240])).
% 1.87/2.09 tff(4244,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~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))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(4245,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[4244, 4243])).
% 1.87/2.09 tff(4246,plain,
% 1.87/2.09 (~b(s(s(z)), s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[4245, 97, 1361, 86, 1702])).
% 1.87/2.09 tff(4247,plain,
% 1.87/2.09 (r(s(s(z)), s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[122, 4246])).
% 1.87/2.09 tff(4248,plain,
% 1.87/2.09 ($false),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[2930, 4247, 4239, 2597, 1960])).
% 1.87/2.09 tff(4249,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.09 tff(4250,plain,
% 1.87/2.09 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[4249, 4231, 1960, 1361, 2597])).
% 1.87/2.09 tff(4251,plain,
% 1.87/2.09 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[3089, 4250, 1])).
% 1.87/2.09 tff(4252,assumption,(r(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 1.87/2.09 tff(4253,plain,
% 1.87/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(4254,plain,
% 1.87/2.09 (((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(4255,plain,
% 1.87/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[4254])).
% 1.87/2.09 tff(4256,plain,
% 1.87/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.09 inference(transitivity,[status(thm)],[4255, 4253])).
% 1.87/2.09 tff(4257,plain,
% 1.87/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(4258,plain,
% 1.87/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[4257, 4256])).
% 1.87/2.09 tff(4259,plain,
% 1.87/2.09 ($false),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[4258, 155, 125, 3, 2597, 1960, 4252])).
% 1.87/2.10 tff(4260,plain,((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.10 tff(4261,plain,
% 1.87/2.10 (~r(s(z), s(s(z)))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[4260, 4251, 2597, 1960, 125])).
% 1.87/2.10 tff(4262,plain,
% 1.87/2.10 (b(s(z), s(s(z)))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[548, 4261])).
% 1.87/2.10 tff(4263,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(4264,plain,
% 1.87/2.10 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(4265,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[4264])).
% 1.87/2.10 tff(4266,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.87/2.10 inference(transitivity,[status(thm)],[4265, 4263])).
% 1.87/2.10 tff(4267,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(4268,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[4267, 4266])).
% 1.87/2.10 tff(4269,plain,
% 1.87/2.10 ($false),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[4268, 97, 535, 1361, 86, 1216])).
% 1.87/2.10 tff(4270,plain,((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.10 tff(4271,plain,
% 1.87/2.10 (~b(s(s(s(z))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[4270, 4262, 1361, 4231])).
% 1.87/2.10 tff(4272,plain,
% 1.87/2.10 (r(s(s(s(z))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[402, 4271])).
% 1.87/2.10 tff(4273,plain,
% 1.87/2.10 (~b(z, s(z))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[3987, 288, 226, 125, 145, 535])).
% 1.87/2.10 tff(4274,plain,
% 1.87/2.10 (r(z, s(z))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[723, 4273])).
% 1.87/2.10 tff(4275,plain,
% 1.87/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(4276,plain,
% 1.87/2.10 (((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(4277,plain,
% 1.87/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[4276])).
% 1.87/2.10 tff(4278,plain,
% 1.87/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.87/2.10 inference(transitivity,[status(thm)],[4277, 4275])).
% 1.87/2.10 tff(4279,plain,
% 1.87/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(4280,plain,
% 1.87/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[4279, 4278])).
% 1.87/2.10 tff(4281,plain,
% 1.87/2.10 ($false),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[4280, 155, 125, 4274, 288, 386, 2630])).
% 1.87/2.10 tff(4282,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.10 tff(4283,plain,
% 1.87/2.10 (~r(s(s(s(elem!1))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[4282, 4272, 125, 4229, 226, 145, 4262])).
% 1.87/2.10 tff(4284,plain,
% 1.87/2.10 (b(s(s(s(elem!1))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[246, 4283])).
% 1.87/2.10 tff(4285,plain,
% 1.87/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(4286,plain,
% 1.87/2.10 (((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(4287,plain,
% 1.87/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[4286])).
% 1.87/2.10 tff(4288,plain,
% 1.87/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.87/2.10 inference(transitivity,[status(thm)],[4287, 4285])).
% 1.87/2.10 tff(4289,plain,
% 1.87/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(4290,plain,
% 1.87/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[4289, 4288])).
% 1.87/2.10 tff(4291,plain,
% 1.87/2.10 (~r(s(s(s(z))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[4290, 155, 226, 81, 2597, 1960])).
% 1.87/2.10 tff(4292,plain,
% 1.87/2.10 (b(s(s(s(z))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[402, 4291])).
% 1.87/2.10 tff(4293,plain,
% 1.87/2.10 (~r(z, s(s(s(z))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[1969, 1961, 226, 1960])).
% 1.87/2.10 tff(4294,plain,
% 1.87/2.10 (b(z, s(s(s(z))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[1318, 4293])).
% 1.87/2.10 tff(4295,plain,
% 1.87/2.10 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.87/2.10 inference(commutativity,[status(thm)],[])).
% 1.87/2.10 tff(4296,plain,
% 1.87/2.10 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.87/2.10 inference(symmetry,[status(thm)],[4295])).
% 1.87/2.10 tff(4297,plain,
% 1.87/2.10 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(elem!1))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[4296])).
% 1.87/2.10 tff(4298,plain,
% 1.87/2.10 (~(s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[286, 4297])).
% 1.87/2.10 tff(4299,plain,
% 1.87/2.10 (~b(z, s(z))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[2587, 3, 81])).
% 1.87/2.10 tff(4300,plain,
% 1.87/2.10 (r(z, s(z))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[723, 4299])).
% 1.87/2.10 tff(4301,plain,
% 1.87/2.10 (~r(s(s(s(elem!1))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[791, 125, 81, 4300])).
% 1.87/2.10 tff(4302,plain,
% 1.87/2.10 (b(s(s(s(elem!1))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[246, 4301])).
% 1.87/2.10 tff(4303,plain,
% 1.87/2.10 (~r(z, s(s(s(elem!1))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[771, 225, 729, 125])).
% 1.87/2.10 tff(4304,plain,
% 1.87/2.10 (b(z, s(s(s(elem!1))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[590, 4303])).
% 1.87/2.10 tff(4305,plain,
% 1.87/2.10 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[985, 97, 126, 4304, 83])).
% 1.87/2.10 tff(4306,plain,
% 1.87/2.10 (r(s(s(z)), s(s(s(elem!1))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[143, 4305])).
% 1.87/2.10 tff(4307,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(4308,plain,
% 1.87/2.10 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(4309,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[4308])).
% 1.87/2.10 tff(4310,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.87/2.10 inference(transitivity,[status(thm)],[4309, 4307])).
% 1.87/2.10 tff(4311,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(4312,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[4311, 4310])).
% 1.87/2.10 tff(4313,plain,
% 1.87/2.10 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[4312, 97, 126, 4304, 83])).
% 1.87/2.10 tff(4314,plain,
% 1.87/2.10 (r(s(s(s(elem!1))), s(s(z)))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[58, 4313])).
% 1.87/2.10 tff(4315,plain,
% 1.87/2.10 ($false),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[161, 155, 3, 225, 4314, 4306])).
% 1.87/2.10 tff(4316,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.10 tff(4317,plain,
% 1.87/2.10 (~r(s(z), s(s(s(elem!1))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[4316, 83, 4302, 3, 4300, 125])).
% 1.87/2.10 tff(4318,plain,
% 1.87/2.10 (b(s(z), s(s(s(elem!1))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[181, 4317])).
% 1.87/2.10 tff(4319,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(4320,plain,
% 1.87/2.10 (((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(4321,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[4320])).
% 1.87/2.10 tff(4322,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.87/2.10 inference(transitivity,[status(thm)],[4321, 4319])).
% 1.87/2.10 tff(4323,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(4324,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[4323, 4322])).
% 1.87/2.10 tff(4325,plain,
% 1.87/2.10 ($false),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[4324, 97, 193, 124, 83, 87, 1331, 1216])).
% 1.87/2.10 tff(4326,plain,((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.10 tff(4327,plain,
% 1.87/2.10 (~b(s(s(s(z))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[4326, 1331, 124, 83, 87, 193])).
% 1.87/2.10 tff(4328,plain,
% 1.87/2.10 (r(s(s(s(z))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[402, 4327])).
% 1.87/2.10 tff(4329,plain,
% 1.87/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(4330,plain,
% 1.87/2.10 (((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(4331,plain,
% 1.87/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[4330])).
% 1.87/2.10 tff(4332,plain,
% 1.87/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.87/2.10 inference(transitivity,[status(thm)],[4331, 4329])).
% 1.87/2.10 tff(4333,plain,
% 1.87/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(4334,plain,
% 1.87/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[4333, 4332])).
% 1.87/2.11 tff(4335,plain,
% 1.87/2.11 (~r(s(s(s(z))), s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[4334, 155, 729, 81, 4328])).
% 1.87/2.11 tff(4336,plain,
% 1.87/2.11 (b(s(s(s(z))), s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[1358, 4335])).
% 1.87/2.11 tff(4337,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $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(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(4338,plain,
% 1.87/2.11 (((~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(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(4339,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $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(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(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[4338])).
% 1.87/2.11 tff(4340,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $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(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(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[4339, 4337])).
% 1.87/2.11 tff(4341,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $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(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(4342,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[4341, 4340])).
% 1.87/2.11 tff(4343,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[4342, 97, 193, 87, 4336, 1331])).
% 1.87/2.11 tff(4344,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(4345,plain,
% 1.87/2.11 (~b(s(s(s(z))), s(s(z)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[4344, 124, 87, 4300, 81, 193, 83])).
% 1.87/2.11 tff(4346,plain,
% 1.87/2.11 (r(s(s(s(z))), s(s(z)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[421, 4345])).
% 1.87/2.11 tff(4347,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(4348,plain,
% 1.87/2.11 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(4349,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[4348])).
% 1.87/2.11 tff(4350,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[4349, 4347])).
% 1.87/2.11 tff(4351,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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))))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(4352,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[4351, 4350])).
% 1.87/2.11 tff(4353,plain,
% 1.87/2.11 (~b(s(s(s(z))), s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[4352, 97, 193, 126, 1702])).
% 1.87/2.11 tff(4354,plain,
% 1.87/2.11 (r(s(s(s(z))), s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[1358, 4353])).
% 1.87/2.11 tff(4355,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(4356,plain,
% 1.87/2.11 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(4357,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[4356])).
% 1.87/2.11 tff(4358,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[4357, 4355])).
% 1.87/2.11 tff(4359,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(4360,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[4359, 4358])).
% 1.87/2.11 tff(4361,plain,
% 1.87/2.11 (~b(s(s(s(z))), z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[4360, 97, 126, 124, 1702])).
% 1.87/2.11 tff(4362,plain,
% 1.87/2.11 (r(s(s(s(z))), z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[402, 4361])).
% 1.87/2.11 tff(4363,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(4364,plain,
% 1.87/2.11 (((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(4365,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[4364])).
% 1.87/2.11 tff(4366,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[4365, 4363])).
% 1.87/2.11 tff(4367,plain,
% 1.87/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(4368,plain,
% 1.87/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[4367, 4366])).
% 1.87/2.11 tff(4369,plain,
% 1.87/2.11 ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[4368, 155, 729, 3, 1960])).
% 1.87/2.11 tff(4370,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[4369, 4362, 4354])).
% 1.87/2.11 tff(4371,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(4372,plain,
% 1.87/2.11 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[4371, 4346, 3, 4300, 126, 124, 193])).
% 1.87/2.11 tff(4373,plain,
% 1.87/2.11 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[985, 97, 126, 124, 83])).
% 1.87/2.11 tff(4374,plain,
% 1.87/2.11 (r(s(s(z)), s(s(s(elem!1))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[143, 4373])).
% 1.87/2.11 tff(4375,plain,
% 1.87/2.11 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[4312, 97, 126, 124, 83])).
% 1.87/2.11 tff(4376,plain,
% 1.87/2.11 (r(s(s(s(elem!1))), s(s(z)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[58, 4375])).
% 1.87/2.11 tff(4377,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), 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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), 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))))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(4378,plain,
% 1.87/2.11 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~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(s(elem!1))), 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))))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(4379,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), 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)))))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[4378])).
% 1.87/2.11 tff(4380,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), 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))))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[4379, 4377])).
% 1.87/2.11 tff(4381,plain,
% 1.87/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~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)))))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(4382,plain,
% 1.87/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), 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)))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[4381, 4380])).
% 1.87/2.11 tff(4383,plain,
% 1.87/2.11 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[4382, 155, 4376, 4374, 4346])).
% 1.87/2.11 tff(4384,plain,
% 1.87/2.11 ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[1678, 53, 4383])).
% 1.87/2.11 tff(4385,plain,
% 1.87/2.11 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[4384, 4372])).
% 1.87/2.11 tff(4386,plain,
% 1.87/2.11 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[4385])).
% 1.87/2.11 tff(4387,plain,
% 1.87/2.11 (s(s(z)) = s(s(elem!1))),
% 1.87/2.11 inference(transitivity,[status(thm)],[73, 4386, 19])).
% 1.87/2.11 tff(4388,plain,
% 1.87/2.11 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[4387])).
% 1.87/2.11 tff(4389,plain,
% 1.87/2.11 (s(z) = s(elem!1)),
% 1.87/2.11 inference(transitivity,[status(thm)],[24, 4388, 29])).
% 1.87/2.11 tff(4390,plain,
% 1.87/2.11 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[4389])).
% 1.87/2.11 tff(4391,plain,
% 1.87/2.11 (z = elem!1),
% 1.87/2.11 inference(transitivity,[status(thm)],[1443, 4390, 85])).
% 1.87/2.11 tff(4392,plain,
% 1.87/2.11 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.87/2.11 inference(monotonicity,[status(thm)],[4391])).
% 1.87/2.11 tff(4393,plain,
% 1.87/2.11 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 1.87/2.11 inference(monotonicity,[status(thm)],[4387])).
% 1.87/2.11 tff(4394,plain,
% 1.87/2.11 (b(s(s(elem!1)), z)),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[83, 4393])).
% 1.87/2.11 tff(4395,plain,
% 1.87/2.11 (b(s(s(elem!1)), elem!1)),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[4394, 4392])).
% 1.87/2.11 tff(4396,plain,
% 1.87/2.11 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[4385])).
% 1.87/2.11 tff(4397,plain,
% 1.87/2.11 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[4396, 1414])).
% 1.87/2.11 tff(4398,plain,
% 1.87/2.11 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[4397])).
% 1.87/2.11 tff(4399,plain,
% 1.87/2.11 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[286, 4398])).
% 1.87/2.11 tff(4400,plain,
% 1.87/2.11 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.87/2.11 inference(symmetry,[status(thm)],[4388])).
% 1.87/2.11 tff(4401,plain,
% 1.87/2.11 (s(elem!1) = s(z)),
% 1.87/2.11 inference(transitivity,[status(thm)],[30, 4400, 23])).
% 1.87/2.11 tff(4402,plain,
% 1.87/2.11 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[4401])).
% 1.87/2.11 tff(4403,plain,
% 1.87/2.11 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.87/2.11 inference(symmetry,[status(thm)],[4402])).
% 1.87/2.11 tff(4404,plain,
% 1.87/2.11 (b(s(elem!1), s(s(s(elem!1))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[193, 4403])).
% 1.87/2.11 tff(4405,plain,
% 1.87/2.11 (~b(s(s(s(s(elem!1)))), z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[3290, 473, 124, 126])).
% 1.87/2.11 tff(4406,plain,
% 1.87/2.11 (r(s(s(s(s(elem!1)))), z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[842, 4405])).
% 1.87/2.11 tff(4407,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(4408,plain,
% 1.87/2.11 (((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(4409,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[4408])).
% 1.87/2.11 tff(4410,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.87/2.11 inference(transitivity,[status(thm)],[4409, 4407])).
% 1.87/2.11 tff(4411,plain,
% 1.87/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(4412,plain,
% 1.87/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[4411, 4410])).
% 1.87/2.11 tff(4413,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[4412, 155, 729, 81, 824, 495])).
% 1.87/2.11 tff(4414,plain,((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(4415,plain,
% 1.87/2.11 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[4414, 4406, 81, 729])).
% 1.87/2.11 tff(4416,plain,
% 1.87/2.11 (b(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[511, 4415])).
% 1.87/2.11 tff(4417,plain,
% 1.87/2.11 (~b(z, s(s(s(s(elem!1)))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[701, 4416, 473, 124])).
% 1.87/2.11 tff(4418,plain,
% 1.87/2.11 (r(z, s(s(s(s(elem!1)))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[1093, 4417])).
% 1.87/2.11 tff(4419,plain,
% 1.87/2.11 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[4418, 3316])).
% 1.87/2.11 tff(4420,plain,
% 1.87/2.11 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[3107, 4406, 1393])).
% 1.87/2.11 tff(4421,plain,
% 1.87/2.11 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(4422,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[4421])).
% 1.87/2.11 tff(4423,plain,
% 1.87/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[4422, 1942])).
% 1.87/2.12 tff(4424,plain,
% 1.87/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(4425,plain,
% 1.87/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[4424, 4423])).
% 1.87/2.12 tff(4426,plain,
% 1.87/2.12 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4425, 155, 4420, 1448, 4419])).
% 1.87/2.12 tff(4427,plain,
% 1.87/2.12 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[1909, 4426, 1393])).
% 1.87/2.12 tff(4428,plain,
% 1.87/2.12 (b(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[280, 4427])).
% 1.87/2.12 tff(4429,plain,
% 1.87/2.12 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[4428, 1517])).
% 1.87/2.12 tff(4430,plain,
% 1.87/2.12 (r(z, s(z)) <=> r(elem!1, s(elem!1))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[1444, 1401])).
% 1.87/2.12 tff(4431,plain,
% 1.87/2.12 (r(elem!1, s(elem!1))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[729, 4430])).
% 1.87/2.12 tff(4432,plain,
% 1.87/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(elem!1))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(4433,plain,
% 1.87/2.12 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(s(elem!1), 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))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(4434,plain,
% 1.87/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(elem!1)))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[4433])).
% 1.87/2.12 tff(4435,plain,
% 1.87/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(elem!1))))),
% 1.87/2.12 inference(transitivity,[status(thm)],[4434, 4432])).
% 1.87/2.12 tff(4436,plain,
% 1.87/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(4437,plain,
% 1.87/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(elem!1)))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[4436, 4435])).
% 1.87/2.12 tff(4438,plain,
% 1.87/2.12 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4437, 155, 4420, 1448, 4431])).
% 1.87/2.12 tff(4439,plain,
% 1.87/2.12 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[1615, 53, 1612, 4438])).
% 1.87/2.12 tff(4440,plain,
% 1.87/2.12 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[1623, 97, 473, 1617, 4439])).
% 1.87/2.12 tff(4441,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4440, 4429])).
% 1.87/2.12 tff(4442,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(4443,plain,
% 1.87/2.12 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4442, 4385, 4404, 124, 81, 4300, 126])).
% 1.87/2.12 tff(4444,plain,
% 1.87/2.12 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[486, 4443, 4399])).
% 1.87/2.12 tff(4445,plain,
% 1.87/2.12 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[3107, 824, 1393])).
% 1.87/2.12 tff(4446,plain,
% 1.87/2.12 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4437, 155, 4445, 1448, 4431])).
% 1.87/2.12 tff(4447,plain,
% 1.87/2.12 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[1615, 53, 1612, 4446])).
% 1.87/2.12 tff(4448,plain,
% 1.87/2.12 (b(s(elem!1), s(s(s(elem!1))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[193, 1514])).
% 1.87/2.12 tff(4449,plain,
% 1.87/2.12 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.87/2.12 inference(transitivity,[status(thm)],[1416, 2507])).
% 1.87/2.12 tff(4450,plain,
% 1.87/2.12 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[4449])).
% 1.87/2.12 tff(4451,plain,
% 1.87/2.12 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[286, 4450])).
% 1.87/2.12 tff(4452,plain,
% 1.87/2.12 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4414, 824, 81, 729])).
% 1.87/2.12 tff(4453,plain,
% 1.87/2.12 (b(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[511, 4452])).
% 1.87/2.12 tff(4454,plain,
% 1.87/2.12 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[950, 4453, 126, 193, 87, 488])).
% 1.87/2.12 tff(4455,plain,
% 1.87/2.12 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[821, 4454, 4451])).
% 1.87/2.12 tff(4456,plain,
% 1.87/2.12 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.87/2.12 inference(monotonicity,[status(thm)],[1444])).
% 1.87/2.12 tff(4457,plain,
% 1.87/2.12 (b(s(s(s(elem!1))), elem!1)),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[126, 4456])).
% 1.87/2.12 tff(4458,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), 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(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(4459,plain,
% 1.87/2.12 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(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)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(4460,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(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(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[4459])).
% 1.87/2.12 tff(4461,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(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(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.87/2.12 inference(transitivity,[status(thm)],[4460, 4458])).
% 1.87/2.12 tff(4462,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(4463,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[4462, 4461])).
% 1.87/2.12 tff(4464,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4463, 97, 4457, 4455, 4448, 4447])).
% 1.87/2.12 tff(4465,plain,((~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(4466,plain,
% 1.87/2.12 (~r(s(s(s(s(elem!1)))), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4465, 4444, 193, 87, 126, 4385, 81, 4300])).
% 1.87/2.12 tff(4467,plain,
% 1.87/2.12 (b(s(s(s(s(elem!1)))), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[842, 4466])).
% 1.87/2.12 tff(4468,plain,
% 1.87/2.12 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.87/2.12 inference(monotonicity,[status(thm)],[1534])).
% 1.87/2.12 tff(4469,plain,
% 1.87/2.12 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 1.87/2.12 inference(symmetry,[status(thm)],[4468])).
% 1.87/2.12 tff(4470,plain,
% 1.87/2.12 ((~b(s(s(s(s(elem!1)))), elem!1)) <=> (~b(s(s(s(s(elem!1)))), z))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[4469])).
% 1.87/2.12 tff(4471,assumption,(~b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.87/2.12 tff(4472,plain,
% 1.87/2.12 (~b(s(s(s(s(elem!1)))), z)),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[4471, 4470])).
% 1.87/2.12 tff(4473,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[876, 4472])).
% 1.87/2.12 tff(4474,plain,((~(z = elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | b(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(4475,plain,
% 1.87/2.12 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4474, 4467, 4391])).
% 1.87/2.12 tff(4476,plain,
% 1.87/2.12 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[4387])).
% 1.87/2.12 tff(4477,plain,
% 1.87/2.12 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.87/2.12 inference(transitivity,[status(thm)],[4476, 1428])).
% 1.87/2.12 tff(4478,plain,
% 1.87/2.12 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.87/2.12 inference(transitivity,[status(thm)],[4477, 1505])).
% 1.87/2.12 tff(4479,plain,
% 1.87/2.12 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[4478])).
% 1.87/2.12 tff(4480,plain,
% 1.87/2.12 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[331, 4479])).
% 1.87/2.12 tff(4481,plain,
% 1.87/2.12 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.87/2.12 inference(symmetry,[status(thm)],[4386])).
% 1.87/2.12 tff(4482,plain,
% 1.87/2.12 (s(s(elem!1)) = s(s(z))),
% 1.87/2.12 inference(transitivity,[status(thm)],[167, 4481, 72])).
% 1.87/2.12 tff(4483,plain,
% 1.87/2.12 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[4482])).
% 1.87/2.12 tff(4484,plain,
% 1.87/2.12 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.87/2.12 inference(symmetry,[status(thm)],[4483])).
% 1.87/2.12 tff(4485,plain,
% 1.87/2.12 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[4376, 4484])).
% 1.87/2.12 tff(4486,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), 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(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), 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)))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(4487,plain,
% 1.87/2.12 (((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), 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)))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(4488,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), 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(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), 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))))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[4487])).
% 1.87/2.12 tff(4489,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), 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(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), 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)))))),
% 1.87/2.12 inference(transitivity,[status(thm)],[4488, 4486])).
% 1.87/2.12 tff(4490,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(4491,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[4490, 4489])).
% 1.87/2.12 tff(4492,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4491, 97, 193, 124, 83, 876, 441, 87])).
% 1.87/2.12 tff(4493,plain,((~b(s(s(z)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(4494,plain,
% 1.87/2.12 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4493, 4467, 193, 124, 83, 87])).
% 1.87/2.12 tff(4495,plain,
% 1.87/2.12 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[452, 4494])).
% 1.87/2.12 tff(4496,plain,
% 1.87/2.12 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[1822, 4495, 4385])).
% 1.87/2.12 tff(4497,assumption,(r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.87/2.12 tff(4498,plain,
% 1.87/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(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)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(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)))))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(4499,plain,
% 1.87/2.12 (((~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(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(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(4500,plain,
% 1.87/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(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))))))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[4499])).
% 1.87/2.12 tff(4501,plain,
% 1.87/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(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)))))))),
% 1.87/2.12 inference(transitivity,[status(thm)],[4500, 4498])).
% 1.87/2.12 tff(4502,plain,
% 1.87/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(4503,plain,
% 1.87/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[4502, 4501])).
% 1.87/2.12 tff(4504,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4503, 155, 1813, 1522, 488, 4497])).
% 1.87/2.12 tff(4505,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(4506,plain,
% 1.87/2.12 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4505, 4496, 4485, 4444])).
% 1.87/2.12 tff(4507,plain,
% 1.87/2.12 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[1631, 4506, 4480])).
% 1.87/2.12 tff(4508,plain,
% 1.87/2.12 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[4391])).
% 1.87/2.12 tff(4509,plain,
% 1.87/2.12 (b(elem!1, s(s(s(elem!1))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[124, 4508])).
% 1.87/2.12 tff(4510,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $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(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(4511,plain,
% 1.87/2.12 (((~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(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(4512,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $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(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $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(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[4511])).
% 1.87/2.12 tff(4513,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $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(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $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(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.87/2.12 inference(transitivity,[status(thm)],[4512, 4510])).
% 1.87/2.12 tff(4514,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $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(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(4515,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[4514, 4513])).
% 1.87/2.12 tff(4516,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4515, 97, 4509, 4507, 4475, 4395])).
% 1.87/2.12 tff(4517,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(4518,plain,
% 1.97/2.13 (~b(z, s(s(s(elem!1))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4517, 4318, 83, 87, 4302, 81, 3])).
% 1.97/2.13 tff(4519,plain,
% 1.97/2.13 (r(z, s(s(s(elem!1))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[590, 4518])).
% 1.97/2.13 tff(4520,plain,
% 1.97/2.13 (~b(s(s(s(z))), s(s(z)))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4342, 97, 193, 87, 1360])).
% 1.97/2.13 tff(4521,plain,
% 1.97/2.13 (r(s(s(s(z))), s(s(z)))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[421, 4520])).
% 1.97/2.13 tff(4522,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $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(s(z)), s(z))) | (~b(s(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(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(4523,plain,
% 1.97/2.13 (((~b(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(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(4524,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $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(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(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[4523])).
% 1.97/2.13 tff(4525,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $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(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(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[4524, 4522])).
% 1.97/2.13 tff(4526,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $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(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(4527,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[4526, 4525])).
% 1.97/2.13 tff(4528,plain,
% 1.97/2.13 (~b(s(s(z)), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4527, 97, 193, 87, 1360])).
% 1.97/2.13 tff(4529,plain,
% 1.97/2.13 (r(s(s(z)), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[437, 4528])).
% 1.97/2.13 tff(4530,plain,
% 1.97/2.13 (~r(z, s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1969, 226, 1961, 1960])).
% 1.97/2.13 tff(4531,plain,
% 1.97/2.13 (b(z, s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1318, 4530])).
% 1.97/2.13 tff(4532,plain,
% 1.97/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(4533,plain,
% 1.97/2.13 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(4534,plain,
% 1.97/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[4533])).
% 1.97/2.13 tff(4535,plain,
% 1.97/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[4534, 4532])).
% 1.97/2.13 tff(4536,plain,
% 1.97/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(4537,plain,
% 1.97/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[4536, 4535])).
% 1.97/2.13 tff(4538,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4537, 155, 125, 729, 570, 226, 224])).
% 1.97/2.13 tff(4539,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(4540,plain,
% 1.97/2.13 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4539, 226, 729, 125, 570])).
% 1.97/2.13 tff(4541,plain,
% 1.97/2.13 (b(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[143, 4540])).
% 1.97/2.13 tff(4542,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(4543,plain,
% 1.97/2.13 (((~b(z, s(s(s(z))))) | (~b(z, s(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(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(4544,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[4543])).
% 1.97/2.13 tff(4545,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[4544, 4542])).
% 1.97/2.13 tff(4546,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(4547,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[4546, 4545])).
% 1.97/2.13 tff(4548,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4547, 97, 126, 83, 4541, 4531])).
% 1.97/2.13 tff(4549,plain,((~r(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(4550,plain,
% 1.97/2.13 (~r(z, s(s(z)))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4549, 4529, 83, 126, 4521, 729, 125, 570])).
% 1.97/2.13 tff(4551,plain,
% 1.97/2.13 (b(z, s(s(z)))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[222, 4550])).
% 1.97/2.13 tff(4552,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(4553,plain,
% 1.97/2.13 (((~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(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(4554,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[4553])).
% 1.97/2.13 tff(4555,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[4554, 4552])).
% 1.97/2.13 tff(4556,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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))))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(4557,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[4556, 4555])).
% 1.97/2.13 tff(4558,plain,
% 1.97/2.13 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4557, 97, 126, 4551, 83])).
% 1.97/2.13 tff(4559,plain,
% 1.97/2.13 (r(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[143, 4558])).
% 1.97/2.13 tff(4560,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(4561,plain,
% 1.97/2.13 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~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))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(4562,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[4561])).
% 1.97/2.13 tff(4563,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[4562, 4560])).
% 1.97/2.13 tff(4564,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(4565,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[4564, 4563])).
% 1.97/2.13 tff(4566,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4565, 97, 126, 204, 60, 83])).
% 1.97/2.13 tff(4567,plain,((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(4568,plain,
% 1.97/2.13 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4567, 4551, 126, 83])).
% 1.97/2.13 tff(4569,plain,
% 1.97/2.13 (r(s(s(s(elem!1))), s(s(z)))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[58, 4568])).
% 1.97/2.13 tff(4570,plain,
% 1.97/2.13 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4382, 155, 4569, 4559, 4521])).
% 1.97/2.13 tff(4571,plain,
% 1.97/2.13 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1678, 53, 1, 4570])).
% 1.97/2.13 tff(4572,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4352, 97, 193, 126, 1360, 4571])).
% 1.97/2.13 tff(4573,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(4574,plain,
% 1.97/2.13 (~b(s(s(s(z))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4573, 1, 4302, 4318, 83, 4300, 125, 4519, 87])).
% 1.97/2.13 tff(4575,plain,
% 1.97/2.13 (r(s(s(s(z))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1358, 4574])).
% 1.97/2.13 tff(4576,plain,
% 1.97/2.13 (((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(4577,plain,
% 1.97/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[4576])).
% 1.97/2.13 tff(4578,plain,
% 1.97/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[4577, 4329])).
% 1.97/2.13 tff(4579,plain,
% 1.97/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(4580,plain,
% 1.97/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[4579, 4578])).
% 1.97/2.13 tff(4581,plain,
% 1.97/2.13 (~r(s(s(s(z))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4580, 155, 4300, 81, 4575])).
% 1.97/2.13 tff(4582,plain,
% 1.97/2.13 (b(s(s(s(z))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[402, 4581])).
% 1.97/2.13 tff(4583,plain,
% 1.97/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(4584,plain,
% 1.97/2.13 (((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(4585,plain,
% 1.97/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[4584])).
% 1.97/2.14 tff(4586,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[4585, 4583])).
% 1.97/2.14 tff(4587,plain,
% 1.97/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(4588,plain,
% 1.97/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[4587, 4586])).
% 1.97/2.14 tff(4589,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4588, 155, 125, 729, 570, 226, 3])).
% 1.97/2.14 tff(4590,plain,((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(4591,plain,
% 1.97/2.14 (~r(z, s(s(z)))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4590, 4519, 4300, 125, 3])).
% 1.97/2.14 tff(4592,plain,
% 1.97/2.14 (b(z, s(s(z)))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[222, 4591])).
% 1.97/2.14 tff(4593,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(4594,plain,
% 1.97/2.14 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(4595,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[4594])).
% 1.97/2.14 tff(4596,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[4595, 4593])).
% 1.97/2.14 tff(4597,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(4598,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[4597, 4596])).
% 1.97/2.14 tff(4599,plain,
% 1.97/2.14 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4598, 97, 4302, 4592, 4582])).
% 1.97/2.14 tff(4600,plain,
% 1.97/2.14 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4567, 4592, 4302, 83])).
% 1.97/2.14 tff(4601,plain,
% 1.97/2.14 (r(s(s(s(elem!1))), s(s(z)))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[58, 4600])).
% 1.97/2.14 tff(4602,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(4603,plain,
% 1.97/2.14 (((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(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)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(4604,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[4603])).
% 1.97/2.14 tff(4605,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[4604, 4602])).
% 1.97/2.14 tff(4606,plain,
% 1.97/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(4607,plain,
% 1.97/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[4606, 4605])).
% 1.97/2.14 tff(4608,plain,
% 1.97/2.14 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4607, 155, 125, 3, 4601, 4575])).
% 1.97/2.14 tff(4609,plain,
% 1.97/2.14 ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[2469, 53, 4608])).
% 1.97/2.14 tff(4610,plain,
% 1.97/2.14 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4609, 4599])).
% 1.97/2.14 tff(4611,plain,
% 1.97/2.14 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[4610, 2679])).
% 1.97/2.14 tff(4612,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1, 4611])).
% 1.97/2.14 tff(4613,plain,((s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(4614,plain,
% 1.97/2.14 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4613, 83, 125, 3, 81, 87])).
% 1.97/2.14 tff(4615,plain,
% 1.97/2.14 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[4614])).
% 1.97/2.14 tff(4616,plain,
% 1.97/2.14 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[4615, 1414])).
% 1.97/2.14 tff(4617,plain,
% 1.97/2.14 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[4616, 2507])).
% 1.97/2.14 tff(4618,plain,
% 1.97/2.14 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[4617])).
% 1.97/2.14 tff(4619,plain,
% 1.97/2.14 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[286, 4618])).
% 1.97/2.14 tff(4620,plain,
% 1.97/2.14 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[4614])).
% 1.97/2.14 tff(4621,plain,
% 1.97/2.14 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.97/2.14 inference(symmetry,[status(thm)],[4620])).
% 1.97/2.14 tff(4622,plain,
% 1.97/2.14 (s(s(elem!1)) = s(s(z))),
% 1.97/2.14 inference(transitivity,[status(thm)],[167, 4621, 72])).
% 1.97/2.14 tff(4623,plain,
% 1.97/2.14 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[4622])).
% 1.97/2.14 tff(4624,plain,
% 1.97/2.14 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.97/2.14 inference(symmetry,[status(thm)],[4623])).
% 1.97/2.14 tff(4625,plain,
% 1.97/2.14 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4557, 97, 4302, 4592, 83])).
% 1.97/2.14 tff(4626,plain,
% 1.97/2.14 (r(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[143, 4625])).
% 1.97/2.14 tff(4627,plain,
% 1.97/2.14 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[4626, 4624])).
% 1.97/2.14 tff(4628,plain,
% 1.97/2.14 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[4622])).
% 1.97/2.14 tff(4629,plain,
% 1.97/2.14 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.97/2.14 inference(symmetry,[status(thm)],[4628])).
% 1.97/2.14 tff(4630,plain,
% 1.97/2.14 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[4601, 4629])).
% 1.97/2.14 tff(4631,plain,
% 1.97/2.14 (s(s(z)) = s(s(elem!1))),
% 1.97/2.14 inference(transitivity,[status(thm)],[73, 4620, 19])).
% 1.97/2.14 tff(4632,plain,
% 1.97/2.14 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[4631])).
% 1.97/2.14 tff(4633,plain,
% 1.97/2.14 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(z)))),
% 1.97/2.14 inference(symmetry,[status(thm)],[4632])).
% 1.97/2.14 tff(4634,plain,
% 1.97/2.14 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[4631])).
% 1.97/2.14 tff(4635,plain,
% 1.97/2.14 (s(z) = s(elem!1)),
% 1.97/2.14 inference(transitivity,[status(thm)],[24, 4634, 29])).
% 1.97/2.14 tff(4636,plain,
% 1.97/2.14 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[4635, 4631])).
% 1.97/2.14 tff(4637,plain,
% 1.97/2.14 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 1.97/2.14 inference(transitivity,[status(thm)],[4636, 4633])).
% 1.97/2.14 tff(4638,plain,
% 1.97/2.14 (r(s(elem!1), s(s(z)))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[3, 4637])).
% 1.97/2.14 tff(4639,plain,
% 1.97/2.14 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(elem!1))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[1396])).
% 1.97/2.14 tff(4640,plain,
% 1.97/2.14 (b(s(s(z)), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.97/2.14 inference(symmetry,[status(thm)],[4639])).
% 1.97/2.14 tff(4641,plain,
% 1.97/2.14 (b(s(s(z)), s(z)) <=> b(s(s(z)), s(elem!1))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[1401])).
% 1.97/2.14 tff(4642,plain,
% 1.97/2.14 (b(s(s(z)), s(elem!1))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[87, 4641])).
% 1.97/2.14 tff(4643,plain,
% 1.97/2.14 (b(s(s(elem!1)), s(elem!1))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[4642, 4640])).
% 1.97/2.14 tff(4644,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(4645,plain,
% 1.97/2.14 (((~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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(4646,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[4645])).
% 1.97/2.14 tff(4647,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[4646, 4644])).
% 1.97/2.14 tff(4648,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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)))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(4649,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[4648, 4647])).
% 1.97/2.14 tff(4650,plain,
% 1.97/2.14 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4649, 97, 4448, 4447])).
% 1.97/2.14 tff(4651,plain,
% 1.97/2.14 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4650, 4643])).
% 1.97/2.14 tff(4652,plain,
% 1.97/2.14 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1484, 4651, 1432])).
% 1.97/2.14 tff(4653,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1)), s(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(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(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(4654,plain,
% 1.97/2.14 (((~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(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(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(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(4655,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(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(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[4654])).
% 1.97/2.14 tff(4656,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(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(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[4655, 4653])).
% 1.97/2.14 tff(4657,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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)))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(4658,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[4657, 4656])).
% 1.97/2.14 tff(4659,plain,
% 1.97/2.14 ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4658, 97, 4448, 4447])).
% 1.97/2.14 tff(4660,plain,
% 1.97/2.14 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4659, 4643])).
% 1.97/2.14 tff(4661,plain,
% 1.97/2.14 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1631, 4660, 1508])).
% 1.97/2.14 tff(4662,plain,
% 1.97/2.14 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(4663,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[4662])).
% 1.97/2.14 tff(4664,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[4663, 1589])).
% 1.97/2.14 tff(4665,plain,
% 1.97/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(4666,plain,
% 1.97/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[4665, 4664])).
% 1.97/2.14 tff(4667,plain,
% 1.97/2.14 ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4666, 155, 1813, 1522])).
% 1.97/2.14 tff(4668,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4667, 1521, 1906])).
% 1.97/2.14 tff(4669,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(z)))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(4670,plain,
% 1.97/2.14 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4669, 4661, 1520, 1393, 4652])).
% 1.97/2.14 tff(4671,plain,
% 1.97/2.14 (b(s(z), s(s(s(s(elem!1)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[280, 4670])).
% 1.97/2.14 tff(4672,plain,
% 1.97/2.14 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[4671, 1517])).
% 1.97/2.14 tff(4673,plain,
% 1.97/2.14 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4465, 824, 193, 87, 126, 1393, 81, 729])).
% 1.97/2.14 tff(4674,plain,
% 1.97/2.14 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[486, 4673, 1418])).
% 1.97/2.14 tff(4675,plain,
% 1.97/2.14 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1623, 97, 4674, 4448, 4447])).
% 1.97/2.14 tff(4676,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4675, 4672])).
% 1.97/2.14 tff(4677,plain,((~r(s(s(s(s(elem!1)))), z)) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(4678,plain,
% 1.97/2.14 (~r(s(s(s(s(elem!1)))), z)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4677, 4614, 4638, 4318, 87, 4302, 81, 4300])).
% 1.97/2.14 tff(4679,plain,
% 1.97/2.14 (b(s(s(s(s(elem!1)))), z)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[842, 4678])).
% 1.97/2.14 tff(4680,plain,
% 1.97/2.14 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[884, 4679, 83, 4592])).
% 1.97/2.14 tff(4681,plain,
% 1.97/2.14 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[452, 4680])).
% 1.97/2.14 tff(4682,plain,
% 1.97/2.14 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1822, 4681, 4614])).
% 1.97/2.14 tff(4683,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(4684,plain,
% 1.97/2.15 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(4685,plain,
% 1.97/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[4684])).
% 1.97/2.15 tff(4686,plain,
% 1.97/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[4685, 4683])).
% 1.97/2.15 tff(4687,plain,
% 1.97/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(4688,plain,
% 1.97/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[4687, 4686])).
% 1.97/2.15 tff(4689,plain,
% 1.97/2.15 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4688, 155, 4682, 4630, 4627])).
% 1.97/2.15 tff(4690,plain,
% 1.97/2.15 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[4635])).
% 1.97/2.15 tff(4691,plain,
% 1.97/2.15 (z = elem!1),
% 1.97/2.15 inference(transitivity,[status(thm)],[1443, 4690, 85])).
% 1.97/2.15 tff(4692,plain,
% 1.97/2.15 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[4691])).
% 1.97/2.15 tff(4693,plain,
% 1.97/2.15 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[4631])).
% 1.97/2.15 tff(4694,plain,
% 1.97/2.15 (b(z, s(s(elem!1)))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[4592, 4693])).
% 1.97/2.15 tff(4695,plain,
% 1.97/2.15 (b(elem!1, s(s(elem!1)))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[4694, 4692])).
% 1.97/2.15 tff(4696,plain,
% 1.97/2.15 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4474, 4679, 4691])).
% 1.97/2.15 tff(4697,plain,
% 1.97/2.15 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.97/2.15 inference(monotonicity,[status(thm)],[4691])).
% 1.97/2.15 tff(4698,plain,
% 1.97/2.15 (b(s(s(s(elem!1))), elem!1)),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[4302, 4697])).
% 1.97/2.15 tff(4699,plain,
% 1.97/2.15 (((~![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(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(4700,plain,
% 1.97/2.15 (((~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(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(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(4701,plain,
% 1.97/2.15 (((~![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(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(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(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[4700])).
% 1.97/2.15 tff(4702,plain,
% 1.97/2.15 (((~![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(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(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(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[4701, 4699])).
% 1.97/2.15 tff(4703,plain,
% 1.97/2.15 ((~![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(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(4704,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[4703, 4702])).
% 1.97/2.15 tff(4705,plain,
% 1.97/2.15 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4704, 97, 4698, 4696, 4695])).
% 1.97/2.15 tff(4706,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[821, 4705, 4689, 4619])).
% 1.97/2.15 tff(4707,plain,((~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(4708,plain,
% 1.97/2.15 (~b(s(s(z)), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4707, 125, 81, 3, 87])).
% 1.97/2.15 tff(4709,plain,
% 1.97/2.15 (r(s(s(z)), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[625, 4708])).
% 1.97/2.15 tff(4710,plain,
% 1.97/2.15 (~r(z, s(s(z)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2054, 4709, 81, 3])).
% 1.97/2.15 tff(4711,plain,
% 1.97/2.15 (b(z, s(s(z)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[222, 4710])).
% 1.97/2.15 tff(4712,plain,
% 1.97/2.15 (((~![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(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(4713,plain,
% 1.97/2.15 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), 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(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(4714,plain,
% 1.97/2.15 (((~![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(z)), s(z))) | (~b(s(s(z)), 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(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[4713])).
% 1.97/2.15 tff(4715,plain,
% 1.97/2.15 (((~![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(z)), s(z))) | (~b(s(s(z)), 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(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.97/2.15 inference(transitivity,[status(thm)],[4714, 4712])).
% 1.97/2.15 tff(4716,plain,
% 1.97/2.15 ((~![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(z)), s(z))) | (~b(s(s(z)), 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)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(4717,plain,
% 1.97/2.15 ((~![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(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[4716, 4715])).
% 1.97/2.15 tff(4718,plain,
% 1.97/2.15 (~b(s(s(s(z))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4717, 97, 204, 87, 1331])).
% 1.97/2.15 tff(4719,plain,
% 1.97/2.15 (r(s(s(s(z))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[402, 4718])).
% 1.97/2.15 tff(4720,plain,
% 1.97/2.15 (((~![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(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(4721,plain,
% 1.97/2.15 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(4722,plain,
% 1.97/2.15 (((~![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(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[4721])).
% 1.97/2.15 tff(4723,plain,
% 1.97/2.15 (((~![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(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[4722, 4720])).
% 1.97/2.15 tff(4724,plain,
% 1.97/2.15 ((~![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(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(4725,plain,
% 1.97/2.15 ((~![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(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[4724, 4723])).
% 1.97/2.15 tff(4726,plain,
% 1.97/2.15 (~b(z, s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4725, 97, 204, 87, 1331])).
% 1.97/2.15 tff(4727,plain,
% 1.97/2.15 (r(z, s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1318, 4726])).
% 1.97/2.15 tff(4728,plain,
% 1.97/2.15 (~r(s(z), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1308, 4727, 4719, 81])).
% 1.97/2.15 tff(4729,plain,
% 1.97/2.15 (b(s(z), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[253, 4728])).
% 1.97/2.15 tff(4730,plain,
% 1.97/2.15 (~r(s(s(s(z))), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4334, 155, 729, 81, 4719])).
% 1.97/2.15 tff(4731,plain,
% 1.97/2.15 (b(s(s(s(z))), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1358, 4730])).
% 1.97/2.15 tff(4732,plain,
% 1.97/2.15 (((~![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(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(4733,plain,
% 1.97/2.15 (((~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(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(4734,plain,
% 1.97/2.15 (((~![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(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(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[4733])).
% 1.97/2.15 tff(4735,plain,
% 1.97/2.15 (((~![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(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(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[4734, 4732])).
% 1.97/2.15 tff(4736,plain,
% 1.97/2.15 ((~![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(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)))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(4737,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[4736, 4735])).
% 1.97/2.15 tff(4738,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4737, 97, 87, 4731, 1331, 4729])).
% 1.97/2.15 tff(4739,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(4740,plain,
% 1.97/2.15 (~b(s(s(s(z))), s(s(z)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4739, 4711, 4300, 81, 87])).
% 1.97/2.15 tff(4741,plain,
% 1.97/2.15 (r(s(s(s(z))), s(s(z)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[421, 4740])).
% 1.97/2.15 tff(4742,plain,
% 1.97/2.15 (~r(z, s(s(s(elem!1))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[771, 225, 4300, 125])).
% 1.97/2.15 tff(4743,plain,
% 1.97/2.15 (~b(z, s(s(s(elem!1))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[659, 225, 81, 4709, 87, 3])).
% 1.97/2.15 tff(4744,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[590, 4743, 4742])).
% 1.97/2.15 tff(4745,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(4746,plain,
% 1.97/2.15 (~r(s(z), s(s(s(elem!1))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4745, 125, 87, 3, 81])).
% 1.97/2.15 tff(4747,plain,
% 1.97/2.15 (b(s(z), s(s(s(elem!1))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[181, 4746])).
% 1.97/2.15 tff(4748,plain,
% 1.97/2.15 (((~![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(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(4749,plain,
% 1.97/2.15 (((~b(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(s(elem!1)))), 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(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(4750,plain,
% 1.97/2.15 (((~![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(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(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[4749])).
% 1.97/2.15 tff(4751,plain,
% 1.97/2.15 (((~![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(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(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[4750, 4748])).
% 1.97/2.15 tff(4752,plain,
% 1.97/2.15 ((~![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(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(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(4753,plain,
% 1.97/2.15 ((~![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(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[4752, 4751])).
% 1.97/2.15 tff(4754,plain,
% 1.97/2.15 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4753, 97, 193, 4453, 1360])).
% 1.97/2.15 tff(4755,plain,
% 1.97/2.15 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1036, 97, 193, 4453, 87])).
% 1.97/2.15 tff(4756,plain,
% 1.97/2.15 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[452, 4755])).
% 1.97/2.15 tff(4757,plain,
% 1.97/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(4758,plain,
% 1.97/2.15 (((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(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(z)))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(4759,plain,
% 1.97/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(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(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[4758])).
% 1.97/2.15 tff(4760,plain,
% 1.97/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(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(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[4759, 4757])).
% 1.97/2.15 tff(4761,plain,
% 1.97/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(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(z))))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(4762,plain,
% 1.97/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[4761, 4760])).
% 1.97/2.16 tff(4763,plain,
% 1.97/2.16 ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4762, 155, 824, 645, 1960])).
% 1.97/2.16 tff(4764,plain,
% 1.97/2.16 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4763, 4756])).
% 1.97/2.16 tff(4765,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[384, 53, 4764, 4754, 286])).
% 1.97/2.16 tff(4766,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(4767,plain,
% 1.97/2.16 (~b(s(s(s(z))), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4766, 824, 4741, 4747, 4709, 87, 81, 4300])).
% 1.97/2.16 tff(4768,plain,
% 1.97/2.16 (r(s(s(s(z))), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1358, 4767])).
% 1.97/2.16 tff(4769,plain,
% 1.97/2.16 ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4368, 155, 4300, 3, 4741])).
% 1.97/2.16 tff(4770,plain,
% 1.97/2.16 (~r(s(s(s(z))), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4769, 4768])).
% 1.97/2.16 tff(4771,plain,
% 1.97/2.16 (b(s(s(s(z))), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[402, 4770])).
% 1.97/2.16 tff(4772,plain,
% 1.97/2.16 (((~![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))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(4773,plain,
% 1.97/2.16 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(4774,plain,
% 1.97/2.16 (((~![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(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[4773])).
% 1.97/2.16 tff(4775,plain,
% 1.97/2.16 (((~![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(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[4774, 4772])).
% 1.97/2.16 tff(4776,plain,
% 1.97/2.16 ((~![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(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(4777,plain,
% 1.97/2.16 ((~![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))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[4776, 4775])).
% 1.97/2.16 tff(4778,plain,
% 1.97/2.16 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4777, 97, 4302, 4711, 4771])).
% 1.97/2.16 tff(4779,plain,
% 1.97/2.16 ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4258, 155, 125, 3, 4741])).
% 1.97/2.16 tff(4780,plain,
% 1.97/2.16 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4779, 4768])).
% 1.97/2.16 tff(4781,plain,
% 1.97/2.16 ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1678, 53, 4780])).
% 1.97/2.16 tff(4782,plain,
% 1.97/2.16 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4781, 4778])).
% 1.97/2.16 tff(4783,plain,
% 1.97/2.16 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[4782])).
% 1.97/2.16 tff(4784,plain,
% 1.97/2.16 (s(s(z)) = s(s(elem!1))),
% 1.97/2.16 inference(transitivity,[status(thm)],[73, 4783, 19])).
% 1.97/2.16 tff(4785,plain,
% 1.97/2.16 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[4784])).
% 1.97/2.16 tff(4786,plain,
% 1.97/2.16 (s(z) = s(elem!1)),
% 1.97/2.16 inference(transitivity,[status(thm)],[24, 4785, 29])).
% 1.97/2.16 tff(4787,plain,
% 1.97/2.16 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[4786, 4784])).
% 1.97/2.16 tff(4788,plain,
% 1.97/2.16 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 1.97/2.16 inference(symmetry,[status(thm)],[4787])).
% 1.97/2.16 tff(4789,plain,
% 1.97/2.16 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(z), s(s(z))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[4788])).
% 1.97/2.16 tff(4790,plain,
% 1.97/2.16 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[4784])).
% 1.97/2.16 tff(4791,plain,
% 1.97/2.16 ((~r(s(elem!1), s(s(z)))) <=> (~r(s(elem!1), s(s(elem!1))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[4790])).
% 1.97/2.16 tff(4792,plain,
% 1.97/2.16 (~r(s(elem!1), s(s(z)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4677, 4782, 824, 4747, 87, 4302, 81, 4300])).
% 1.97/2.16 tff(4793,plain,
% 1.97/2.16 (~r(s(elem!1), s(s(elem!1)))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[4792, 4791])).
% 1.97/2.16 tff(4794,plain,
% 1.97/2.16 (~r(s(z), s(s(z)))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[4793, 4789])).
% 1.97/2.16 tff(4795,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3, 4794])).
% 1.97/2.16 tff(4796,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(4797,plain,
% 1.97/2.16 (~r(s(s(s(s(elem!1)))), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4796, 125, 87, 81, 3])).
% 1.97/2.16 tff(4798,plain,
% 1.97/2.16 (b(s(s(s(s(elem!1)))), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[842, 4797])).
% 1.97/2.16 tff(4799,plain,
% 1.97/2.16 (((~![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(z)), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, 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(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(4800,plain,
% 1.97/2.16 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(4801,plain,
% 1.97/2.16 (((~![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(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, 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(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[4800])).
% 1.97/2.16 tff(4802,plain,
% 1.97/2.16 (((~![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(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, 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(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[4801, 4799])).
% 1.97/2.16 tff(4803,plain,
% 1.97/2.16 ((~![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(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(4804,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[4803, 4802])).
% 1.97/2.16 tff(4805,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4804, 97, 204, 876, 441, 87])).
% 1.97/2.16 tff(4806,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(4807,plain,
% 1.97/2.16 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4806, 4711, 4798, 87])).
% 1.97/2.16 tff(4808,plain,
% 1.97/2.16 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[452, 4807])).
% 1.97/2.16 tff(4809,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(4810,plain,
% 1.97/2.16 (((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(4811,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[4810])).
% 1.97/2.16 tff(4812,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[4811, 4809])).
% 1.97/2.16 tff(4813,plain,
% 1.97/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(4814,plain,
% 1.97/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[4813, 4812])).
% 1.97/2.16 tff(4815,plain,
% 1.97/2.16 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4814, 155, 81, 4709, 4808, 3])).
% 1.97/2.16 tff(4816,plain,
% 1.97/2.16 (b(s(z), s(s(s(s(elem!1)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[280, 4815])).
% 1.97/2.16 tff(4817,plain,
% 1.97/2.16 (((~![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))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(4818,plain,
% 1.97/2.16 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(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))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(4819,plain,
% 1.97/2.16 (((~![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(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(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(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[4818])).
% 1.97/2.16 tff(4820,plain,
% 1.97/2.16 (((~![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(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(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(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[4819, 4817])).
% 1.97/2.16 tff(4821,plain,
% 1.97/2.16 ((~![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(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(4822,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[4821, 4820])).
% 1.97/2.16 tff(4823,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4822, 97, 193, 126, 255, 339, 876, 87])).
% 1.97/2.16 tff(4824,plain,((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(4825,plain,
% 1.97/2.16 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4824, 4816, 87, 4747, 4798, 4302])).
% 1.97/2.16 tff(4826,plain,
% 1.97/2.16 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[336, 4825])).
% 1.97/2.16 tff(4827,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(4828,plain,
% 1.97/2.16 (((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(4829,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[4828])).
% 1.97/2.16 tff(4830,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[4829, 4827])).
% 1.97/2.16 tff(4831,plain,
% 1.97/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(4832,plain,
% 1.97/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[4831, 4830])).
% 1.97/2.16 tff(4833,plain,
% 1.97/2.16 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4832, 155, 4826, 4808, 4741])).
% 1.97/2.16 tff(4834,plain,
% 1.97/2.16 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(4835,plain,
% 1.97/2.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(4836,plain,
% 1.97/2.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[4835, 4834])).
% 1.97/2.17 tff(4837,plain,
% 1.97/2.17 ((s(s(s(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4836, 53, 4833])).
% 1.97/2.17 tff(4838,plain,
% 1.97/2.17 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4837, 4298])).
% 1.97/2.17 tff(4839,plain,
% 1.97/2.17 (~r(s(z), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2294, 155, 81, 4709, 3, 4741])).
% 1.97/2.17 tff(4840,plain,
% 1.97/2.17 (b(s(z), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[253, 4839])).
% 1.97/2.17 tff(4841,plain,
% 1.97/2.17 (((~![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(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(4842,plain,
% 1.97/2.17 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(4843,plain,
% 1.97/2.17 (((~![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(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z)))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[4842])).
% 1.97/2.17 tff(4844,plain,
% 1.97/2.17 (((~![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(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[4843, 4841])).
% 1.97/2.17 tff(4845,plain,
% 1.97/2.17 ((~![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(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(4846,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z)))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[4845, 4844])).
% 1.97/2.17 tff(4847,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4846, 97, 4816, 4798, 4840, 4838])).
% 1.97/2.17 tff(4848,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(4849,plain,
% 1.97/2.17 (~r(s(s(s(elem!1))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4848, 87, 81, 3])).
% 1.97/2.17 tff(4850,plain,
% 1.97/2.17 (b(s(s(s(elem!1))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[493, 4849])).
% 1.97/2.17 tff(4851,plain,
% 1.97/2.17 (((~![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(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(4852,plain,
% 1.97/2.17 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(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(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(4853,plain,
% 1.97/2.17 (((~![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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(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(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[4852])).
% 1.97/2.17 tff(4854,plain,
% 1.97/2.17 (((~![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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(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(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[4853, 4851])).
% 1.97/2.17 tff(4855,plain,
% 1.97/2.17 ((~![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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(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))))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(4856,plain,
% 1.97/2.17 ((~![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(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[4855, 4854])).
% 1.97/2.17 tff(4857,plain,
% 1.97/2.17 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4856, 97, 1139, 255, 87])).
% 1.97/2.17 tff(4858,plain,
% 1.97/2.17 (r(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[143, 4857])).
% 1.97/2.17 tff(4859,plain,
% 1.97/2.17 (((~![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(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(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(4860,plain,
% 1.97/2.17 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(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(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(s(s(elem!1)))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(4861,plain,
% 1.97/2.17 (((~![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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(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(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(s(s(elem!1))))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[4860])).
% 1.97/2.17 tff(4862,plain,
% 1.97/2.17 (((~![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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(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(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(s(s(elem!1)))))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[4861, 4859])).
% 1.97/2.17 tff(4863,plain,
% 1.97/2.17 ((~![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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(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)))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(4864,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[4863, 4862])).
% 1.97/2.17 tff(4865,plain,
% 1.97/2.17 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4864, 97, 1139, 255, 87])).
% 1.97/2.17 tff(4866,plain,
% 1.97/2.17 (r(s(s(s(elem!1))), s(s(z)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[58, 4865])).
% 1.97/2.17 tff(4867,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[161, 155, 3, 225, 4866, 4858])).
% 1.97/2.17 tff(4868,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(4869,plain,
% 1.97/2.17 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4868, 225, 3, 4850, 87])).
% 1.97/2.17 tff(4870,plain,
% 1.97/2.17 (r(s(z), s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[280, 4869])).
% 1.97/2.17 tff(4871,plain,
% 1.97/2.17 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[234, 226, 3, 225, 81])).
% 1.97/2.17 tff(4872,plain,
% 1.97/2.17 (b(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[143, 4871])).
% 1.97/2.17 tff(4873,plain,
% 1.97/2.17 (~r(z, s(s(z)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[296, 2596, 3, 225, 81])).
% 1.97/2.17 tff(4874,plain,
% 1.97/2.17 (b(z, s(s(z)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[222, 4873])).
% 1.97/2.17 tff(4875,plain,
% 1.97/2.17 (~r(z, s(s(z)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[296, 288, 3, 225, 81])).
% 1.97/2.17 tff(4876,plain,
% 1.97/2.17 (b(z, s(s(z)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[222, 4875])).
% 1.97/2.17 tff(4877,plain,
% 1.97/2.17 (~b(s(s(s(z))), s(s(z)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4739, 4876, 4300, 81, 87])).
% 1.97/2.17 tff(4878,plain,
% 1.97/2.17 (r(s(s(s(z))), s(s(z)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[421, 4877])).
% 1.97/2.17 tff(4879,plain,
% 1.97/2.17 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4414, 824, 81, 4300])).
% 1.97/2.17 tff(4880,plain,
% 1.97/2.17 (b(s(s(s(s(elem!1)))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[511, 4879])).
% 1.97/2.17 tff(4881,plain,
% 1.97/2.17 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(4882,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[4881])).
% 1.97/2.17 tff(4883,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.97/2.17 inference(transitivity,[status(thm)],[4882, 1193])).
% 1.97/2.17 tff(4884,plain,
% 1.97/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z)))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(4885,plain,
% 1.97/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[4884, 4883])).
% 1.97/2.17 tff(4886,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4885, 155, 287, 463, 81, 824])).
% 1.97/2.17 tff(4887,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(4888,plain,
% 1.97/2.17 (~r(z, s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4887, 824, 81, 287])).
% 1.97/2.17 tff(4889,plain,
% 1.97/2.17 (b(z, s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1093, 4888])).
% 1.97/2.17 tff(4890,plain,
% 1.97/2.17 (~r(s(s(z)), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[659, 124, 81, 225, 87, 3])).
% 1.97/2.17 tff(4891,plain,
% 1.97/2.17 (b(s(s(z)), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[625, 4890])).
% 1.97/2.17 tff(4892,plain,
% 1.97/2.17 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[669, 4891, 372, 513])).
% 1.97/2.17 tff(4893,plain,
% 1.97/2.17 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[212, 124, 204, 87])).
% 1.97/2.17 tff(4894,plain,
% 1.97/2.17 (r(s(s(s(elem!1))), s(s(z)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[58, 4893])).
% 1.97/2.17 tff(4895,plain,
% 1.97/2.17 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[317, 4894, 225, 287, 3])).
% 1.97/2.17 tff(4896,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[336, 4895, 4892])).
% 1.97/2.17 tff(4897,plain,((~b(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(4898,plain,
% 1.97/2.17 (~b(z, s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4897, 4889, 287, 3, 225, 4880, 4876, 87, 81])).
% 1.97/2.17 tff(4899,plain,
% 1.97/2.17 (r(z, s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[590, 4898])).
% 1.97/2.17 tff(4900,plain,
% 1.97/2.17 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[578, 570, 81, 225, 287])).
% 1.97/2.17 tff(4901,plain,
% 1.97/2.17 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4141, 570, 4138])).
% 1.97/2.17 tff(4902,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[486, 4901, 4900, 2718])).
% 1.97/2.17 tff(4903,plain,((~r(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(4904,plain,
% 1.97/2.17 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4903, 4899, 4888, 81, 225, 287])).
% 1.97/2.17 tff(4905,plain,
% 1.97/2.17 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2141, 4904, 4850, 4880])).
% 1.97/2.17 tff(4906,plain,
% 1.97/2.17 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[336, 4905])).
% 1.97/2.17 tff(4907,plain,
% 1.97/2.17 (~r(s(z), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2171, 4906, 4878, 3, 287])).
% 1.97/2.17 tff(4908,plain,
% 1.97/2.17 (b(s(z), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[253, 4907])).
% 1.97/2.17 tff(4909,plain,
% 1.97/2.17 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[832, 4899, 288, 824])).
% 1.97/2.17 tff(4910,plain,
% 1.97/2.17 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4141, 4899, 4888])).
% 1.97/2.17 tff(4911,plain,
% 1.97/2.17 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[523, 4910])).
% 1.97/2.17 tff(4912,plain,
% 1.97/2.17 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[821, 4911, 4909])).
% 1.97/2.17 tff(4913,plain,
% 1.97/2.17 (((~![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(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), 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(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(4914,plain,
% 1.97/2.17 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(4915,plain,
% 1.97/2.17 (((~![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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[4914])).
% 1.97/2.17 tff(4916,plain,
% 1.97/2.17 (((~![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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[4915, 4913])).
% 1.97/2.17 tff(4917,plain,
% 1.97/2.17 ((~![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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(4918,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[4917, 4916])).
% 1.97/2.17 tff(4919,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4918, 97, 4850, 4912, 4880, 4908])).
% 1.97/2.17 tff(4920,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(4921,plain,
% 1.97/2.17 (~r(s(s(s(s(elem!1)))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4920, 287, 3, 81, 225, 2596, 87])).
% 1.97/2.17 tff(4922,plain,
% 1.97/2.17 (b(s(s(s(s(elem!1)))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[842, 4921])).
% 1.97/2.17 tff(4923,plain,
% 1.97/2.17 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4806, 4922, 4874, 87])).
% 1.97/2.17 tff(4924,plain,
% 1.97/2.17 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[452, 4923])).
% 1.97/2.17 tff(4925,plain,
% 1.97/2.17 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1178, 4924, 3, 225, 287])).
% 1.97/2.17 tff(4926,plain,
% 1.97/2.17 (b(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[143, 4925])).
% 1.97/2.17 tff(4927,plain,
% 1.97/2.17 (~b(s(s(s(z))), s(s(z)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4739, 4874, 4300, 81, 87])).
% 1.97/2.17 tff(4928,plain,
% 1.97/2.17 (r(s(s(s(z))), s(s(z)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[421, 4927])).
% 1.97/2.17 tff(4929,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[469, 155, 287, 463, 81, 288, 225])).
% 1.97/2.17 tff(4930,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(4931,plain,
% 1.97/2.17 (~r(z, s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4930, 287, 81, 2596, 225])).
% 1.97/2.17 tff(4932,plain,
% 1.97/2.17 (b(z, s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1093, 4931])).
% 1.97/2.17 tff(4933,plain,
% 1.97/2.17 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3434, 4922, 239])).
% 1.97/2.17 tff(4934,plain,
% 1.97/2.17 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[486, 2718, 472])).
% 1.97/2.17 tff(4935,plain,
% 1.97/2.17 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[924, 4934, 225, 287])).
% 1.97/2.17 tff(4936,plain,
% 1.97/2.17 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[821, 4935, 3701])).
% 1.97/2.17 tff(4937,plain,
% 1.97/2.17 (b(z, s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1093, 4138])).
% 1.97/2.17 tff(4938,plain,
% 1.97/2.17 (~r(z, s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4903, 2718, 4138, 81, 225, 287])).
% 1.97/2.17 tff(4939,plain,
% 1.97/2.17 (b(z, s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[590, 4938])).
% 1.97/2.17 tff(4940,plain,
% 1.97/2.17 (~r(s(s(z)), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[659, 4939, 81, 225, 87, 3])).
% 1.97/2.17 tff(4941,plain,
% 1.97/2.17 (b(s(s(z)), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[625, 4940])).
% 1.97/2.17 tff(4942,plain,
% 1.97/2.17 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1124, 4941, 4937, 4936])).
% 1.97/2.17 tff(4943,plain,
% 1.97/2.17 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[212, 4939, 204, 87])).
% 1.97/2.17 tff(4944,plain,
% 1.97/2.17 (r(s(s(s(elem!1))), s(s(z)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[58, 4943])).
% 1.97/2.17 tff(4945,plain,
% 1.97/2.17 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[317, 4944, 225, 287, 3])).
% 1.97/2.17 tff(4946,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[336, 4945, 4942])).
% 1.97/2.17 tff(4947,plain,(b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | r(z, s(s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(4948,plain,
% 1.97/2.17 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4947, 287, 225, 3, 4874, 87, 81, 4931, 4933])).
% 1.97/2.17 tff(4949,plain,
% 1.97/2.17 (~b(z, s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3793, 4948, 4922, 4932])).
% 1.97/2.17 tff(4950,plain,
% 1.97/2.17 (r(z, s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[590, 4949])).
% 1.97/2.17 tff(4951,plain,
% 1.97/2.17 (~r(s(s(z)), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2064, 4950, 225, 3, 81])).
% 1.97/2.17 tff(4952,plain,
% 1.97/2.17 (b(s(s(z)), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[625, 4951])).
% 1.97/2.17 tff(4953,plain,
% 1.97/2.17 (((~![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(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(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(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(4954,plain,
% 1.97/2.17 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(4955,plain,
% 1.97/2.17 (((~![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(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(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(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[4954])).
% 1.97/2.17 tff(4956,plain,
% 1.97/2.17 (((~![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(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(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(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.97/2.17 inference(transitivity,[status(thm)],[4955, 4953])).
% 1.97/2.17 tff(4957,plain,
% 1.97/2.17 ((~![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(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(4958,plain,
% 1.97/2.17 ((~![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(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[4957, 4956])).
% 1.97/2.17 tff(4959,plain,
% 1.97/2.17 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4958, 97, 4932, 4952, 4922])).
% 1.97/2.17 tff(4960,plain,
% 1.97/2.17 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[336, 4959])).
% 1.97/2.17 tff(4961,plain,
% 1.97/2.17 (~r(s(z), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2171, 4960, 4928, 3, 287])).
% 1.97/2.17 tff(4962,plain,
% 1.97/2.17 (b(s(z), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[253, 4961])).
% 1.97/2.18 tff(4963,plain,
% 1.97/2.18 (((~![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(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(4964,plain,
% 1.97/2.18 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(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(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(4965,plain,
% 1.97/2.18 (((~![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(z), s(s(s(z))))) | (~b(s(z), s(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(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[4964])).
% 1.97/2.18 tff(4966,plain,
% 1.97/2.18 (((~![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(z), s(s(s(z))))) | (~b(s(z), s(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(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[4965, 4963])).
% 1.97/2.18 tff(4967,plain,
% 1.97/2.18 ((~![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(z), s(s(s(z))))) | (~b(s(z), s(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))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(4968,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[4967, 4966])).
% 1.97/2.18 tff(4969,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4968, 97, 4850, 87, 4962, 4926])).
% 1.97/2.18 tff(4970,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(4971,plain,
% 1.97/2.18 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4970, 239, 3, 225, 81, 87])).
% 1.97/2.18 tff(4972,plain,
% 1.97/2.18 (b(s(z), s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[280, 4971])).
% 1.97/2.18 tff(4973,plain,
% 1.97/2.18 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4856, 97, 4850, 4972, 87])).
% 1.97/2.18 tff(4974,plain,
% 1.97/2.18 (r(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[143, 4973])).
% 1.97/2.18 tff(4975,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(4976,plain,
% 1.97/2.18 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(4977,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[4976])).
% 1.97/2.18 tff(4978,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[4977, 4975])).
% 1.97/2.18 tff(4979,plain,
% 1.97/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(4980,plain,
% 1.97/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[4979, 4978])).
% 1.97/2.18 tff(4981,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4980, 155, 81, 2596, 3, 225, 4974])).
% 1.97/2.18 tff(4982,plain,(b(s(s(s(elem!1))), z) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(4983,plain,
% 1.97/2.18 (b(s(s(s(elem!1))), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4982, 225, 3, 81, 87])).
% 1.97/2.18 tff(4984,plain,
% 1.97/2.18 (~r(s(s(z)), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2054, 226, 81, 3])).
% 1.97/2.18 tff(4985,plain,
% 1.97/2.18 (b(s(s(z)), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[625, 4984])).
% 1.97/2.18 tff(4986,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[985, 97, 126, 124, 83, 127])).
% 1.97/2.18 tff(4987,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(4988,plain,
% 1.97/2.18 (~b(z, s(s(s(elem!1))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4987, 4985, 4983, 4872])).
% 1.97/2.18 tff(4989,plain,
% 1.97/2.18 (r(z, s(s(s(elem!1))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[590, 4988])).
% 1.97/2.18 tff(4990,plain,
% 1.97/2.18 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1954, 226, 81, 4870, 3])).
% 1.97/2.18 tff(4991,plain,
% 1.97/2.18 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[336, 4990])).
% 1.97/2.18 tff(4992,plain,
% 1.97/2.18 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[486, 2718, 4900])).
% 1.97/2.18 tff(4993,plain,
% 1.97/2.18 (~(s(s(s(z))) = elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1742, 4992])).
% 1.97/2.18 tff(4994,plain,
% 1.97/2.18 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[349, 4992])).
% 1.97/2.18 tff(4995,plain,
% 1.97/2.18 (s(s(s(s(elem!1)))) = elem!1),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1734, 4994])).
% 1.97/2.18 tff(4996,plain,
% 1.97/2.18 (r(z, s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4903, 2718, 570, 81, 225, 287])).
% 1.97/2.18 tff(4997,plain,
% 1.97/2.18 (~r(s(s(s(s(elem!1)))), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4887, 4996, 81, 287])).
% 1.97/2.18 tff(4998,plain,
% 1.97/2.18 (b(s(s(s(s(elem!1)))), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[842, 4997])).
% 1.97/2.18 tff(4999,plain,
% 1.97/2.18 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3802, 4996, 287, 729, 226])).
% 1.97/2.18 tff(5000,plain,
% 1.97/2.18 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[452, 4999])).
% 1.97/2.18 tff(5001,plain,
% 1.97/2.18 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3198, 97, 339, 441, 1331])).
% 1.97/2.18 tff(5002,plain,
% 1.97/2.18 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[384, 53, 5001, 286])).
% 1.97/2.18 tff(5003,plain,
% 1.97/2.18 (~r(z, s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2449, 5002, 3718, 463])).
% 1.97/2.18 tff(5004,plain,
% 1.97/2.18 (b(z, s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1318, 5003])).
% 1.97/2.18 tff(5005,plain,
% 1.97/2.18 (((~![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(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(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(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(5006,plain,
% 1.97/2.18 (((~b(z, s(s(s(z))))) | (~b(z, s(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(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(5007,plain,
% 1.97/2.18 (((~![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(s(z))))) | (~b(z, s(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(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[5006])).
% 1.97/2.18 tff(5008,plain,
% 1.97/2.18 (((~![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(s(z))))) | (~b(z, s(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(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[5007, 5005])).
% 1.97/2.18 tff(5009,plain,
% 1.97/2.18 ((~![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(s(z))))) | (~b(z, s(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)))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(5010,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[5009, 5008])).
% 1.97/2.18 tff(5011,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[5010, 97, 83, 876, 441, 5004])).
% 1.97/2.18 tff(5012,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(s(s(z))) = elem!1) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(5013,plain,
% 1.97/2.18 (~b(s(s(s(z))), s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[5012, 5000, 4998, 4996, 4995, 4993, 339, 83])).
% 1.97/2.18 tff(5014,plain,
% 1.97/2.18 (r(s(s(s(z))), s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[421, 5013])).
% 1.97/2.18 tff(5015,plain,
% 1.97/2.18 (b(s(s(s(s(elem!1)))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1154, 4992, 1139])).
% 1.97/2.18 tff(5016,plain,
% 1.97/2.18 (((~![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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), 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(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(5017,plain,
% 1.97/2.18 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(5018,plain,
% 1.97/2.18 (((~![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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[5017])).
% 1.97/2.18 tff(5019,plain,
% 1.97/2.18 (((~![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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[5018, 5016])).
% 1.97/2.18 tff(5020,plain,
% 1.97/2.18 ((~![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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(5021,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[5020, 5019])).
% 1.97/2.18 tff(5022,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[5021, 97, 339, 513, 87, 86])).
% 1.97/2.18 tff(5023,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(5024,plain,
% 1.97/2.18 (~b(s(z), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[5023, 5015, 339, 87])).
% 1.97/2.18 tff(5025,plain,
% 1.97/2.18 (r(s(z), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[253, 5024])).
% 1.97/2.18 tff(5026,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(5027,plain,
% 1.97/2.18 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(5028,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[5027])).
% 1.97/2.18 tff(5029,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[5028, 5026])).
% 1.97/2.18 tff(5030,plain,
% 1.97/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(5031,plain,
% 1.97/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[5030, 5029])).
% 1.97/2.18 tff(5032,plain,
% 1.97/2.18 (~r(z, s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[5031, 155, 729, 226, 5025, 5014])).
% 1.97/2.18 tff(5033,plain,
% 1.97/2.18 (b(z, s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1318, 5032])).
% 1.97/2.18 tff(5034,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[5010, 97, 83, 4998, 5000, 5033])).
% 1.97/2.18 tff(5035,plain,(b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(5036,plain,
% 1.97/2.18 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[5035, 4985, 4300, 226, 4991, 87, 4870, 4850, 81, 4989, 225])).
% 1.97/2.18 tff(5037,plain,
% 1.97/2.18 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2141, 5036, 4850, 4991])).
% 1.97/2.18 tff(5038,plain,
% 1.97/2.18 (r(s(s(s(s(elem!1)))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[511, 5037])).
% 1.97/2.18 tff(5039,plain,
% 1.97/2.18 (~r(s(s(s(s(elem!1)))), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4414, 5038, 81, 4300])).
% 1.97/2.18 tff(5040,plain,
% 1.97/2.18 (b(s(s(s(s(elem!1)))), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[842, 5039])).
% 1.97/2.18 tff(5041,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(5042,plain,
% 1.97/2.19 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(5043,plain,
% 1.97/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[5042])).
% 1.97/2.19 tff(5044,plain,
% 1.97/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[5043, 5041])).
% 1.97/2.19 tff(5045,plain,
% 1.97/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(5046,plain,
% 1.97/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[5045, 5044])).
% 1.97/2.19 tff(5047,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5046, 155, 729, 287, 463, 495])).
% 1.97/2.19 tff(5048,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(5049,plain,
% 1.97/2.19 (~r(z, s(s(s(s(elem!1)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5048, 5038, 4300, 4870])).
% 1.97/2.19 tff(5050,plain,
% 1.97/2.19 (b(z, s(s(s(s(elem!1)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1093, 5049])).
% 1.97/2.19 tff(5051,plain,
% 1.97/2.19 (((~![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(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(5052,plain,
% 1.97/2.19 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(5053,plain,
% 1.97/2.19 (((~![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(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[5052])).
% 1.97/2.19 tff(5054,plain,
% 1.97/2.19 (((~![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(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.97/2.19 inference(transitivity,[status(thm)],[5053, 5051])).
% 1.97/2.19 tff(5055,plain,
% 1.97/2.19 ((~![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(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(5056,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[5055, 5054])).
% 1.97/2.19 tff(5057,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5056, 97, 126, 372, 473, 876])).
% 1.97/2.19 tff(5058,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(5059,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5058, 5050, 5040, 4983, 5036])).
% 1.97/2.19 tff(5060,plain,((~r(z, s(s(z)))) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(5061,plain,
% 1.97/2.19 (~r(z, s(s(z)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5060, 225, 87, 81, 3])).
% 1.97/2.19 tff(5062,plain,
% 1.97/2.19 (b(z, s(s(z)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[222, 5061])).
% 1.97/2.19 tff(5063,plain,
% 1.97/2.19 (~b(s(s(z)), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4567, 60, 4983, 5062])).
% 1.97/2.19 tff(5064,plain,
% 1.97/2.19 (r(s(s(z)), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[625, 5063])).
% 1.97/2.19 tff(5065,plain,
% 1.97/2.19 (~b(z, s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[212, 60, 5062, 87])).
% 1.97/2.19 tff(5066,plain,
% 1.97/2.19 (r(z, s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[590, 5065])).
% 1.97/2.19 tff(5067,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2064, 5066, 5064, 225, 3, 81])).
% 1.97/2.19 tff(5068,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(5069,plain,
% 1.97/2.19 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5068, 225, 3, 81, 87])).
% 1.97/2.19 tff(5070,plain,
% 1.97/2.19 (r(s(s(s(elem!1))), s(s(z)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[58, 5069])).
% 1.97/2.19 tff(5071,plain,
% 1.97/2.19 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[317, 5070, 225, 4870, 3])).
% 1.97/2.19 tff(5072,plain,
% 1.97/2.19 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[336, 5071])).
% 1.97/2.19 tff(5073,plain,
% 1.97/2.19 (~r(s(s(z)), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[653, 5070, 81, 225, 3])).
% 1.97/2.19 tff(5074,plain,
% 1.97/2.19 (b(s(s(z)), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[625, 5073])).
% 1.97/2.19 tff(5075,plain,
% 1.97/2.19 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4557, 97, 4983, 5062, 5074])).
% 1.97/2.19 tff(5076,plain,
% 1.97/2.19 (r(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[143, 5075])).
% 1.97/2.19 tff(5077,plain,
% 1.97/2.19 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2103, 5076, 3, 225, 4870])).
% 1.97/2.19 tff(5078,plain,
% 1.97/2.19 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2161, 5075, 5072])).
% 1.97/2.19 tff(5079,plain,
% 1.97/2.19 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[486, 5078, 5077])).
% 1.97/2.19 tff(5080,plain,
% 1.97/2.19 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2141, 5079, 4850, 5072])).
% 1.97/2.19 tff(5081,plain,
% 1.97/2.19 (r(s(s(s(s(elem!1)))), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[511, 5080])).
% 1.97/2.19 tff(5082,plain,
% 1.97/2.19 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1178, 5076, 3, 225, 4870])).
% 1.97/2.19 tff(5083,plain,
% 1.97/2.19 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[452, 5082])).
% 1.97/2.19 tff(5084,plain,
% 1.97/2.19 (~b(s(s(s(s(elem!1)))), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[884, 5083, 5062, 5074])).
% 1.97/2.19 tff(5085,plain,
% 1.97/2.19 (r(s(s(s(s(elem!1)))), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[842, 5084])).
% 1.97/2.19 tff(5086,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4414, 5085, 5081, 81, 4300])).
% 1.97/2.19 tff(5087,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(5088,plain,
% 1.97/2.19 (~r(s(z), s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5087, 87, 3, 81])).
% 1.97/2.19 tff(5089,plain,
% 1.97/2.19 (b(s(z), s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[181, 5088])).
% 1.97/2.19 tff(5090,plain,
% 1.97/2.19 (((~![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(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(5091,plain,
% 1.97/2.19 (((~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(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(5092,plain,
% 1.97/2.19 (((~![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(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(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[5091])).
% 1.97/2.19 tff(5093,plain,
% 1.97/2.19 (((~![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(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(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[5092, 5090])).
% 1.97/2.19 tff(5094,plain,
% 1.97/2.19 ((~![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(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))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(5095,plain,
% 1.97/2.19 ((~![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(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[5094, 5093])).
% 1.97/2.19 tff(5096,plain,
% 1.97/2.19 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5095, 97, 4850, 5089, 87])).
% 1.97/2.19 tff(5097,plain,
% 1.97/2.19 (r(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[143, 5096])).
% 1.97/2.19 tff(5098,plain,
% 1.97/2.19 (((~![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(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~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(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(5099,plain,
% 1.97/2.19 (((~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(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(5100,plain,
% 1.97/2.19 (((~![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(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(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[5099])).
% 1.97/2.19 tff(5101,plain,
% 1.97/2.19 (((~![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(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(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[5100, 5098])).
% 1.97/2.19 tff(5102,plain,
% 1.97/2.19 ((~![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(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)))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(5103,plain,
% 1.97/2.19 ((~![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(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[5102, 5101])).
% 1.97/2.19 tff(5104,plain,
% 1.97/2.19 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5103, 97, 4850, 5089, 87])).
% 1.97/2.19 tff(5105,plain,
% 1.97/2.19 (r(s(s(s(elem!1))), s(s(z)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[58, 5104])).
% 1.97/2.19 tff(5106,plain,
% 1.97/2.19 (~r(z, s(s(z)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2054, 645, 81, 3])).
% 1.97/2.19 tff(5107,plain,
% 1.97/2.19 (b(z, s(s(z)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[222, 5106])).
% 1.97/2.19 tff(5108,plain,
% 1.97/2.19 (~b(s(s(s(z))), s(s(z)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4739, 5107, 4300, 81, 87])).
% 1.97/2.19 tff(5109,plain,
% 1.97/2.19 (r(s(s(s(z))), s(s(z)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[421, 5108])).
% 1.97/2.19 tff(5110,plain,
% 1.97/2.19 (~r(s(z), s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2294, 155, 81, 645, 3, 5109])).
% 1.97/2.19 tff(5111,plain,
% 1.97/2.19 (b(s(z), s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[253, 5110])).
% 1.97/2.19 tff(5112,plain,
% 1.97/2.19 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1710, 5111, 4850, 5089])).
% 1.97/2.19 tff(5113,plain,
% 1.97/2.19 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4382, 155, 5105, 5097, 5109])).
% 1.97/2.19 tff(5114,plain,
% 1.97/2.19 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1678, 53, 5113, 5112])).
% 1.97/2.19 tff(5115,plain,
% 1.97/2.19 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[5114])).
% 1.97/2.19 tff(5116,plain,
% 1.97/2.19 (s(s(z)) = s(s(elem!1))),
% 1.97/2.19 inference(transitivity,[status(thm)],[73, 5115, 19])).
% 1.97/2.19 tff(5117,plain,
% 1.97/2.19 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[5116])).
% 1.97/2.19 tff(5118,plain,
% 1.97/2.19 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.97/2.19 inference(symmetry,[status(thm)],[5117])).
% 1.97/2.19 tff(5119,plain,
% 1.97/2.19 (s(elem!1) = s(z)),
% 1.97/2.19 inference(transitivity,[status(thm)],[30, 5118, 23])).
% 1.97/2.19 tff(5120,plain,
% 1.97/2.19 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[5119])).
% 1.97/2.19 tff(5121,plain,
% 1.97/2.19 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.97/2.19 inference(symmetry,[status(thm)],[5120])).
% 1.97/2.19 tff(5122,plain,
% 1.97/2.19 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[255, 5121])).
% 1.97/2.19 tff(5123,plain,
% 1.97/2.19 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[5119])).
% 1.97/2.19 tff(5124,plain,
% 1.97/2.19 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.97/2.19 inference(symmetry,[status(thm)],[5123])).
% 1.97/2.19 tff(5125,plain,
% 1.97/2.19 (b(s(elem!1), s(s(s(elem!1))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[5089, 5124])).
% 1.97/2.19 tff(5126,plain,
% 1.97/2.19 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1775, 5113, 4850, 5089, 5111])).
% 1.97/2.19 tff(5127,plain,
% 1.97/2.19 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[523, 5126])).
% 1.97/2.19 tff(5128,plain,
% 1.97/2.19 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.97/2.19 inference(symmetry,[status(thm)],[5115])).
% 1.97/2.19 tff(5129,plain,
% 1.97/2.19 (s(s(elem!1)) = s(s(z))),
% 1.97/2.19 inference(transitivity,[status(thm)],[167, 5128, 72])).
% 1.97/2.19 tff(5130,plain,
% 1.97/2.19 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[5129])).
% 1.97/2.19 tff(5131,plain,
% 1.97/2.19 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.97/2.19 inference(symmetry,[status(thm)],[5130])).
% 1.97/2.19 tff(5132,plain,
% 1.97/2.19 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[5097, 5131])).
% 1.97/2.19 tff(5133,plain,
% 1.97/2.19 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[5129])).
% 1.97/2.19 tff(5134,plain,
% 1.97/2.19 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.97/2.19 inference(symmetry,[status(thm)],[5133])).
% 1.97/2.19 tff(5135,plain,
% 1.97/2.19 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[5105, 5134])).
% 1.97/2.19 tff(5136,plain,
% 1.97/2.19 (b(s(s(s(z))), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1846, 5114, 4850])).
% 1.97/2.19 tff(5137,plain,
% 1.97/2.19 (~r(s(s(s(s(elem!1)))), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4766, 5136, 5089, 5109, 645, 87, 81, 4300])).
% 1.97/2.19 tff(5138,plain,
% 1.97/2.19 (b(s(s(s(s(elem!1)))), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[842, 5137])).
% 1.97/2.19 tff(5139,plain,
% 1.97/2.19 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4806, 5138, 5107, 87])).
% 1.97/2.19 tff(5140,plain,
% 1.97/2.19 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[452, 5139])).
% 1.97/2.19 tff(5141,plain,
% 1.97/2.19 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1822, 5140, 5114])).
% 1.97/2.19 tff(5142,plain,
% 1.97/2.19 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4688, 155, 5141, 5135, 5132])).
% 1.97/2.19 tff(5143,plain,
% 1.97/2.19 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[821, 5142, 5127])).
% 1.97/2.19 tff(5144,plain,
% 1.97/2.19 (s(z) = s(elem!1)),
% 1.97/2.19 inference(transitivity,[status(thm)],[24, 5117, 29])).
% 1.97/2.19 tff(5145,plain,
% 1.97/2.19 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[5144])).
% 1.97/2.19 tff(5146,plain,
% 1.97/2.19 (z = elem!1),
% 1.97/2.19 inference(transitivity,[status(thm)],[1443, 5145, 85])).
% 1.97/2.19 tff(5147,plain,
% 1.97/2.19 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.97/2.19 inference(monotonicity,[status(thm)],[5146])).
% 1.97/2.19 tff(5148,plain,
% 1.97/2.19 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 1.97/2.19 inference(monotonicity,[status(thm)],[5116])).
% 1.97/2.19 tff(5149,plain,
% 1.97/2.19 (r(s(s(elem!1)), z)),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[645, 5148])).
% 1.97/2.19 tff(5150,plain,
% 1.97/2.19 (r(s(s(elem!1)), elem!1)),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[5149, 5147])).
% 1.97/2.19 tff(5151,plain,
% 1.97/2.19 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 1.97/2.19 inference(monotonicity,[status(thm)],[5146])).
% 1.97/2.19 tff(5152,plain,
% 1.97/2.19 (r(s(s(s(elem!1))), elem!1)),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[288, 5151])).
% 1.97/2.19 tff(5153,plain,
% 1.97/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(5154,plain,
% 1.97/2.19 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(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))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(5155,plain,
% 1.97/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[5154])).
% 1.97/2.19 tff(5156,plain,
% 1.97/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.97/2.19 inference(transitivity,[status(thm)],[5155, 5153])).
% 1.97/2.19 tff(5157,plain,
% 1.97/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(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)))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(5158,plain,
% 1.97/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[5157, 5156])).
% 1.97/2.19 tff(5159,plain,
% 1.97/2.19 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5158, 155, 5141, 5135, 5152, 5150])).
% 1.97/2.19 tff(5160,plain,
% 1.97/2.19 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[486, 5159, 5126])).
% 1.97/2.19 tff(5161,plain,
% 1.97/2.19 (((~![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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(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(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(5162,plain,
% 1.97/2.19 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(5163,plain,
% 1.97/2.19 (((~![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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[5162])).
% 1.97/2.19 tff(5164,plain,
% 1.97/2.19 (((~![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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[5163, 5161])).
% 1.97/2.19 tff(5165,plain,
% 1.97/2.19 ((~![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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(5166,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[5165, 5164])).
% 1.97/2.19 tff(5167,plain,
% 1.97/2.19 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5166, 97, 5160, 5143, 5125])).
% 1.97/2.20 tff(5168,plain,
% 1.97/2.20 ($false),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[5167, 5122])).
% 1.97/2.20 tff(5169,plain,((~r(s(s(z)), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.20 tff(5170,plain,
% 1.97/2.20 (~r(s(s(z)), z)),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[5169, 255, 288, 87, 81, 3])).
% 1.97/2.20 tff(5171,plain,
% 1.97/2.20 (b(s(s(z)), z)),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[625, 5170])).
% 1.97/2.20 tff(5172,plain,
% 1.97/2.20 (~b(z, s(s(s(elem!1))))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[4344, 1331, 87, 729, 81, 193, 83])).
% 1.97/2.20 tff(5173,plain,
% 1.97/2.20 (r(z, s(s(s(elem!1))))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[590, 5172])).
% 1.97/2.20 tff(5174,plain,
% 1.97/2.20 (~b(z, s(s(z)))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[4739, 1331, 729, 81, 87])).
% 1.97/2.20 tff(5175,plain,
% 1.97/2.20 (r(z, s(s(z)))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[222, 5174])).
% 1.97/2.20 tff(5176,plain,
% 1.97/2.20 (r(s(s(z)), s(s(s(elem!1))))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[141, 53, 42, 4857])).
% 1.97/2.20 tff(5177,plain,
% 1.97/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.20 inference(rewrite,[status(thm)],[])).
% 1.97/2.20 tff(5178,plain,
% 1.97/2.20 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~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)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.20 inference(rewrite,[status(thm)],[])).
% 1.97/2.20 tff(5179,plain,
% 1.97/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.97/2.20 inference(monotonicity,[status(thm)],[5178])).
% 1.97/2.20 tff(5180,plain,
% 1.97/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.97/2.20 inference(transitivity,[status(thm)],[5179, 5177])).
% 1.97/2.20 tff(5181,plain,
% 1.97/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.97/2.20 inference(quant_inst,[status(thm)],[])).
% 1.97/2.20 tff(5182,plain,
% 1.97/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.97/2.20 inference(modus_ponens,[status(thm)],[5181, 5180])).
% 1.97/2.20 tff(5183,plain,
% 1.97/2.20 ($false),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[5182, 155, 570, 226, 4866, 5176])).
% 1.97/2.20 tff(5184,plain,((~b(s(s(z)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.20 tff(5185,plain,
% 1.97/2.20 ($false),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[5184, 5175, 5173, 87, 1139, 255])).
% 1.97/2.20 tff(5186,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(5187,plain,
% 2.04/2.20 (~b(s(s(s(z))), s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5186, 255, 4850, 87, 4300, 81, 5089, 5171])).
% 2.04/2.20 tff(5188,plain,
% 2.04/2.20 (r(s(s(s(z))), s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[421, 5187])).
% 2.04/2.20 tff(5189,plain,
% 2.04/2.20 (~r(z, s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5184, 570, 87, 4850, 255])).
% 2.04/2.20 tff(5190,plain,
% 2.04/2.20 (b(z, s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[222, 5189])).
% 2.04/2.20 tff(5191,plain,
% 2.04/2.20 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4382, 155, 5105, 5097, 5188])).
% 2.04/2.20 tff(5192,plain,
% 2.04/2.20 (((~![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(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(5193,plain,
% 2.04/2.20 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(5194,plain,
% 2.04/2.20 (((~![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(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[5193])).
% 2.04/2.20 tff(5195,plain,
% 2.04/2.20 (((~![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(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[5194, 5192])).
% 2.04/2.20 tff(5196,plain,
% 2.04/2.20 ((~![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(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(5197,plain,
% 2.04/2.20 ((~![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(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[5196, 5195])).
% 2.04/2.20 tff(5198,plain,
% 2.04/2.20 (~b(s(s(s(z))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5197, 97, 255, 1766, 1765])).
% 2.04/2.20 tff(5199,plain,
% 2.04/2.20 (r(s(s(s(z))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1358, 5198])).
% 2.04/2.20 tff(5200,plain,
% 2.04/2.20 (~r(s(s(s(z))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4369, 5199])).
% 2.04/2.20 tff(5201,plain,
% 2.04/2.20 (b(s(s(s(z))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[402, 5200])).
% 2.04/2.20 tff(5202,plain,
% 2.04/2.20 (~b(s(z), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1775, 340, 1139, 193, 1749])).
% 2.04/2.20 tff(5203,plain,
% 2.04/2.20 (r(s(z), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[253, 5202])).
% 2.04/2.20 tff(5204,plain,
% 2.04/2.20 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2641, 5203, 3, 1960])).
% 2.04/2.20 tff(5205,plain,
% 2.04/2.20 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[437, 5204])).
% 2.04/2.20 tff(5206,plain,
% 2.04/2.20 (((~![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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(5207,plain,
% 2.04/2.20 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(5208,plain,
% 2.04/2.20 (((~![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(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(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(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[5207])).
% 2.04/2.20 tff(5209,plain,
% 2.04/2.20 (((~![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(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(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(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.04/2.20 inference(transitivity,[status(thm)],[5208, 5206])).
% 2.04/2.20 tff(5210,plain,
% 2.04/2.20 ((~![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(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(5211,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[5210, 5209])).
% 2.04/2.20 tff(5212,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5211, 97, 204, 83, 5205, 5201])).
% 2.04/2.20 tff(5213,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | r(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)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(5214,plain,
% 2.04/2.20 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5213, 5190, 5171, 4300, 3, 5188, 255, 5191, 4850, 5089])).
% 2.04/2.20 tff(5215,plain,
% 2.04/2.20 (~r(z, s(s(s(s(elem!1)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1872, 3656, 288, 824])).
% 2.04/2.20 tff(5216,plain,
% 2.04/2.20 (b(z, s(s(s(s(elem!1)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1093, 5215])).
% 2.04/2.20 tff(5217,plain,
% 2.04/2.20 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1804, 4880, 4850, 5089])).
% 2.04/2.20 tff(5218,plain,
% 2.04/2.20 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[821, 3701, 5217])).
% 2.04/2.20 tff(5219,plain,
% 2.04/2.20 (~r(z, s(s(s(elem!1))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[832, 5218, 288, 824])).
% 2.04/2.20 tff(5220,plain,
% 2.04/2.20 (b(z, s(s(s(elem!1))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[590, 5219])).
% 2.04/2.20 tff(5221,plain,
% 2.04/2.20 (~b(s(s(s(z))), s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4344, 5220, 87, 4300, 81, 5089, 83])).
% 2.04/2.20 tff(5222,plain,
% 2.04/2.20 (r(s(s(s(z))), s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[421, 5221])).
% 2.04/2.20 tff(5223,plain,
% 2.04/2.20 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2641, 338, 3, 1960])).
% 2.04/2.20 tff(5224,plain,
% 2.04/2.20 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[437, 5223])).
% 2.04/2.20 tff(5225,plain,
% 2.04/2.20 (((~![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)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(5226,plain,
% 2.04/2.20 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(5227,plain,
% 2.04/2.20 (((~![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(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(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(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[5226])).
% 2.04/2.20 tff(5228,plain,
% 2.04/2.20 (((~![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(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(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(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.04/2.20 inference(transitivity,[status(thm)],[5227, 5225])).
% 2.04/2.20 tff(5229,plain,
% 2.04/2.20 ((~![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(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(5230,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[5229, 5228])).
% 2.04/2.20 tff(5231,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5230, 97, 372, 83, 1361, 1216])).
% 2.04/2.20 tff(5232,plain,((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(5233,plain,
% 2.04/2.20 (~b(s(s(s(z))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5232, 5224, 83, 372])).
% 2.04/2.20 tff(5234,plain,
% 2.04/2.20 (r(s(s(s(z))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[402, 5233])).
% 2.04/2.20 tff(5235,plain,
% 2.04/2.20 ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4368, 155, 4300, 3, 1960])).
% 2.04/2.20 tff(5236,plain,
% 2.04/2.20 (~r(s(s(s(z))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5235, 5234])).
% 2.04/2.20 tff(5237,plain,
% 2.04/2.20 (b(s(s(s(z))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1358, 5236])).
% 2.04/2.20 tff(5238,plain,
% 2.04/2.20 (~r(z, s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1308, 5234, 338, 81])).
% 2.04/2.20 tff(5239,plain,
% 2.04/2.20 (b(z, s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1318, 5238])).
% 2.04/2.20 tff(5240,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1369, 5239, 5237, 1139, 124, 83, 5224])).
% 2.04/2.20 tff(5241,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(5242,plain,
% 2.04/2.20 (~r(s(z), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5241, 5220, 4850, 83, 81, 3, 5222, 5216])).
% 2.04/2.20 tff(5243,plain,
% 2.04/2.20 (b(s(z), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[253, 5242])).
% 2.04/2.20 tff(5244,plain,
% 2.04/2.20 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1710, 5243, 4850, 5089])).
% 2.04/2.20 tff(5245,plain,
% 2.04/2.20 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4382, 155, 5105, 5097, 5222])).
% 2.04/2.20 tff(5246,plain,
% 2.04/2.20 ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1678, 53, 5245])).
% 2.04/2.20 tff(5247,plain,
% 2.04/2.20 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5246, 5244])).
% 2.04/2.20 tff(5248,plain,
% 2.04/2.20 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[5247])).
% 2.04/2.20 tff(5249,plain,
% 2.04/2.20 (s(s(z)) = s(s(elem!1))),
% 2.04/2.20 inference(transitivity,[status(thm)],[73, 5248, 19])).
% 2.04/2.20 tff(5250,plain,
% 2.04/2.20 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[5249])).
% 2.04/2.20 tff(5251,plain,
% 2.04/2.20 (s(z) = s(elem!1)),
% 2.04/2.20 inference(transitivity,[status(thm)],[24, 5250, 29])).
% 2.04/2.20 tff(5252,plain,
% 2.04/2.20 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[5251])).
% 2.04/2.20 tff(5253,plain,
% 2.04/2.20 (z = elem!1),
% 2.04/2.20 inference(transitivity,[status(thm)],[1443, 5252, 85])).
% 2.04/2.20 tff(5254,plain,
% 2.04/2.20 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[5253])).
% 2.04/2.20 tff(5255,plain,
% 2.04/2.20 (r(s(s(s(elem!1))), elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[288, 5254])).
% 2.04/2.20 tff(5256,plain,
% 2.04/2.20 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.04/2.20 inference(symmetry,[status(thm)],[5248])).
% 2.04/2.20 tff(5257,plain,
% 2.04/2.20 (s(s(elem!1)) = s(s(z))),
% 2.04/2.20 inference(transitivity,[status(thm)],[167, 5256, 72])).
% 2.04/2.20 tff(5258,plain,
% 2.04/2.20 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[5257])).
% 2.04/2.20 tff(5259,plain,
% 2.04/2.20 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.20 inference(symmetry,[status(thm)],[5258])).
% 2.04/2.20 tff(5260,plain,
% 2.04/2.20 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[5105, 5259])).
% 2.04/2.20 tff(5261,plain,
% 2.04/2.20 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3107, 5247, 824])).
% 2.04/2.20 tff(5262,plain,
% 2.04/2.20 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[5249])).
% 2.04/2.20 tff(5263,plain,
% 2.04/2.20 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[669, 5216, 4880, 83])).
% 2.04/2.20 tff(5264,plain,
% 2.04/2.20 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[336, 5263])).
% 2.04/2.20 tff(5265,plain,
% 2.04/2.20 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[5264, 5262])).
% 2.04/2.20 tff(5266,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(5267,plain,
% 2.04/2.20 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), 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)))))) | (~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(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(5268,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), 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)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[5267])).
% 2.04/2.20 tff(5269,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), 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)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[5268, 5266])).
% 2.04/2.20 tff(5270,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), 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)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(5271,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[5270, 5269])).
% 2.04/2.20 tff(5272,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5271, 155, 5265, 3656, 5261, 5260, 5255])).
% 2.04/2.20 tff(5273,plain,((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(5274,plain,
% 2.04/2.20 (~r(s(s(s(s(elem!1)))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5273, 472, 288, 83, 81, 3, 87, 2718])).
% 2.04/2.20 tff(5275,plain,
% 2.04/2.20 (b(s(s(s(s(elem!1)))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[842, 5274])).
% 2.04/2.20 tff(5276,plain,
% 2.04/2.20 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4806, 5275, 204, 87])).
% 2.04/2.20 tff(5277,plain,
% 2.04/2.20 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[452, 5276])).
% 2.04/2.20 tff(5278,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1044, 155, 488, 309, 1170, 145])).
% 2.04/2.20 tff(5279,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(5280,plain,
% 2.04/2.21 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5279, 3656, 5277, 5105])).
% 2.04/2.21 tff(5281,plain,
% 2.04/2.21 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[336, 5280])).
% 2.04/2.21 tff(5282,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(5283,plain,
% 2.04/2.21 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(5284,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[5283])).
% 2.04/2.21 tff(5285,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[5284, 5282])).
% 2.04/2.21 tff(5286,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(5287,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[5286, 5285])).
% 2.04/2.21 tff(5288,plain,
% 2.04/2.21 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5287, 155, 5277, 5105, 5097])).
% 2.04/2.21 tff(5289,plain,
% 2.04/2.21 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[821, 5288, 3701])).
% 2.04/2.21 tff(5290,plain,
% 2.04/2.21 (~b(z, s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1124, 5289, 5281, 83])).
% 2.04/2.21 tff(5291,plain,
% 2.04/2.21 (r(z, s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1093, 5290])).
% 2.04/2.21 tff(5292,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(5293,plain,
% 2.04/2.21 (((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(5294,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[5293])).
% 2.04/2.21 tff(5295,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[5294, 5292])).
% 2.04/2.21 tff(5296,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(5297,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[5296, 5295])).
% 2.04/2.21 tff(5298,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5297, 155, 5291, 3656, 288, 5277, 5105])).
% 2.04/2.21 tff(5299,plain,((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(5300,plain,
% 2.04/2.21 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5299, 5214, 5171, 5190, 87, 81, 3, 288])).
% 2.04/2.21 tff(5301,plain,
% 2.04/2.21 (((~![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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(5302,plain,
% 2.04/2.21 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(5303,plain,
% 2.04/2.21 (((~![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(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(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(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[5302])).
% 2.04/2.21 tff(5304,plain,
% 2.04/2.21 (((~![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(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(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(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[5303, 5301])).
% 2.04/2.21 tff(5305,plain,
% 2.04/2.21 ((~![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(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(5306,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[5305, 5304])).
% 2.04/2.21 tff(5307,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5306, 97, 1139, 255, 473, 876])).
% 2.04/2.21 tff(5308,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(5309,plain,
% 2.04/2.21 (~b(s(s(s(s(elem!1)))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5308, 5300, 255, 4850])).
% 2.04/2.21 tff(5310,plain,
% 2.04/2.21 (r(s(s(s(s(elem!1)))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[842, 5309])).
% 2.04/2.21 tff(5311,plain,
% 2.04/2.21 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4414, 5310, 81, 4300])).
% 2.04/2.21 tff(5312,plain,
% 2.04/2.21 (b(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[511, 5311])).
% 2.04/2.21 tff(5313,plain,
% 2.04/2.21 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[523, 5214])).
% 2.04/2.21 tff(5314,plain,
% 2.04/2.21 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[832, 5310, 288, 570])).
% 2.04/2.21 tff(5315,plain,
% 2.04/2.21 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[821, 5314, 5313])).
% 2.04/2.21 tff(5316,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1804, 5315, 5312, 4850, 5089])).
% 2.04/2.21 tff(5317,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(5318,plain,
% 2.04/2.21 (~r(z, s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5317, 255, 81, 288, 87, 3])).
% 2.04/2.21 tff(5319,plain,
% 2.04/2.21 (b(z, s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[590, 5318])).
% 2.04/2.21 tff(5320,plain,
% 2.04/2.21 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4382, 155, 5105, 5097, 1960])).
% 2.04/2.21 tff(5321,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5241, 5203, 370, 1139, 83, 81, 3, 1960, 124])).
% 2.04/2.21 tff(5322,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(5323,plain,
% 2.04/2.21 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5322, 83, 4850, 81, 3, 1960, 124, 5089, 5320])).
% 2.04/2.21 tff(5324,plain,
% 2.04/2.21 (~b(z, s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5299, 2718, 83, 5323, 87, 81, 3, 288])).
% 2.04/2.21 tff(5325,plain,
% 2.04/2.21 (r(z, s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[222, 5324])).
% 2.04/2.21 tff(5326,plain,
% 2.04/2.21 (~r(s(s(s(s(elem!1)))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5273, 2718, 288, 83, 81, 3, 87, 5323])).
% 2.04/2.21 tff(5327,plain,
% 2.04/2.21 (b(s(s(s(s(elem!1)))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[842, 5326])).
% 2.04/2.21 tff(5328,plain,
% 2.04/2.21 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4493, 5327, 5089, 83, 124, 87])).
% 2.04/2.21 tff(5329,plain,
% 2.04/2.21 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[452, 5328])).
% 2.04/2.21 tff(5330,plain,
% 2.04/2.21 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[523, 5323])).
% 2.04/2.21 tff(5331,plain,
% 2.04/2.21 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[486, 2718, 5323])).
% 2.04/2.21 tff(5332,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(5333,plain,
% 2.04/2.21 (((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(5334,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[5333])).
% 2.04/2.21 tff(5335,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[5334, 5332])).
% 2.04/2.21 tff(5336,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(5337,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[5336, 5335])).
% 2.04/2.21 tff(5338,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5337, 155, 488, 309, 226, 288, 145])).
% 2.04/2.21 tff(5339,plain,((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(5340,plain,
% 2.04/2.21 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5339, 5325, 5331, 288, 5105])).
% 2.04/2.21 tff(5341,plain,
% 2.04/2.21 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[336, 5340])).
% 2.04/2.21 tff(5342,plain,
% 2.04/2.21 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5023, 86, 339, 87])).
% 2.04/2.21 tff(5343,plain,
% 2.04/2.21 (r(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[511, 5342])).
% 2.04/2.21 tff(5344,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(5345,plain,
% 2.04/2.21 (((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(5346,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[5345])).
% 2.04/2.21 tff(5347,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[5346, 5344])).
% 2.04/2.21 tff(5348,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(5349,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[5348, 5347])).
% 2.04/2.21 tff(5350,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5349, 155, 729, 463, 226, 3, 495])).
% 2.04/2.21 tff(5351,plain,((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(5352,plain,
% 2.04/2.21 (~r(z, s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5351, 5343, 3, 729, 226])).
% 2.04/2.21 tff(5353,plain,
% 2.04/2.21 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5103, 97, 1139, 193, 87])).
% 2.04/2.21 tff(5354,plain,
% 2.04/2.21 (r(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[58, 5353])).
% 2.04/2.21 tff(5355,plain,
% 2.04/2.21 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5095, 97, 1139, 193, 87])).
% 2.04/2.21 tff(5356,plain,
% 2.04/2.21 (r(s(s(z)), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[143, 5355])).
% 2.04/2.21 tff(5357,plain,
% 2.04/2.21 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1710, 86, 1139, 193])).
% 2.04/2.21 tff(5358,plain,
% 2.04/2.21 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4382, 155, 5354, 5356, 1960])).
% 2.04/2.21 tff(5359,plain,
% 2.04/2.21 ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1678, 53, 5358])).
% 2.04/2.21 tff(5360,plain,
% 2.04/2.21 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5359, 5357])).
% 2.04/2.21 tff(5361,plain,
% 2.04/2.21 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1822, 5360, 1170])).
% 2.04/2.21 tff(5362,plain,
% 2.04/2.21 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1124, 372, 339, 83])).
% 2.04/2.21 tff(5363,plain,
% 2.04/2.21 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[821, 5362, 802])).
% 2.04/2.21 tff(5364,plain,
% 2.04/2.21 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[1396])).
% 2.04/2.21 tff(5365,plain,
% 2.04/2.21 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[5364])).
% 2.04/2.21 tff(5366,plain,
% 2.04/2.21 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[224, 5365])).
% 2.04/2.21 tff(5367,plain,
% 2.04/2.21 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[1396])).
% 2.04/2.21 tff(5368,plain,
% 2.04/2.21 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.21 inference(symmetry,[status(thm)],[5367])).
% 2.04/2.21 tff(5369,plain,
% 2.04/2.21 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[145, 5368])).
% 2.04/2.21 tff(5370,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4688, 155, 1813, 5369, 5366, 823])).
% 2.04/2.21 tff(5371,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(5372,plain,
% 2.04/2.21 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5371, 5363, 1813, 224, 145])).
% 2.04/2.21 tff(5373,plain,
% 2.04/2.21 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4382, 155, 145, 224, 1960])).
% 2.04/2.21 tff(5374,plain,
% 2.04/2.21 ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1678, 53, 5373])).
% 2.04/2.21 tff(5375,plain,
% 2.04/2.21 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5374, 5372])).
% 2.04/2.21 tff(5376,plain,
% 2.04/2.21 (~b(s(z), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1710, 5375, 1139, 193])).
% 2.04/2.21 tff(5377,plain,
% 2.04/2.21 (r(s(z), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[253, 5376])).
% 2.04/2.21 tff(5378,plain,
% 2.04/2.21 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2641, 5377, 3, 1960])).
% 2.04/2.21 tff(5379,plain,
% 2.04/2.21 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[437, 5378])).
% 2.04/2.21 tff(5380,plain,
% 2.04/2.21 (~b(s(s(s(z))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5232, 5379, 83, 372])).
% 2.04/2.21 tff(5381,plain,
% 2.04/2.21 (r(s(s(s(z))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[402, 5380])).
% 2.04/2.21 tff(5382,plain,
% 2.04/2.21 (~r(s(s(s(z))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4369, 5381])).
% 2.04/2.22 tff(5383,plain,
% 2.04/2.22 (b(s(s(s(z))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1358, 5382])).
% 2.04/2.22 tff(5384,plain,
% 2.04/2.22 (((~![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(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(5385,plain,
% 2.04/2.22 (((~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(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(5386,plain,
% 2.04/2.22 (((~![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(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(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[5385])).
% 2.04/2.22 tff(5387,plain,
% 2.04/2.22 (((~![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(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(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[5386, 5384])).
% 2.04/2.22 tff(5388,plain,
% 2.04/2.22 ((~![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(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))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(5389,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[5388, 5387])).
% 2.04/2.22 tff(5390,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5389, 97, 1139, 193, 5383, 5375])).
% 2.04/2.22 tff(5391,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(5392,plain,
% 2.04/2.22 (~b(z, s(s(s(s(elem!1)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5391, 5361, 193, 729, 3, 1960, 83, 1139, 5356, 5354, 802, 339])).
% 2.04/2.22 tff(5393,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1093, 5392, 5352])).
% 2.04/2.22 tff(5394,plain,((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(5395,plain,
% 2.04/2.22 (~b(s(z), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5394, 5341, 4300, 3, 1960, 83, 4850, 5330, 5089, 5325, 5329, 87])).
% 2.04/2.22 tff(5396,plain,
% 2.04/2.22 (r(s(z), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[253, 5395])).
% 2.04/2.22 tff(5397,plain,
% 2.04/2.22 (~r(s(s(s(z))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1327, 5396, 3, 81, 5325])).
% 2.04/2.22 tff(5398,plain,
% 2.04/2.22 (b(s(s(s(z))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[402, 5397])).
% 2.04/2.22 tff(5399,plain,
% 2.04/2.22 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2641, 5396, 3, 1960])).
% 2.04/2.22 tff(5400,plain,
% 2.04/2.22 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[437, 5399])).
% 2.04/2.22 tff(5401,plain,
% 2.04/2.22 (((~![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(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(5402,plain,
% 2.04/2.22 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(5403,plain,
% 2.04/2.22 (((~![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(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(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(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[5402])).
% 2.04/2.22 tff(5404,plain,
% 2.04/2.22 (((~![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(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(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(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.04/2.22 inference(transitivity,[status(thm)],[5403, 5401])).
% 2.04/2.22 tff(5405,plain,
% 2.04/2.22 ((~![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(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(5406,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[5405, 5404])).
% 2.04/2.22 tff(5407,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5406, 97, 124, 83, 5400, 5398])).
% 2.04/2.22 tff(5408,plain,(b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(5409,plain,
% 2.04/2.22 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5408, 5319, 5171, 3, 81, 5188, 87, 288])).
% 2.04/2.22 tff(5410,plain,
% 2.04/2.22 (((~![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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(5411,plain,
% 2.04/2.22 (((~b(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(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(5412,plain,
% 2.04/2.22 (((~![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(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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[5411])).
% 2.04/2.22 tff(5413,plain,
% 2.04/2.22 (((~![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(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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[5412, 5410])).
% 2.04/2.22 tff(5414,plain,
% 2.04/2.22 ((~![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(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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(5415,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[5414, 5413])).
% 2.04/2.22 tff(5416,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5415, 97, 1545, 193, 255, 473])).
% 2.04/2.22 tff(5417,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(5418,plain,
% 2.04/2.22 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5417, 5409, 5089, 255])).
% 2.04/2.22 tff(5419,plain,
% 2.04/2.22 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5322, 5171, 4850, 81, 3, 5188, 5319, 5089, 5191])).
% 2.04/2.22 tff(5420,plain,
% 2.04/2.22 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[523, 5419])).
% 2.04/2.22 tff(5421,plain,
% 2.04/2.22 (~b(s(s(s(s(elem!1)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5308, 5409, 255, 4850])).
% 2.04/2.22 tff(5422,plain,
% 2.04/2.22 (r(s(s(s(s(elem!1)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[842, 5421])).
% 2.04/2.22 tff(5423,plain,
% 2.04/2.22 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4414, 5422, 81, 4300])).
% 2.04/2.22 tff(5424,plain,
% 2.04/2.22 (b(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[511, 5423])).
% 2.04/2.22 tff(5425,plain,
% 2.04/2.22 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1804, 5424, 4850, 5089])).
% 2.04/2.22 tff(5426,plain,
% 2.04/2.22 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[821, 5425, 5420])).
% 2.04/2.22 tff(5427,plain,
% 2.04/2.22 (~b(s(s(s(z))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5389, 97, 1139, 193, 1702])).
% 2.04/2.22 tff(5428,plain,
% 2.04/2.22 (r(s(s(s(z))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1358, 5427])).
% 2.04/2.22 tff(5429,plain,
% 2.04/2.22 (((~![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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(5430,plain,
% 2.04/2.22 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(5431,plain,
% 2.04/2.22 (((~![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(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[5430])).
% 2.04/2.22 tff(5432,plain,
% 2.04/2.22 (((~![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(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[5431, 5429])).
% 2.04/2.22 tff(5433,plain,
% 2.04/2.22 ((~![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(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), 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)))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(5434,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[5433, 5432])).
% 2.04/2.22 tff(5435,plain,
% 2.04/2.22 (~b(s(s(s(z))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5434, 97, 1139, 124, 1702])).
% 2.04/2.22 tff(5436,plain,
% 2.04/2.22 (r(s(s(s(z))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[402, 5435])).
% 2.04/2.22 tff(5437,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4369, 5436, 5428])).
% 2.04/2.22 tff(5438,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(5439,plain,
% 2.04/2.22 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5438, 5188, 3, 4300, 4850, 5319, 5089])).
% 2.04/2.22 tff(5440,plain,
% 2.04/2.22 ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1678, 53, 5191])).
% 2.04/2.22 tff(5441,plain,
% 2.04/2.22 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5440, 5439])).
% 2.04/2.22 tff(5442,plain,
% 2.04/2.22 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5371, 5441, 5426, 5097, 5105])).
% 2.04/2.22 tff(5443,plain,
% 2.04/2.22 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1484, 5442, 5418])).
% 2.04/2.22 tff(5444,plain,
% 2.04/2.22 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1822, 5442, 5441])).
% 2.04/2.22 tff(5445,plain,
% 2.04/2.22 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[452, 5444])).
% 2.04/2.22 tff(5446,plain,
% 2.04/2.22 (s(s(s(elem!1))) = s(elem!1)),
% 2.04/2.22 inference(transitivity,[status(thm)],[271, 1726, 29])).
% 2.04/2.22 tff(5447,plain,
% 2.04/2.22 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[5446])).
% 2.04/2.22 tff(5448,plain,
% 2.04/2.22 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(elem!1))))),
% 2.04/2.22 inference(symmetry,[status(thm)],[5447])).
% 2.04/2.22 tff(5449,plain,
% 2.04/2.22 ((~b(s(z), s(elem!1))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[5448])).
% 2.04/2.22 tff(5450,plain,
% 2.04/2.22 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[1725])).
% 2.04/2.22 tff(5451,plain,
% 2.04/2.22 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.04/2.22 inference(symmetry,[status(thm)],[5450])).
% 2.04/2.22 tff(5452,plain,
% 2.04/2.22 ((~b(s(s(s(elem!1))), s(s(elem!1)))) <=> (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[5451])).
% 2.04/2.22 tff(5453,assumption,(~b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 2.04/2.22 tff(5454,plain,
% 2.04/2.22 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[5453, 5452])).
% 2.04/2.22 tff(5455,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[473, 5454])).
% 2.04/2.22 tff(5456,plain,((~(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)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(5457,plain,
% 2.04/2.22 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5456, 1725, 473])).
% 2.04/2.22 tff(5458,plain,
% 2.04/2.22 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.04/2.22 inference(symmetry,[status(thm)],[1725])).
% 2.04/2.22 tff(5459,plain,
% 2.04/2.22 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[5458])).
% 2.04/2.22 tff(5460,plain,
% 2.04/2.22 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 2.04/2.22 inference(symmetry,[status(thm)],[5459])).
% 2.04/2.22 tff(5461,plain,
% 2.04/2.22 (b(s(s(elem!1)), s(s(z)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[441, 5460])).
% 2.04/2.22 tff(5462,plain,
% 2.04/2.22 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[1728])).
% 2.04/2.22 tff(5463,plain,
% 2.04/2.22 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.04/2.22 inference(symmetry,[status(thm)],[5462])).
% 2.04/2.22 tff(5464,plain,
% 2.04/2.22 (b(s(elem!1), s(s(elem!1)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[1529, 5463])).
% 2.04/2.22 tff(5465,plain,
% 2.04/2.22 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[5458])).
% 2.04/2.22 tff(5466,plain,
% 2.04/2.22 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(elem!1)))),
% 2.04/2.22 inference(symmetry,[status(thm)],[5465])).
% 2.04/2.22 tff(5467,plain,
% 2.04/2.22 (b(s(z), s(s(elem!1)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[255, 5466])).
% 2.04/2.22 tff(5468,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 2.04/2.22 tff(5469,plain,
% 2.04/2.22 (((~![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(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(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(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(elem!1))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(5470,plain,
% 2.04/2.22 (((~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(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(elem!1))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(5471,plain,
% 2.04/2.22 (((~![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(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(elem!1)))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[5470])).
% 2.04/2.22 tff(5472,plain,
% 2.04/2.22 (((~![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(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(elem!1))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[5471, 5469])).
% 2.04/2.22 tff(5473,plain,
% 2.04/2.22 ((~![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(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(5474,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(elem!1)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[5473, 5472])).
% 2.04/2.22 tff(5475,plain,
% 2.04/2.22 ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5474, 97, 5468])).
% 2.04/2.22 tff(5476,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5475, 5467, 5464, 5461])).
% 2.04/2.22 tff(5477,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(elem!1))) | (~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(5478,plain,
% 2.04/2.22 (~b(s(z), s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5477, 5457, 255, 441, 1725])).
% 2.04/2.22 tff(5479,plain,
% 2.04/2.22 (~b(s(z), s(s(s(elem!1))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[5478, 5449])).
% 2.04/2.22 tff(5480,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[193, 5479])).
% 2.04/2.22 tff(5481,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(5482,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5481, 5445, 5443, 255, 5089, 5409])).
% 2.04/2.23 tff(5483,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(5484,plain,
% 2.04/2.23 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5483, 288, 81, 87, 3])).
% 2.04/2.23 tff(5485,plain,
% 2.04/2.23 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1248, 5484, 5089])).
% 2.04/2.23 tff(5486,plain,
% 2.04/2.23 (r(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[280, 5484])).
% 2.04/2.23 tff(5487,plain,
% 2.04/2.23 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[5144, 5116])).
% 2.04/2.23 tff(5488,plain,
% 2.04/2.23 (r(s(elem!1), s(s(elem!1)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[3, 5487])).
% 2.04/2.23 tff(5489,plain,
% 2.04/2.23 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1909, 5114, 287])).
% 2.04/2.23 tff(5490,plain,
% 2.04/2.23 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[5146])).
% 2.04/2.23 tff(5491,plain,
% 2.04/2.23 (r(s(z), z) <=> r(s(elem!1), z)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[5144])).
% 2.04/2.23 tff(5492,plain,
% 2.04/2.23 (r(s(elem!1), z)),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[81, 5491])).
% 2.04/2.23 tff(5493,plain,
% 2.04/2.23 (r(s(elem!1), elem!1)),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[5492, 5490])).
% 2.04/2.23 tff(5494,plain,
% 2.04/2.23 (~r(s(s(s(s(elem!1)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4766, 5136, 5089, 645, 5109, 87, 81, 4300])).
% 2.04/2.23 tff(5495,plain,
% 2.04/2.23 (b(s(s(s(s(elem!1)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[842, 5494])).
% 2.04/2.23 tff(5496,plain,
% 2.04/2.23 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4806, 5495, 5107, 87])).
% 2.04/2.23 tff(5497,plain,
% 2.04/2.23 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[452, 5496])).
% 2.04/2.23 tff(5498,plain,
% 2.04/2.23 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1822, 5497, 5114])).
% 2.04/2.23 tff(5499,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(5500,plain,
% 2.04/2.23 (((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(5501,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[5500])).
% 2.04/2.23 tff(5502,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.04/2.23 inference(transitivity,[status(thm)],[5501, 5499])).
% 2.04/2.23 tff(5503,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(5504,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[5503, 5502])).
% 2.04/2.23 tff(5505,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5504, 155, 5498, 5150, 5493, 5489, 5488])).
% 2.04/2.23 tff(5506,plain,((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(5507,plain,
% 2.04/2.23 (~r(s(s(z)), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5506, 5486, 81, 87, 3])).
% 2.04/2.23 tff(5508,plain,
% 2.04/2.23 (b(s(s(z)), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[625, 5507])).
% 2.04/2.23 tff(5509,plain,
% 2.04/2.23 (~b(z, s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5299, 2718, 5508, 5485, 87, 81, 3, 288])).
% 2.04/2.23 tff(5510,plain,
% 2.04/2.23 (r(z, s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[222, 5509])).
% 2.04/2.23 tff(5511,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5182, 155, 5173, 5175, 145, 224])).
% 2.04/2.23 tff(5512,plain,((~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(5513,plain,
% 2.04/2.23 (~b(s(s(s(z))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5512, 5508, 5097, 4300, 81, 87, 5089, 5105])).
% 2.04/2.23 tff(5514,plain,
% 2.04/2.23 (r(s(s(s(z))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[421, 5513])).
% 2.04/2.23 tff(5515,plain,
% 2.04/2.23 (~b(z, s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5408, 2718, 5508, 3, 81, 5514, 87, 288])).
% 2.04/2.23 tff(5516,plain,
% 2.04/2.23 (r(z, s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[590, 5515])).
% 2.04/2.23 tff(5517,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5182, 155, 5516, 5510, 5105, 5097])).
% 2.04/2.23 tff(5518,plain,(b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(5519,plain,
% 2.04/2.23 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5518, 288, 81, 87, 3])).
% 2.04/2.23 tff(5520,plain,
% 2.04/2.23 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[523, 5485])).
% 2.04/2.23 tff(5521,plain,
% 2.04/2.23 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[821, 5217, 5520])).
% 2.04/2.23 tff(5522,plain,
% 2.04/2.23 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5273, 824, 288, 5508, 81, 3, 87, 5485])).
% 2.04/2.23 tff(5523,plain,
% 2.04/2.23 (~r(z, s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4887, 824, 81, 5486])).
% 2.04/2.23 tff(5524,plain,
% 2.04/2.23 (b(z, s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1093, 5523])).
% 2.04/2.23 tff(5525,plain,
% 2.04/2.23 (~b(z, s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[701, 5524, 4880, 5522])).
% 2.04/2.23 tff(5526,plain,
% 2.04/2.23 (r(z, s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[590, 5525])).
% 2.04/2.23 tff(5527,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[832, 5526, 5521, 288, 824])).
% 2.04/2.23 tff(5528,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(5529,plain,
% 2.04/2.23 (~r(s(s(s(s(elem!1)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5528, 288, 81, 3, 87])).
% 2.04/2.23 tff(5530,plain,
% 2.04/2.23 (b(s(s(s(s(elem!1)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[842, 5529])).
% 2.04/2.23 tff(5531,plain,
% 2.04/2.23 (~r(s(s(z)), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5506, 287, 81, 87, 3])).
% 2.04/2.23 tff(5532,plain,
% 2.04/2.23 (b(s(s(z)), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[625, 5531])).
% 2.04/2.23 tff(5533,plain,
% 2.04/2.23 (~b(s(s(s(z))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5512, 5532, 5097, 4300, 81, 87, 5089, 5105])).
% 2.04/2.23 tff(5534,plain,
% 2.04/2.23 (r(s(s(s(z))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[421, 5533])).
% 2.04/2.23 tff(5535,plain,
% 2.04/2.23 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2141, 339, 1139, 473])).
% 2.04/2.23 tff(5536,plain,
% 2.04/2.23 (r(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[511, 5535])).
% 2.04/2.23 tff(5537,plain,
% 2.04/2.23 (~r(s(s(s(s(elem!1)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4414, 5536, 81, 729])).
% 2.04/2.23 tff(5538,plain,
% 2.04/2.23 (b(s(s(s(s(elem!1)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[842, 5537])).
% 2.04/2.23 tff(5539,plain,
% 2.04/2.23 (((~![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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), 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(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(5540,plain,
% 2.04/2.23 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(5541,plain,
% 2.04/2.23 (((~![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(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(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(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[5540])).
% 2.04/2.23 tff(5542,plain,
% 2.04/2.23 (((~![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(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(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(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[5541, 5539])).
% 2.04/2.23 tff(5543,plain,
% 2.04/2.23 ((~![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(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(5544,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[5543, 5542])).
% 2.04/2.23 tff(5545,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5544, 97, 339, 204, 83, 5538])).
% 2.04/2.23 tff(5546,plain,((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(5547,plain,
% 2.04/2.23 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5546, 204, 5532, 81, 4300, 4850, 473])).
% 2.04/2.23 tff(5548,plain,
% 2.04/2.23 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[336, 5547])).
% 2.04/2.23 tff(5549,plain,
% 2.04/2.23 (~r(s(z), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2171, 5548, 287, 3, 5534])).
% 2.04/2.23 tff(5550,plain,
% 2.04/2.23 (b(s(z), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[253, 5549])).
% 2.04/2.23 tff(5551,plain,
% 2.04/2.23 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1710, 5550, 4850, 5089])).
% 2.04/2.23 tff(5552,plain,
% 2.04/2.23 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4382, 155, 5105, 5097, 5534])).
% 2.04/2.23 tff(5553,plain,
% 2.04/2.23 ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1678, 53, 5552])).
% 2.04/2.23 tff(5554,plain,
% 2.04/2.23 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5553, 5551])).
% 2.04/2.23 tff(5555,plain,
% 2.04/2.23 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[5554])).
% 2.04/2.23 tff(5556,plain,
% 2.04/2.23 (s(s(z)) = s(s(elem!1))),
% 2.04/2.23 inference(transitivity,[status(thm)],[73, 5555, 19])).
% 2.04/2.23 tff(5557,plain,
% 2.04/2.23 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[5556])).
% 2.04/2.23 tff(5558,plain,
% 2.04/2.23 (s(z) = s(elem!1)),
% 2.04/2.23 inference(transitivity,[status(thm)],[24, 5557, 29])).
% 2.04/2.23 tff(5559,plain,
% 2.04/2.23 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[5558, 5556])).
% 2.04/2.23 tff(5560,plain,
% 2.04/2.23 (r(s(elem!1), s(s(elem!1)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[3, 5559])).
% 2.04/2.23 tff(5561,plain,
% 2.04/2.23 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1909, 5554, 287])).
% 2.04/2.23 tff(5562,plain,
% 2.04/2.23 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[5556])).
% 2.04/2.23 tff(5563,plain,
% 2.04/2.23 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[5548, 5562])).
% 2.04/2.23 tff(5564,plain,
% 2.04/2.23 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4806, 204, 876, 87])).
% 2.04/2.23 tff(5565,plain,
% 2.04/2.23 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[452, 5564])).
% 2.04/2.23 tff(5566,plain,
% 2.04/2.23 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1822, 5554, 5565])).
% 2.04/2.23 tff(5567,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4666, 155, 5566, 5563, 5561, 5560])).
% 2.04/2.23 tff(5568,plain,((~b(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(5569,plain,
% 2.04/2.23 (~b(z, s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5568, 5486, 3, 5530, 87, 81, 5519])).
% 2.04/2.23 tff(5570,plain,
% 2.04/2.23 (r(z, s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[222, 5569])).
% 2.04/2.23 tff(5571,plain,
% 2.04/2.23 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1954, 5570, 81, 5486, 3])).
% 2.04/2.23 tff(5572,plain,
% 2.04/2.23 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[336, 5571])).
% 2.04/2.23 tff(5573,plain,
% 2.04/2.23 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2141, 5572, 4850, 5519])).
% 2.04/2.23 tff(5574,plain,
% 2.04/2.23 (r(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[511, 5573])).
% 2.04/2.23 tff(5575,plain,
% 2.04/2.23 (~r(z, s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5048, 5574, 4300, 5486])).
% 2.04/2.23 tff(5576,plain,
% 2.04/2.23 (b(z, s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1093, 5575])).
% 2.04/2.23 tff(5577,plain,
% 2.04/2.23 (~b(z, s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[3793, 5576, 5530, 5519])).
% 2.04/2.23 tff(5578,plain,
% 2.04/2.23 (r(z, s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[590, 5577])).
% 2.04/2.23 tff(5579,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5182, 155, 5578, 5570, 5105, 5097])).
% 2.04/2.23 tff(5580,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(5581,plain,
% 2.04/2.23 (~r(s(s(s(elem!1))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5580, 87, 3, 81])).
% 2.04/2.23 tff(5582,plain,
% 2.04/2.23 (b(s(s(s(elem!1))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[246, 5581])).
% 2.04/2.23 tff(5583,plain,
% 2.04/2.23 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5506, 645, 81, 87, 3])).
% 2.04/2.23 tff(5584,plain,
% 2.04/2.23 (b(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[280, 5583])).
% 2.04/2.23 tff(5585,plain,
% 2.04/2.23 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4824, 5495, 87, 5089, 5582, 5584])).
% 2.04/2.23 tff(5586,plain,
% 2.04/2.23 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[336, 5585])).
% 2.04/2.23 tff(5587,plain,
% 2.04/2.23 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1775, 5111, 4850, 5089, 5113])).
% 2.04/2.23 tff(5588,plain,
% 2.04/2.23 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5308, 5495, 5584, 4850])).
% 2.04/2.23 tff(5589,plain,
% 2.04/2.23 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[486, 5588, 5587])).
% 2.04/2.23 tff(5590,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5279, 5589, 5497, 5586, 5105])).
% 2.04/2.23 tff(5591,plain,((~r(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(5592,plain,
% 2.04/2.23 (~r(s(s(z)), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5591, 87, 81, 3])).
% 2.04/2.23 tff(5593,plain,
% 2.04/2.23 (b(s(s(z)), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[625, 5592])).
% 2.04/2.23 tff(5594,plain,
% 2.04/2.23 (~b(z, s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4517, 5593, 5089, 87, 5582, 81, 3])).
% 2.04/2.23 tff(5595,plain,
% 2.04/2.23 (r(z, s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[590, 5594])).
% 2.04/2.23 tff(5596,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(5597,plain,
% 2.04/2.23 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(5598,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[5597])).
% 2.04/2.23 tff(5599,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[5598, 5596])).
% 2.04/2.23 tff(5600,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(5601,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[5600, 5599])).
% 2.04/2.23 tff(5602,plain,
% 2.04/2.23 (~r(z, s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5601, 155, 4300, 5595, 3, 5097])).
% 2.04/2.23 tff(5603,plain,
% 2.04/2.23 (b(z, s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[222, 5602])).
% 2.04/2.23 tff(5604,plain,
% 2.04/2.23 (~b(s(s(s(z))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5512, 5593, 5097, 4300, 81, 87, 5089, 5105])).
% 2.04/2.23 tff(5605,plain,
% 2.04/2.23 (r(s(s(s(z))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[421, 5604])).
% 2.04/2.23 tff(5606,plain,
% 2.04/2.23 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4382, 155, 5105, 5097, 5605])).
% 2.04/2.23 tff(5607,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5213, 1767, 340, 83, 729, 3, 1960, 204, 1749, 1139, 193])).
% 2.04/2.23 tff(5608,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | r(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)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(5609,plain,
% 2.04/2.23 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5608, 5593, 4300, 3, 5605, 5603, 5606, 4850, 5089])).
% 2.04/2.23 tff(5610,plain,
% 2.04/2.23 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[821, 3701, 816])).
% 2.04/2.23 tff(5611,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[950, 5610, 3656, 126, 193, 87, 513])).
% 2.04/2.23 tff(5612,plain,((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(5613,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5612, 1805, 513, 193, 87, 126, 472, 2718])).
% 2.04/2.23 tff(5614,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(5615,plain,
% 2.04/2.23 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5614, 2718, 87, 5582, 5609, 5089, 4850])).
% 2.04/2.23 tff(5616,plain,
% 2.04/2.23 (r(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[511, 5615])).
% 2.04/2.23 tff(5617,plain,
% 2.04/2.23 (~r(s(s(s(s(elem!1)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4414, 5616, 81, 4300])).
% 2.04/2.23 tff(5618,plain,
% 2.04/2.23 (b(s(s(s(s(elem!1)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[842, 5617])).
% 2.04/2.23 tff(5619,plain,
% 2.04/2.23 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4806, 5618, 5603, 87])).
% 2.04/2.23 tff(5620,plain,
% 2.04/2.23 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[452, 5619])).
% 2.04/2.23 tff(5621,plain,
% 2.04/2.23 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[486, 2718, 5609])).
% 2.04/2.23 tff(5622,plain,
% 2.04/2.23 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5279, 5620, 5621, 5105])).
% 2.04/2.23 tff(5623,plain,
% 2.04/2.23 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[336, 5622])).
% 2.04/2.23 tff(5624,plain,
% 2.04/2.23 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[523, 5609])).
% 2.04/2.23 tff(5625,plain,
% 2.04/2.23 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4824, 5623, 87, 5089, 5582, 5618])).
% 2.04/2.23 tff(5626,plain,
% 2.04/2.23 (r(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[280, 5625])).
% 2.04/2.23 tff(5627,plain,
% 2.04/2.23 (~r(z, s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5048, 5626, 4300, 5616])).
% 2.04/2.23 tff(5628,plain,
% 2.04/2.23 (b(z, s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1093, 5627])).
% 2.04/2.23 tff(5629,plain,
% 2.04/2.23 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5391, 5628, 5089, 4300, 3, 5593, 5605, 4850, 5097, 5105, 5624, 5623])).
% 2.04/2.23 tff(5630,plain,
% 2.04/2.23 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1822, 5629, 5620])).
% 2.04/2.23 tff(5631,plain,
% 2.04/2.23 ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1678, 53, 5606])).
% 2.04/2.23 tff(5632,plain,
% 2.04/2.23 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5631, 5630])).
% 2.04/2.23 tff(5633,plain,
% 2.04/2.23 (~b(s(z), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1710, 5632, 4850, 5089])).
% 2.04/2.23 tff(5634,plain,
% 2.04/2.23 (r(s(z), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[253, 5633])).
% 2.04/2.23 tff(5635,plain,
% 2.04/2.23 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2641, 5634, 3, 5605])).
% 2.04/2.23 tff(5636,plain,
% 2.04/2.23 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[437, 5635])).
% 2.04/2.23 tff(5637,plain,
% 2.04/2.23 (~b(s(s(s(z))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5232, 5636, 5593, 5628])).
% 2.04/2.23 tff(5638,plain,
% 2.04/2.23 (r(s(s(s(z))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[402, 5637])).
% 2.04/2.23 tff(5639,plain,
% 2.04/2.23 ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4368, 155, 4300, 3, 5605])).
% 2.04/2.23 tff(5640,plain,
% 2.04/2.23 (~r(s(s(s(z))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5639, 5638])).
% 2.04/2.23 tff(5641,plain,
% 2.04/2.23 (b(s(s(s(z))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1358, 5640])).
% 2.04/2.23 tff(5642,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5389, 97, 4850, 5089, 5641, 5632])).
% 2.04/2.23 tff(5643,plain,(b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(5644,plain,
% 2.04/2.23 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5643, 87, 3, 81])).
% 2.04/2.23 tff(5645,plain,
% 2.04/2.23 (~r(s(s(s(z))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4369, 5428])).
% 2.04/2.23 tff(5646,plain,
% 2.04/2.23 (b(s(s(s(z))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[402, 5645])).
% 2.04/2.23 tff(5647,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4777, 97, 126, 204, 5646, 1702])).
% 2.04/2.23 tff(5648,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(5649,plain,
% 2.04/2.23 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5648, 5582, 5603, 4300, 3, 5605, 4850, 5089])).
% 2.04/2.23 tff(5650,plain,
% 2.04/2.23 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5631, 5649])).
% 2.04/2.23 tff(5651,plain,
% 2.04/2.23 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[5650])).
% 2.04/2.23 tff(5652,plain,
% 2.04/2.23 (s(s(z)) = s(s(elem!1))),
% 2.04/2.23 inference(transitivity,[status(thm)],[73, 5651, 19])).
% 2.04/2.23 tff(5653,plain,
% 2.04/2.23 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[5652])).
% 2.04/2.23 tff(5654,plain,
% 2.04/2.23 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(z)))),
% 2.04/2.23 inference(symmetry,[status(thm)],[5653])).
% 2.04/2.23 tff(5655,plain,
% 2.04/2.23 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[5652])).
% 2.04/2.23 tff(5656,plain,
% 2.04/2.23 (s(z) = s(elem!1)),
% 2.04/2.23 inference(transitivity,[status(thm)],[24, 5655, 29])).
% 2.04/2.23 tff(5657,plain,
% 2.04/2.23 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[5656, 5652])).
% 2.04/2.23 tff(5658,plain,
% 2.04/2.23 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 2.04/2.23 inference(transitivity,[status(thm)],[5657, 5654])).
% 2.04/2.23 tff(5659,plain,
% 2.04/2.23 (r(s(elem!1), s(s(z)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[3, 5658])).
% 2.04/2.23 tff(5660,plain,
% 2.04/2.23 (~r(s(s(s(s(elem!1)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4677, 5659, 5582, 5089, 87, 5650, 81, 4300])).
% 2.04/2.23 tff(5661,plain,
% 2.04/2.23 (b(s(s(s(s(elem!1)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[842, 5660])).
% 2.04/2.24 tff(5662,plain,
% 2.04/2.24 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5308, 5661, 5644, 4850])).
% 2.04/2.24 tff(5663,plain,
% 2.04/2.24 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5568, 5661, 3, 5603, 87, 81, 5644])).
% 2.04/2.24 tff(5664,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[280, 5663, 5662])).
% 2.04/2.24 tff(5665,plain,((~b(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(5666,plain,
% 2.04/2.24 (~b(s(s(z)), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5665, 3, 81])).
% 2.04/2.24 tff(5667,plain,
% 2.04/2.24 (r(s(s(z)), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[122, 5666])).
% 2.04/2.24 tff(5668,plain,
% 2.04/2.24 (~r(z, s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[871, 155, 4300, 5667, 3])).
% 2.04/2.24 tff(5669,plain,
% 2.04/2.24 (b(z, s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[222, 5668])).
% 2.04/2.24 tff(5670,plain,
% 2.04/2.24 (~r(s(s(z)), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[966, 155, 4300, 81, 5667])).
% 2.04/2.24 tff(5671,plain,
% 2.04/2.24 (b(s(s(z)), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[625, 5670])).
% 2.04/2.24 tff(5672,plain,
% 2.04/2.24 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2313, 125, 3, 5667])).
% 2.04/2.24 tff(5673,plain,
% 2.04/2.24 (b(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[58, 5672])).
% 2.04/2.24 tff(5674,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4567, 5673, 4302, 5671, 5669])).
% 2.04/2.24 tff(5675,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(5676,plain,
% 2.04/2.24 (~r(s(z), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5675, 81, 125])).
% 2.04/2.24 tff(5677,plain,
% 2.04/2.24 (b(s(z), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[548, 5676])).
% 2.04/2.24 tff(5678,plain,
% 2.04/2.24 (~r(s(s(s(elem!1))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[791, 729, 125, 81])).
% 2.04/2.24 tff(5679,plain,
% 2.04/2.24 (b(s(s(s(elem!1))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[246, 5678])).
% 2.04/2.24 tff(5680,plain,
% 2.04/2.24 (~b(s(s(z)), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4549, 5679, 125, 226, 729, 1961, 1960, 570])).
% 2.04/2.24 tff(5681,plain,
% 2.04/2.24 (r(s(s(z)), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[625, 5680])).
% 2.04/2.24 tff(5682,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(5683,plain,
% 2.04/2.24 (((~r(s(z), z)) | (~r(s(s(z)), z)) | (~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)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(5684,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[5683])).
% 2.04/2.24 tff(5685,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[5684, 5682])).
% 2.04/2.24 tff(5686,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(5687,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[5686, 5685])).
% 2.04/2.24 tff(5688,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5687, 155, 81, 645, 2, 1961, 2597])).
% 2.04/2.24 tff(5689,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(5690,plain,
% 2.04/2.24 (~r(s(s(z)), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5689, 5681, 2597, 81, 1961])).
% 2.04/2.24 tff(5691,plain,
% 2.04/2.24 (b(s(s(z)), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[122, 5690])).
% 2.04/2.24 tff(5692,plain,
% 2.04/2.24 (~r(s(z), s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[771, 729, 125, 570])).
% 2.04/2.24 tff(5693,plain,
% 2.04/2.24 (b(s(z), s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[181, 5692])).
% 2.04/2.24 tff(5694,plain,
% 2.04/2.24 (((~![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(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(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(5695,plain,
% 2.04/2.24 (((~b(s(s(z)), 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(s(z)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(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(s(z)))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(5696,plain,
% 2.04/2.24 (((~![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(z)), 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(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(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(s(z))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[5695])).
% 2.04/2.24 tff(5697,plain,
% 2.04/2.24 (((~![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(z)), 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(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(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(s(z)))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[5696, 5694])).
% 2.04/2.24 tff(5698,plain,
% 2.04/2.24 ((~![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(z)), 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(s(z)))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(5699,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[5698, 5697])).
% 2.04/2.24 tff(5700,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5699, 97, 5693, 60, 5691, 5677])).
% 2.04/2.24 tff(5701,plain,((~r(z, s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(5702,plain,
% 2.04/2.24 (~r(z, s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5701, 570, 2597, 81, 1961, 125, 226, 1960, 60])).
% 2.04/2.24 tff(5703,plain,
% 2.04/2.24 (b(z, s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[723, 5702])).
% 2.04/2.24 tff(5704,plain,
% 2.04/2.24 (~b(s(z), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2615, 5703, 4294, 4292])).
% 2.04/2.24 tff(5705,plain,
% 2.04/2.24 (r(s(z), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[253, 5704])).
% 2.04/2.24 tff(5706,plain,
% 2.04/2.24 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(5707,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[5706])).
% 2.04/2.24 tff(5708,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[5707, 2933])).
% 2.04/2.24 tff(5709,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(5710,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[5709, 5708])).
% 2.04/2.24 tff(5711,plain,
% 2.04/2.24 (~r(s(s(z)), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5710, 155, 5705, 1961, 2597])).
% 2.04/2.24 tff(5712,plain,
% 2.04/2.24 (b(s(s(z)), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[122, 5711])).
% 2.04/2.24 tff(5713,plain,
% 2.04/2.24 (~b(s(z), s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5699, 97, 60, 5712, 5677])).
% 2.04/2.24 tff(5714,plain,
% 2.04/2.24 (r(s(z), s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[181, 5713])).
% 2.04/2.24 tff(5715,plain,
% 2.04/2.24 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2638, 5705, 2597, 125])).
% 2.04/2.24 tff(5716,plain,
% 2.04/2.24 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2687, 5715, 2466])).
% 2.04/2.24 tff(5717,plain,
% 2.04/2.24 (((~![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(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(5718,plain,
% 2.04/2.24 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(5719,plain,
% 2.04/2.24 (((~![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(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(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))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[5718])).
% 2.04/2.24 tff(5720,plain,
% 2.04/2.24 (((~![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(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(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))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[5719, 5717])).
% 2.04/2.24 tff(5721,plain,
% 2.04/2.24 ((~![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(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(5722,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[5721, 5720])).
% 2.04/2.24 tff(5723,plain,
% 2.04/2.24 (~b(s(s(s(elem!1))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5722, 97, 4294, 4292, 5716])).
% 2.04/2.24 tff(5724,plain,
% 2.04/2.24 (r(s(s(s(elem!1))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[246, 5723])).
% 2.04/2.24 tff(5725,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[709, 155, 570, 81, 5724, 5714])).
% 2.04/2.24 tff(5726,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(5727,plain,
% 2.04/2.24 (~r(z, s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5726, 60, 81, 1961, 2597, 4228, 125, 226, 1960])).
% 2.04/2.24 tff(5728,plain,
% 2.04/2.24 (b(z, s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[590, 5727])).
% 2.04/2.24 tff(5729,plain,
% 2.04/2.24 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(5730,plain,
% 2.04/2.24 (((~![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(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[5729])).
% 2.04/2.24 tff(5731,plain,
% 2.04/2.24 (((~![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(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[5730, 4355])).
% 2.04/2.24 tff(5732,plain,
% 2.04/2.24 ((~![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(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(5733,plain,
% 2.04/2.24 ((~![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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[5732, 5731])).
% 2.04/2.24 tff(5734,plain,
% 2.04/2.24 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5733, 97, 126, 124, 1216])).
% 2.04/2.24 tff(5735,plain,
% 2.04/2.24 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3089, 5734, 1])).
% 2.04/2.24 tff(5736,plain,
% 2.04/2.24 (((~![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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(5737,plain,
% 2.04/2.24 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(5738,plain,
% 2.04/2.24 (((~![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(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[5737])).
% 2.04/2.24 tff(5739,plain,
% 2.04/2.24 (((~![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(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[5738, 5736])).
% 2.04/2.24 tff(5740,plain,
% 2.04/2.24 ((~![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(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(5741,plain,
% 2.04/2.24 ((~![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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[5740, 5739])).
% 2.04/2.24 tff(5742,plain,
% 2.04/2.24 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5741, 97, 126, 124, 1216])).
% 2.04/2.24 tff(5743,plain,
% 2.04/2.24 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2687, 5742, 4228])).
% 2.04/2.24 tff(5744,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(5745,plain,
% 2.04/2.24 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(5746,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[5745])).
% 2.04/2.24 tff(5747,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[5746, 5744])).
% 2.04/2.24 tff(5748,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(5749,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[5748, 5747])).
% 2.04/2.24 tff(5750,plain,
% 2.04/2.24 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5749, 155, 1961, 5743, 5735])).
% 2.04/2.24 tff(5751,plain,
% 2.04/2.24 (b(s(s(z)), s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[143, 5750])).
% 2.04/2.24 tff(5752,plain,
% 2.04/2.24 (~b(s(s(z)), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4987, 5751, 124, 126])).
% 2.04/2.24 tff(5753,plain,
% 2.04/2.24 (r(s(s(z)), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[625, 5752])).
% 2.04/2.24 tff(5754,plain,
% 2.04/2.24 (~r(s(s(z)), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5689, 5753, 2597, 81, 1961])).
% 2.04/2.24 tff(5755,plain,
% 2.04/2.24 (b(s(s(z)), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[122, 5754])).
% 2.04/2.25 tff(5756,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3015, 155, 125, 225, 2597, 4252])).
% 2.04/2.25 tff(5757,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(5758,plain,
% 2.04/2.25 (~r(s(z), s(s(s(elem!1))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5757, 5735, 2597, 125])).
% 2.04/2.25 tff(5759,plain,
% 2.04/2.25 (b(s(z), s(s(s(elem!1))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[181, 5758])).
% 2.04/2.25 tff(5760,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5699, 97, 5759, 60, 5755, 5677])).
% 2.04/2.25 tff(5761,plain,((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(5762,plain,
% 2.04/2.25 (~b(s(s(s(elem!1))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5761, 60, 2597, 81, 1961, 5728, 125, 1, 4292])).
% 2.04/2.25 tff(5763,plain,
% 2.04/2.25 (r(s(s(s(elem!1))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[246, 5762])).
% 2.04/2.25 tff(5764,plain,
% 2.04/2.25 (~r(z, s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[791, 5763, 125, 81])).
% 2.04/2.25 tff(5765,plain,
% 2.04/2.25 (b(z, s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[723, 5764])).
% 2.04/2.25 tff(5766,plain,
% 2.04/2.25 (~b(s(z), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2615, 5765, 4294, 4292])).
% 2.04/2.25 tff(5767,plain,
% 2.04/2.25 (r(s(z), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[253, 5766])).
% 2.04/2.25 tff(5768,plain,
% 2.04/2.25 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2638, 5767, 2597, 125])).
% 2.04/2.25 tff(5769,plain,
% 2.04/2.25 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2687, 5768, 4228])).
% 2.04/2.25 tff(5770,plain,
% 2.04/2.25 (((~![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(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(5771,plain,
% 2.04/2.25 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(5772,plain,
% 2.04/2.25 (((~![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(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(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(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[5771])).
% 2.04/2.25 tff(5773,plain,
% 2.04/2.25 (((~![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(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(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(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[5772, 5770])).
% 2.04/2.25 tff(5774,plain,
% 2.04/2.25 ((~![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(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(5775,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[5774, 5773])).
% 2.04/2.25 tff(5776,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5775, 97, 5728, 4294, 4292, 5769])).
% 2.04/2.25 tff(5777,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(5778,plain,
% 2.04/2.25 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5777, 1961, 125, 81, 2597, 1, 226, 1960])).
% 2.04/2.25 tff(5779,plain,
% 2.04/2.25 (r(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[58, 5778])).
% 2.04/2.25 tff(5780,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(5781,plain,
% 2.04/2.25 (((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(5782,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[5781])).
% 2.04/2.25 tff(5783,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[5782, 5780])).
% 2.04/2.25 tff(5784,plain,
% 2.04/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(5785,plain,
% 2.04/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[5784, 5783])).
% 2.04/2.25 tff(5786,plain,
% 2.04/2.25 (~r(s(s(s(elem!1))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5785, 155, 125, 226, 81, 5779])).
% 2.04/2.25 tff(5787,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(5788,plain,
% 2.04/2.25 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(5789,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[5788])).
% 2.04/2.25 tff(5790,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[5789, 5787])).
% 2.04/2.25 tff(5791,plain,
% 2.04/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(5792,plain,
% 2.04/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[5791, 5790])).
% 2.04/2.25 tff(5793,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5792, 155, 145, 1961, 1960, 2630])).
% 2.04/2.25 tff(5794,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(5795,plain,
% 2.04/2.25 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5794, 5779, 1960, 1961])).
% 2.04/2.25 tff(5796,plain,
% 2.04/2.25 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2687, 5795, 4228])).
% 2.04/2.25 tff(5797,plain,
% 2.04/2.25 (~b(s(s(s(elem!1))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5722, 97, 4294, 4292, 5796])).
% 2.04/2.25 tff(5798,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[246, 5797, 5786])).
% 2.04/2.25 tff(5799,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(5800,plain,
% 2.04/2.25 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5799, 81, 226, 125, 1960, 2597, 1])).
% 2.04/2.25 tff(5801,plain,
% 2.04/2.25 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[437, 5800])).
% 2.04/2.25 tff(5802,plain,
% 2.04/2.25 (~b(s(z), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4270, 5677, 5801, 4292])).
% 2.04/2.25 tff(5803,plain,
% 2.04/2.25 (r(s(z), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[253, 5802])).
% 2.04/2.25 tff(5804,plain,
% 2.04/2.25 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2638, 5803, 2597, 125])).
% 2.04/2.25 tff(5805,plain,
% 2.04/2.25 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2687, 5804, 4228])).
% 2.04/2.25 tff(5806,plain,
% 2.04/2.25 (((~![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(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(5807,plain,
% 2.04/2.25 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(5808,plain,
% 2.04/2.25 (((~![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(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(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(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[5807])).
% 2.04/2.25 tff(5809,plain,
% 2.04/2.25 (((~![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(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(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(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[5808, 5806])).
% 2.04/2.25 tff(5810,plain,
% 2.04/2.25 ((~![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(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(5811,plain,
% 2.04/2.25 ((~![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(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[5810, 5809])).
% 2.04/2.25 tff(5812,plain,
% 2.04/2.25 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5811, 97, 5801, 4292, 5805])).
% 2.04/2.25 tff(5813,plain,
% 2.04/2.25 (r(s(s(z)), s(s(s(elem!1))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[143, 5812])).
% 2.04/2.25 tff(5814,plain,
% 2.04/2.25 (((~![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(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(5815,plain,
% 2.04/2.25 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(5816,plain,
% 2.04/2.25 (((~![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(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[5815])).
% 2.04/2.25 tff(5817,plain,
% 2.04/2.25 (((~![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(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[5816, 5814])).
% 2.04/2.25 tff(5818,plain,
% 2.04/2.25 ((~![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(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(5819,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[5818, 5817])).
% 2.04/2.25 tff(5820,plain,
% 2.04/2.25 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5819, 97, 5801, 4292, 5805])).
% 2.04/2.25 tff(5821,plain,
% 2.04/2.25 (r(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[58, 5820])).
% 2.04/2.25 tff(5822,plain,
% 2.04/2.25 (~r(z, s(s(s(elem!1))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5182, 155, 226, 5821, 5813])).
% 2.04/2.25 tff(5823,plain,
% 2.04/2.25 (b(z, s(s(s(elem!1))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[590, 5822])).
% 2.04/2.25 tff(5824,plain,
% 2.04/2.25 (~r(s(s(s(elem!1))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5785, 155, 125, 226, 81, 5821])).
% 2.04/2.25 tff(5825,plain,
% 2.04/2.25 (b(s(s(s(elem!1))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[246, 5824])).
% 2.04/2.25 tff(5826,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5741, 97, 5825, 5823, 4292, 5805])).
% 2.04/2.25 tff(5827,plain,((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(5828,plain,
% 2.04/2.25 (~r(s(z), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5827, 125, 226, 2597, 1960, 1])).
% 2.04/2.25 tff(5829,plain,
% 2.04/2.25 (b(s(z), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[568, 5828])).
% 2.04/2.25 tff(5830,plain,
% 2.04/2.25 (~r(s(z), s(s(s(elem!1))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5757, 4251, 2597, 125])).
% 2.04/2.25 tff(5831,plain,
% 2.04/2.25 (b(s(z), s(s(s(elem!1))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[181, 5830])).
% 2.04/2.25 tff(5832,plain,
% 2.04/2.25 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(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), s(s(s(elem!1))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5833,plain,
% 2.04/2.26 (((~![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(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[5832])).
% 2.04/2.26 tff(5834,plain,
% 2.04/2.26 (((~![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(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[5833, 953])).
% 2.04/2.26 tff(5835,plain,
% 2.04/2.26 ((~![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(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(5836,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[5835, 5834])).
% 2.04/2.26 tff(5837,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5836, 97, 193, 550, 126, 124])).
% 2.04/2.26 tff(5838,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(5839,plain,
% 2.04/2.26 (~b(z, s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5838, 5831, 5829, 4284])).
% 2.04/2.26 tff(5840,plain,
% 2.04/2.26 (r(z, s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[590, 5839])).
% 2.04/2.26 tff(5841,plain,
% 2.04/2.26 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[3089, 1, 3087])).
% 2.04/2.26 tff(5842,plain,
% 2.04/2.26 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2687, 4228, 2684])).
% 2.04/2.26 tff(5843,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5844,plain,
% 2.04/2.26 (((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5845,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[5844])).
% 2.04/2.26 tff(5846,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[5845, 5843])).
% 2.04/2.26 tff(5847,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(elem!1))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(5848,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[5847, 5846])).
% 2.04/2.26 tff(5849,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5848, 155, 570, 1300, 2630, 4252])).
% 2.04/2.26 tff(5850,plain,((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(5851,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5850, 5842, 5841, 570, 1300])).
% 2.04/2.26 tff(5852,plain,((s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(z)))) | b(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(5853,plain,
% 2.04/2.26 (~r(z, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5852, 5840, 2684, 1, 4250])).
% 2.04/2.26 tff(5854,plain,
% 2.04/2.26 (b(z, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1318, 5853])).
% 2.04/2.26 tff(5855,plain,
% 2.04/2.26 (((~![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(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5856,plain,
% 2.04/2.26 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5857,plain,
% 2.04/2.26 (((~![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(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), 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(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[5856])).
% 2.04/2.26 tff(5858,plain,
% 2.04/2.26 (((~![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(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), 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(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[5857, 5855])).
% 2.04/2.26 tff(5859,plain,
% 2.04/2.26 ((~![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(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(5860,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[5859, 5858])).
% 2.04/2.26 tff(5861,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5860, 97, 5831, 5829, 4284, 5854])).
% 2.04/2.26 tff(5862,plain,(b(s(s(s(elem!1))), s(s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(5863,plain,
% 2.04/2.26 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5862, 1361, 125, 226, 145, 1, 2597, 1960])).
% 2.04/2.26 tff(5864,plain,
% 2.04/2.26 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4260, 3, 2597, 1960, 125])).
% 2.04/2.26 tff(5865,plain,
% 2.04/2.26 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[3089, 5864, 1])).
% 2.04/2.26 tff(5866,plain,
% 2.04/2.26 (((~![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(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(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(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5867,plain,
% 2.04/2.26 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5868,plain,
% 2.04/2.26 (((~![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(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(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(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[5867])).
% 2.04/2.26 tff(5869,plain,
% 2.04/2.26 (((~![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(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(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(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[5868, 5866])).
% 2.04/2.26 tff(5870,plain,
% 2.04/2.26 ((~![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(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(5871,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[5870, 5869])).
% 2.04/2.26 tff(5872,plain,
% 2.04/2.26 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5871, 97, 1361, 5865, 5863])).
% 2.04/2.26 tff(5873,plain,
% 2.04/2.26 (r(s(s(z)), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[143, 5872])).
% 2.04/2.26 tff(5874,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[161, 155, 3, 225, 145, 224])).
% 2.04/2.26 tff(5875,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(5876,plain,
% 2.04/2.26 (~r(s(z), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5875, 5873, 3, 145])).
% 2.04/2.26 tff(5877,plain,
% 2.04/2.26 (b(s(z), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[181, 5876])).
% 2.04/2.26 tff(5878,plain,
% 2.04/2.26 (~r(z, s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5182, 155, 226, 145, 5873])).
% 2.04/2.26 tff(5879,plain,
% 2.04/2.26 (b(z, s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[590, 5878])).
% 2.04/2.26 tff(5880,plain,
% 2.04/2.26 (~b(s(s(s(elem!1))), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5838, 5879, 5829, 5877])).
% 2.04/2.26 tff(5881,plain,
% 2.04/2.26 (r(s(s(s(elem!1))), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[246, 5880])).
% 2.04/2.26 tff(5882,plain,
% 2.04/2.26 (~r(s(s(z)), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2671, 5881, 226, 145])).
% 2.04/2.26 tff(5883,plain,
% 2.04/2.26 (b(s(s(z)), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[625, 5882])).
% 2.04/2.26 tff(5884,plain,
% 2.04/2.26 (~b(z, s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2023, 5883, 5877, 2982])).
% 2.04/2.26 tff(5885,plain,
% 2.04/2.26 (r(z, s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[723, 5884])).
% 2.04/2.26 tff(5886,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5887,plain,
% 2.04/2.26 (((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5888,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[5887])).
% 2.04/2.26 tff(5889,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))),
% 2.04/2.26 inference(transitivity,[status(thm)],[5888, 5886])).
% 2.04/2.26 tff(5890,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(5891,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[5890, 5889])).
% 2.04/2.26 tff(5892,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5891, 155, 125, 5885, 5881, 3, 145])).
% 2.04/2.26 tff(5893,plain,((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(5894,plain,
% 2.04/2.26 (~r(s(z), s(s(z)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5893, 1361, 145, 226, 125, 1, 2597, 1960])).
% 2.04/2.26 tff(5895,plain,
% 2.04/2.26 (b(s(z), s(s(z)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[548, 5894])).
% 2.04/2.26 tff(5896,plain,
% 2.04/2.26 (~r(s(s(z)), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2671, 288, 226, 145])).
% 2.04/2.26 tff(5897,plain,
% 2.04/2.26 (b(s(s(z)), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[625, 5896])).
% 2.04/2.26 tff(5898,plain,
% 2.04/2.26 (~b(z, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2972, 5897, 5829, 5895])).
% 2.04/2.26 tff(5899,plain,
% 2.04/2.26 (r(z, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1318, 5898])).
% 2.04/2.26 tff(5900,plain,
% 2.04/2.26 (~b(z, s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[3987, 288, 226, 125, 145, 5895])).
% 2.04/2.26 tff(5901,plain,
% 2.04/2.26 (r(z, s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[723, 5900])).
% 2.04/2.26 tff(5902,plain,
% 2.04/2.26 (~b(s(z), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4249, 1702, 1960, 1361, 2597])).
% 2.04/2.26 tff(5903,plain,
% 2.04/2.26 (r(s(z), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[253, 5902])).
% 2.04/2.26 tff(5904,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5905,plain,
% 2.04/2.26 (((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5906,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[5905])).
% 2.04/2.26 tff(5907,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[5906, 5904])).
% 2.04/2.26 tff(5908,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(5909,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[5908, 5907])).
% 2.04/2.26 tff(5910,plain,
% 2.04/2.26 (~r(z, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5909, 155, 729, 5903, 2597])).
% 2.04/2.26 tff(5911,plain,
% 2.04/2.26 (b(z, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1318, 5910])).
% 2.04/2.26 tff(5912,plain,
% 2.04/2.26 (((~![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(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5913,plain,
% 2.04/2.26 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~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(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5914,plain,
% 2.04/2.26 (((~![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(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~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(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[5913])).
% 2.04/2.26 tff(5915,plain,
% 2.04/2.26 (((~![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(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~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(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[5914, 5912])).
% 2.04/2.26 tff(5916,plain,
% 2.04/2.26 ((~![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(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~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)))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(5917,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[5916, 5915])).
% 2.04/2.26 tff(5918,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5917, 97, 83, 1361, 5911, 1702])).
% 2.04/2.26 tff(5919,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(5920,plain,
% 2.04/2.26 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5919, 5897, 1361, 5901, 2597, 1960])).
% 2.04/2.26 tff(5921,plain,
% 2.04/2.26 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[3089, 5920, 1])).
% 2.04/2.27 tff(5922,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(5923,plain,
% 2.04/2.27 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(5924,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[5923])).
% 2.04/2.27 tff(5925,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[5924, 5922])).
% 2.04/2.27 tff(5926,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(5927,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[5926, 5925])).
% 2.04/2.27 tff(5928,plain,
% 2.04/2.27 ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5927, 155, 125, 5901, 5921])).
% 2.04/2.27 tff(5929,plain,
% 2.04/2.27 (~r(z, s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5928, 5899])).
% 2.04/2.27 tff(5930,plain,
% 2.04/2.27 (b(z, s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[590, 5929])).
% 2.04/2.27 tff(5931,plain,
% 2.04/2.27 (((~![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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(5932,plain,
% 2.04/2.27 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(5933,plain,
% 2.04/2.27 (((~![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(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), 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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[5932])).
% 2.04/2.27 tff(5934,plain,
% 2.04/2.27 (((~![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(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), 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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.27 inference(transitivity,[status(thm)],[5933, 5931])).
% 2.04/2.27 tff(5935,plain,
% 2.04/2.27 ((~![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(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(5936,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[5935, 5934])).
% 2.04/2.27 tff(5937,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5936, 97, 5829, 5930, 5897, 5895])).
% 2.04/2.27 tff(5938,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(5939,plain,
% 2.04/2.27 (~r(s(s(s(elem!1))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5938, 1361, 1, 125, 2597, 1960, 226, 145])).
% 2.04/2.27 tff(5940,plain,
% 2.04/2.27 (b(s(s(s(elem!1))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[246, 5939])).
% 2.04/2.27 tff(5941,assumption,(b(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 2.04/2.27 tff(5942,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(5943,plain,
% 2.04/2.27 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z)))))) <=> ((~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(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(5944,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[5943])).
% 2.04/2.27 tff(5945,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[5944, 5942])).
% 2.04/2.27 tff(5946,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(5947,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[5946, 5945])).
% 2.04/2.27 tff(5948,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5947, 155, 570, 226, 1300, 224, 1960])).
% 2.04/2.27 tff(5949,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(5950,plain,
% 2.04/2.27 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5949, 1300, 226, 1960, 570])).
% 2.04/2.27 tff(5951,plain,
% 2.04/2.27 (b(s(s(z)), s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[143, 5950])).
% 2.04/2.27 tff(5952,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(5953,plain,
% 2.04/2.27 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(5954,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[5953])).
% 2.04/2.27 tff(5955,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[5954, 5952])).
% 2.04/2.27 tff(5956,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(5957,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[5956, 5955])).
% 2.04/2.27 tff(5958,plain,
% 2.04/2.27 ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5957, 155, 125, 570, 2597])).
% 2.04/2.27 tff(5959,plain,
% 2.04/2.27 (~r(s(s(s(z))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5958, 4252])).
% 2.04/2.27 tff(5960,plain,
% 2.04/2.27 (b(s(s(s(z))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[402, 5959])).
% 2.04/2.27 tff(5961,plain,
% 2.04/2.27 (~b(s(z), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4270, 5960, 1361, 535])).
% 2.04/2.27 tff(5962,plain,
% 2.04/2.27 (r(s(z), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[253, 5961])).
% 2.04/2.27 tff(5963,plain,
% 2.04/2.27 (~r(z, s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5031, 155, 226, 1300, 5962, 1960])).
% 2.04/2.27 tff(5964,plain,
% 2.04/2.27 (b(z, s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[723, 5963])).
% 2.04/2.27 tff(5965,plain,
% 2.04/2.27 (~r(s(z), s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5757, 4252, 2597, 125])).
% 2.04/2.27 tff(5966,plain,
% 2.04/2.27 (b(s(z), s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[181, 5965])).
% 2.04/2.27 tff(5967,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4212, 97, 5966, 550, 5964, 126])).
% 2.04/2.27 tff(5968,plain,((~r(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(5969,plain,
% 2.04/2.27 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5968, 1300, 126, 226, 5829, 1960, 1361, 535, 125, 570, 2597])).
% 2.04/2.27 tff(5970,plain,
% 2.04/2.27 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3089, 5969, 1])).
% 2.04/2.27 tff(5971,plain,
% 2.04/2.27 (~b(s(z), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4249, 5970, 1960, 1361, 2597])).
% 2.04/2.27 tff(5972,plain,
% 2.04/2.27 (r(s(z), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[253, 5971])).
% 2.04/2.27 tff(5973,plain,
% 2.04/2.27 (~r(z, s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5031, 155, 226, 1300, 5972, 1960])).
% 2.04/2.27 tff(5974,plain,
% 2.04/2.27 (b(z, s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[723, 5973])).
% 2.04/2.27 tff(5975,plain,
% 2.04/2.27 (~b(s(s(z)), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[135, 5974, 5951, 126])).
% 2.04/2.27 tff(5976,plain,
% 2.04/2.27 (r(s(s(z)), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[625, 5975])).
% 2.04/2.27 tff(5977,plain,
% 2.04/2.27 (~r(s(s(s(z))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2693, 155, 226, 5976, 1960])).
% 2.04/2.27 tff(5978,plain,
% 2.04/2.27 (b(s(s(s(z))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[402, 5977])).
% 2.04/2.27 tff(5979,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5811, 97, 1361, 5951, 5978, 5941])).
% 2.04/2.27 tff(5980,plain,((~r(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(5981,plain,
% 2.04/2.27 (~r(z, s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5980, 570, 5941, 226, 1960, 126, 2597, 1, 535, 125, 1361])).
% 2.04/2.27 tff(5982,plain,
% 2.04/2.27 (b(z, s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1318, 5981])).
% 2.04/2.27 tff(5983,plain,
% 2.04/2.27 (~b(s(z), s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5860, 97, 5829, 126, 5982])).
% 2.04/2.27 tff(5984,plain,
% 2.04/2.27 (r(s(z), s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[181, 5983])).
% 2.04/2.27 tff(5985,plain,
% 2.04/2.27 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5757, 5984, 2597, 125])).
% 2.04/2.27 tff(5986,plain,
% 2.04/2.27 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3089, 5985, 1])).
% 2.04/2.27 tff(5987,plain,
% 2.04/2.27 (~b(s(s(z)), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2972, 5982, 5829, 535])).
% 2.04/2.27 tff(5988,plain,
% 2.04/2.27 (r(s(s(z)), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[625, 5987])).
% 2.04/2.27 tff(5989,plain,
% 2.04/2.27 (~r(s(s(s(z))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2693, 155, 226, 5988, 1960])).
% 2.04/2.27 tff(5990,plain,
% 2.04/2.27 (b(s(s(s(z))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[402, 5989])).
% 2.04/2.27 tff(5991,plain,
% 2.04/2.27 (~r(z, s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[771, 5984, 125, 570])).
% 2.04/2.27 tff(5992,plain,
% 2.04/2.27 (b(z, s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[723, 5991])).
% 2.04/2.27 tff(5993,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3413, 97, 5992, 126, 5990, 5986])).
% 2.04/2.27 tff(5994,plain,((~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(5995,plain,
% 2.04/2.27 (~r(z, s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5994, 5940, 1, 2597, 125, 226, 1960, 5895, 5863, 1361])).
% 2.04/2.27 tff(5996,plain,
% 2.04/2.27 (b(z, s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[590, 5995])).
% 2.04/2.27 tff(5997,plain,
% 2.04/2.27 (~b(s(z), s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5838, 5996, 5829, 5940])).
% 2.04/2.27 tff(5998,plain,
% 2.04/2.27 (r(s(z), s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[181, 5997])).
% 2.04/2.27 tff(5999,plain,
% 2.04/2.27 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5757, 5998, 2597, 125])).
% 2.04/2.27 tff(6000,plain,
% 2.04/2.27 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3089, 5999, 1])).
% 2.04/2.27 tff(6001,plain,
% 2.04/2.27 (~b(s(s(s(z))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4360, 97, 5940, 5996, 6000])).
% 2.04/2.27 tff(6002,plain,
% 2.04/2.27 (r(s(s(s(z))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[402, 6001])).
% 2.04/2.27 tff(6003,plain,
% 2.04/2.27 (((~![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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(6004,plain,
% 2.04/2.27 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(6005,plain,
% 2.04/2.27 (((~![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))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[6004])).
% 2.04/2.27 tff(6006,plain,
% 2.04/2.27 (((~![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))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[6005, 6003])).
% 2.04/2.27 tff(6007,plain,
% 2.04/2.27 ((~![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))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(6008,plain,
% 2.04/2.27 ((~![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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[6007, 6006])).
% 2.04/2.27 tff(6009,plain,
% 2.04/2.27 (~b(z, s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[6008, 97, 5940, 5996, 6000])).
% 2.04/2.27 tff(6010,plain,
% 2.04/2.27 (r(z, s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1318, 6009])).
% 2.04/2.27 tff(6011,plain,
% 2.04/2.27 (~b(s(z), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4249, 6000, 1960, 1361, 2597])).
% 2.04/2.27 tff(6012,plain,
% 2.04/2.27 (r(s(z), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[253, 6011])).
% 2.04/2.27 tff(6013,plain,
% 2.04/2.27 ((~r(z, s(z))) | (~r(z, s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5031, 155, 226, 6012, 1960])).
% 2.04/2.27 tff(6014,plain,
% 2.04/2.27 (~r(z, s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[6013, 6010])).
% 2.04/2.27 tff(6015,plain,
% 2.04/2.27 (b(z, s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[723, 6014])).
% 2.04/2.27 tff(6016,plain,
% 2.04/2.27 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5871, 97, 1361, 6000, 5863])).
% 2.04/2.27 tff(6017,plain,
% 2.04/2.27 (r(s(s(z)), s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[143, 6016])).
% 2.04/2.27 tff(6018,plain,
% 2.04/2.27 (~r(s(s(z)), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1273, 6017, 125, 5998])).
% 2.04/2.27 tff(6019,plain,
% 2.04/2.27 (b(s(s(z)), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[122, 6018])).
% 2.04/2.27 tff(6020,plain,
% 2.04/2.27 (~b(s(s(z)), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2651, 6019, 5895, 6015])).
% 2.04/2.27 tff(6021,plain,
% 2.04/2.27 (r(s(s(z)), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[625, 6020])).
% 2.04/2.27 tff(6022,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2625, 155, 226, 6021, 1960, 6002])).
% 2.04/2.27 tff(6023,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(6024,plain,
% 2.04/2.27 (~b(s(s(z)), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[6023, 145, 1960, 125, 2597, 1, 226])).
% 2.04/2.27 tff(6025,plain,
% 2.04/2.27 (r(s(s(z)), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[437, 6024])).
% 2.04/2.27 tff(6026,plain,
% 2.04/2.27 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5794, 6025, 1960, 145])).
% 2.04/2.27 tff(6027,plain,
% 2.04/2.27 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2687, 6026, 4228])).
% 2.04/2.27 tff(6028,plain,
% 2.04/2.27 (~r(z, s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1969, 6025, 226, 1960])).
% 2.04/2.27 tff(6029,plain,
% 2.04/2.27 (b(z, s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1318, 6028])).
% 2.04/2.27 tff(6030,plain,
% 2.04/2.27 (~r(s(z), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2641, 3, 1961, 1960])).
% 2.04/2.27 tff(6031,plain,
% 2.04/2.27 (b(s(z), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[253, 6030])).
% 2.04/2.27 tff(6032,plain,
% 2.04/2.27 (((~![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(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(6033,plain,
% 2.04/2.27 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(6034,plain,
% 2.04/2.28 (((~![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(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~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(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6033])).
% 2.04/2.28 tff(6035,plain,
% 2.04/2.28 (((~![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(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~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(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[6034, 6032])).
% 2.04/2.28 tff(6036,plain,
% 2.04/2.28 ((~![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(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(6037,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[6036, 6035])).
% 2.04/2.28 tff(6038,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6037, 97, 550, 6031, 1330, 5865])).
% 2.04/2.28 tff(6039,plain,((~r(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(6040,plain,
% 2.04/2.28 (~r(s(z), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6039, 6029, 5829, 1, 6025, 1960, 2597, 125])).
% 2.04/2.28 tff(6041,plain,
% 2.04/2.28 (b(s(z), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[548, 6040])).
% 2.04/2.28 tff(6042,plain,
% 2.04/2.28 (~b(s(s(z)), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2972, 6041, 5829, 6029])).
% 2.04/2.28 tff(6043,plain,
% 2.04/2.28 (r(s(s(z)), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[625, 6042])).
% 2.04/2.28 tff(6044,plain,
% 2.04/2.28 (~r(s(s(s(z))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2693, 155, 226, 6043, 1960])).
% 2.04/2.28 tff(6045,plain,
% 2.04/2.28 (b(s(s(s(z))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[402, 6044])).
% 2.04/2.28 tff(6046,plain,
% 2.04/2.28 (~r(s(s(s(elem!1))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2671, 6043, 226, 145])).
% 2.04/2.28 tff(6047,plain,
% 2.04/2.28 (b(s(s(s(elem!1))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[246, 6046])).
% 2.04/2.28 tff(6048,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[5722, 97, 6047, 6029, 6045, 6027])).
% 2.04/2.28 tff(6049,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(6050,plain,
% 2.04/2.28 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6049, 4227, 494, 1960, 4222, 4223])).
% 2.04/2.28 tff(6051,plain,
% 2.04/2.28 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6050])).
% 2.04/2.28 tff(6052,plain,
% 2.04/2.28 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.04/2.28 inference(symmetry,[status(thm)],[6051])).
% 2.04/2.28 tff(6053,plain,
% 2.04/2.28 (s(s(elem!1)) = s(s(z))),
% 2.04/2.28 inference(transitivity,[status(thm)],[167, 6052, 72])).
% 2.04/2.28 tff(6054,plain,
% 2.04/2.28 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6053])).
% 2.04/2.28 tff(6055,plain,
% 2.04/2.28 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.28 inference(symmetry,[status(thm)],[6054])).
% 2.04/2.28 tff(6056,plain,
% 2.04/2.28 (~r(z, s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1969, 4222, 1961, 1960])).
% 2.04/2.28 tff(6057,plain,
% 2.04/2.28 (b(z, s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1318, 6056])).
% 2.04/2.28 tff(6058,plain,
% 2.04/2.28 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[5757, 4227, 4214, 494])).
% 2.04/2.28 tff(6059,plain,
% 2.04/2.28 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[914, 372, 126, 124])).
% 2.04/2.28 tff(6060,plain,
% 2.04/2.28 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[558, 372, 550, 61])).
% 2.04/2.28 tff(6061,plain,
% 2.04/2.28 (r(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[511, 6060])).
% 2.04/2.28 tff(6062,plain,
% 2.04/2.28 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1136, 6061, 125, 225])).
% 2.04/2.28 tff(6063,plain,
% 2.04/2.28 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[821, 6062, 6059])).
% 2.04/2.28 tff(6064,plain,
% 2.04/2.28 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[523, 6063])).
% 2.04/2.28 tff(6065,plain,
% 2.04/2.28 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[349, 6064])).
% 2.04/2.28 tff(6066,plain,
% 2.04/2.28 (s(s(s(s(elem!1)))) = elem!1),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1734, 6065])).
% 2.04/2.28 tff(6067,plain,
% 2.04/2.28 (~(s(s(s(z))) = elem!1)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1742, 6064])).
% 2.04/2.28 tff(6068,plain,
% 2.04/2.28 (elem!1 = s(s(s(s(elem!1))))),
% 2.04/2.28 inference(symmetry,[status(thm)],[6066])).
% 2.04/2.28 tff(6069,plain,
% 2.04/2.28 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6068])).
% 2.04/2.28 tff(6070,plain,
% 2.04/2.28 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), elem!1)),
% 2.04/2.28 inference(symmetry,[status(thm)],[6069])).
% 2.04/2.28 tff(6071,plain,
% 2.04/2.28 ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(z))), elem!1))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6070])).
% 2.04/2.28 tff(6072,plain,
% 2.04/2.28 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6064])).
% 2.04/2.28 tff(6073,plain,
% 2.04/2.28 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6072])).
% 2.04/2.28 tff(6074,plain,
% 2.04/2.28 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[1749, 6073])).
% 2.04/2.28 tff(6075,plain,
% 2.04/2.28 (~r(s(s(s(z))), elem!1)),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[6074, 6071])).
% 2.04/2.28 tff(6076,plain,
% 2.04/2.28 (b(s(s(s(z))), elem!1)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1755, 6075, 6067])).
% 2.04/2.28 tff(6077,plain,
% 2.04/2.28 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1764, 6076, 6066])).
% 2.04/2.28 tff(6078,plain,
% 2.04/2.28 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6064])).
% 2.04/2.28 tff(6079,plain,
% 2.04/2.28 (b(s(s(s(s(elem!1)))), z)),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[126, 6078])).
% 2.04/2.28 tff(6080,plain,
% 2.04/2.28 (((~![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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(6081,plain,
% 2.04/2.28 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(6082,plain,
% 2.04/2.28 (((~![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)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z)))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6081])).
% 2.04/2.28 tff(6083,plain,
% 2.04/2.28 (((~![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)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[6082, 6080])).
% 2.04/2.28 tff(6084,plain,
% 2.04/2.28 ((~![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)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(6085,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z)))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[6084, 6083])).
% 2.04/2.28 tff(6086,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6085, 97, 372, 6079, 1330, 6077])).
% 2.04/2.28 tff(6087,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(6088,plain,
% 2.04/2.28 (~b(z, s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6087, 6058, 3008, 126, 494, 4214, 61, 550, 6057])).
% 2.04/2.28 tff(6089,plain,
% 2.04/2.28 (r(z, s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1093, 6088])).
% 2.04/2.28 tff(6090,plain,
% 2.04/2.28 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[5794, 4223, 1960, 1961])).
% 2.04/2.28 tff(6091,plain,
% 2.04/2.28 (((~![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(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(6092,plain,
% 2.04/2.28 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(6093,plain,
% 2.04/2.28 (((~![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(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6092])).
% 2.04/2.28 tff(6094,plain,
% 2.04/2.28 (((~![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(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[6093, 6091])).
% 2.04/2.28 tff(6095,plain,
% 2.04/2.28 ((~![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(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(6096,plain,
% 2.04/2.28 ((~![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(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[6095, 6094])).
% 2.04/2.28 tff(6097,plain,
% 2.04/2.28 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6096, 97, 61, 126, 4225])).
% 2.04/2.28 tff(6098,plain,
% 2.04/2.28 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2687, 6097, 6090])).
% 2.04/2.28 tff(6099,plain,
% 2.04/2.28 (~b(s(s(s(s(elem!1)))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[3648, 488, 125, 550, 124])).
% 2.04/2.28 tff(6100,plain,
% 2.04/2.28 (r(s(s(s(s(elem!1)))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[842, 6099])).
% 2.04/2.28 tff(6101,plain,
% 2.04/2.28 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[3107, 6100, 1393])).
% 2.04/2.28 tff(6102,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(6103,plain,
% 2.04/2.28 (((~r(s(s(elem!1)), 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)))), 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)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(6104,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6103])).
% 2.04/2.28 tff(6105,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.04/2.28 inference(transitivity,[status(thm)],[6104, 6102])).
% 2.04/2.28 tff(6106,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(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)))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(6107,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[6106, 6105])).
% 2.04/2.28 tff(6108,plain,
% 2.04/2.28 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6107, 155, 6101, 3321, 3843])).
% 2.04/2.28 tff(6109,plain,
% 2.04/2.28 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1822, 6108, 1393])).
% 2.04/2.28 tff(6110,plain,
% 2.04/2.28 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[452, 6109])).
% 2.04/2.28 tff(6111,plain,
% 2.04/2.28 (~b(s(z), s(s(s(elem!1))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[5836, 97, 550, 126, 124])).
% 2.04/2.28 tff(6112,plain,
% 2.04/2.28 (r(s(z), s(s(s(elem!1))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[181, 6111])).
% 2.04/2.28 tff(6113,plain,
% 2.04/2.28 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[821, 6059, 802])).
% 2.04/2.28 tff(6114,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1136, 6113, 6061, 125, 225])).
% 2.04/2.28 tff(6115,plain,((~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(6116,plain,
% 2.04/2.28 (~b(z, s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6115, 61, 126, 125, 6112, 124, 550, 4451])).
% 2.04/2.28 tff(6117,plain,
% 2.04/2.28 (r(z, s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1093, 6116])).
% 2.04/2.28 tff(6118,plain,
% 2.04/2.28 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[3326, 6117, 645, 1393, 6100])).
% 2.04/2.28 tff(6119,plain,
% 2.04/2.28 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[336, 6118])).
% 2.04/2.28 tff(6120,plain,
% 2.04/2.28 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[3267, 6119, 535, 6110])).
% 2.04/2.28 tff(6121,plain,
% 2.04/2.28 (r(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[280, 6120])).
% 2.04/2.28 tff(6122,plain,
% 2.04/2.28 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[3253, 6119, 535, 226, 645, 338, 2597, 550, 2508, 61])).
% 2.04/2.28 tff(6123,plain,
% 2.04/2.28 (r(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[511, 6122])).
% 2.04/2.28 tff(6124,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[503, 6123, 6121, 125, 488])).
% 2.04/2.28 tff(6125,plain,((~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~(s(s(s(elem!1))) = s(s(s(z))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(6126,plain,
% 2.04/2.28 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6125, 6098, 4218, 61, 494, 550, 4222, 4227, 4220, 4216, 6050, 126, 3008])).
% 2.04/2.28 tff(6127,plain,
% 2.04/2.28 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[3021, 6089, 585])).
% 2.04/2.28 tff(6128,plain,
% 2.04/2.28 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[486, 6127, 6126])).
% 2.04/2.28 tff(6129,plain,
% 2.04/2.28 (~b(s(s(s(s(elem!1)))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[3290, 6128, 3008, 126])).
% 2.04/2.28 tff(6130,plain,
% 2.04/2.28 (r(s(s(s(s(elem!1)))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[842, 6129])).
% 2.04/2.28 tff(6131,plain,
% 2.04/2.28 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[3326, 6130, 6050, 4220, 6089])).
% 2.04/2.28 tff(6132,plain,
% 2.04/2.28 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[336, 6131])).
% 2.04/2.28 tff(6133,plain,
% 2.04/2.28 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[3240, 6132, 550, 87])).
% 2.04/2.28 tff(6134,plain,
% 2.04/2.28 (r(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[511, 6133])).
% 2.04/2.28 tff(6135,plain,
% 2.04/2.28 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1136, 6134, 494, 4214])).
% 2.04/2.28 tff(6136,plain,
% 2.04/2.28 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4129, 6135, 6127, 6126, 6132])).
% 2.04/2.28 tff(6137,plain,
% 2.04/2.28 (r(s(s(z)), s(s(s(elem!1))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[143, 6136])).
% 2.04/2.28 tff(6138,plain,
% 2.04/2.28 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[6137, 6055])).
% 2.04/2.28 tff(6139,plain,
% 2.04/2.28 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6053])).
% 2.04/2.28 tff(6140,plain,
% 2.04/2.28 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.28 inference(symmetry,[status(thm)],[6139])).
% 2.04/2.28 tff(6141,plain,
% 2.04/2.28 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[4223, 6140])).
% 2.04/2.28 tff(6142,plain,
% 2.04/2.28 (s(s(z)) = s(s(elem!1))),
% 2.04/2.28 inference(transitivity,[status(thm)],[73, 6051, 19])).
% 2.04/2.28 tff(6143,plain,
% 2.04/2.28 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6142])).
% 2.04/2.28 tff(6144,plain,
% 2.04/2.28 (s(z) = s(elem!1)),
% 2.04/2.28 inference(transitivity,[status(thm)],[24, 6143, 29])).
% 2.04/2.28 tff(6145,plain,
% 2.04/2.28 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6144])).
% 2.04/2.28 tff(6146,plain,
% 2.04/2.28 (z = elem!1),
% 2.04/2.28 inference(transitivity,[status(thm)],[1443, 6145, 85])).
% 2.04/2.28 tff(6147,plain,
% 2.04/2.28 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6146, 6142])).
% 2.04/2.28 tff(6148,plain,
% 2.04/2.28 (r(elem!1, s(s(elem!1)))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[4222, 6147])).
% 2.04/2.28 tff(6149,plain,
% 2.04/2.28 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6146])).
% 2.04/2.28 tff(6150,plain,
% 2.04/2.28 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6142])).
% 2.04/2.28 tff(6151,plain,
% 2.04/2.28 (r(s(s(elem!1)), z)),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[4220, 6150])).
% 2.04/2.28 tff(6152,plain,
% 2.04/2.28 (r(s(s(elem!1)), elem!1)),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[6151, 6149])).
% 2.04/2.28 tff(6153,plain,
% 2.04/2.28 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6146])).
% 2.04/2.28 tff(6154,plain,
% 2.04/2.28 (b(elem!1, s(s(s(elem!1))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[3008, 6153])).
% 2.04/2.28 tff(6155,plain,
% 2.04/2.28 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6146])).
% 2.04/2.28 tff(6156,plain,
% 2.04/2.28 (b(s(s(s(elem!1))), elem!1)),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[126, 6155])).
% 2.04/2.28 tff(6157,plain,
% 2.04/2.28 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.04/2.28 inference(symmetry,[status(thm)],[6143])).
% 2.04/2.28 tff(6158,plain,
% 2.04/2.28 (s(elem!1) = s(z)),
% 2.04/2.28 inference(transitivity,[status(thm)],[30, 6157, 23])).
% 2.04/2.28 tff(6159,plain,
% 2.04/2.28 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(z))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6158])).
% 2.04/2.28 tff(6160,plain,
% 2.04/2.28 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(z) = s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[6159, 265])).
% 2.04/2.28 tff(6161,plain,
% 2.04/2.28 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.04/2.28 inference(symmetry,[status(thm)],[6160])).
% 2.04/2.28 tff(6162,plain,
% 2.04/2.28 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6161])).
% 2.04/2.28 tff(6163,plain,
% 2.04/2.28 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[275, 6162])).
% 2.04/2.28 tff(6164,assumption,(s(s(s(s(s(elem!1))))) = s(s(elem!1))), introduced(assumption)).
% 2.04/2.28 tff(6165,plain,
% 2.04/2.28 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6164])).
% 2.04/2.28 tff(6166,plain,
% 2.04/2.28 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(6167,plain,
% 2.04/2.28 (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6166, 15])).
% 2.04/2.28 tff(6168,plain,
% 2.04/2.28 (s(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.04/2.28 inference(symmetry,[status(thm)],[6167])).
% 2.04/2.28 tff(6169,plain,
% 2.04/2.28 (s(s(s(s(elem!1)))) = s(elem!1)),
% 2.04/2.28 inference(transitivity,[status(thm)],[6168, 6165, 29])).
% 2.04/2.28 tff(6170,assumption,(~(s(s(s(s(elem!1)))) = s(elem!1))), introduced(assumption)).
% 2.04/2.28 tff(6171,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6170, 6169])).
% 2.04/2.28 tff(6172,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,[]))).
% 2.04/2.28 tff(6173,plain,
% 2.04/2.28 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6172, 6163])).
% 2.04/2.28 tff(6174,plain,
% 2.04/2.28 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6142])).
% 2.04/2.28 tff(6175,plain,
% 2.04/2.28 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2905, 6130, 4218, 61, 87])).
% 2.04/2.28 tff(6176,plain,
% 2.04/2.28 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[452, 6175])).
% 2.04/2.28 tff(6177,plain,
% 2.04/2.28 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[6176, 6174])).
% 2.04/2.28 tff(6178,plain,
% 2.04/2.28 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(z)))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6053])).
% 2.04/2.28 tff(6179,plain,
% 2.04/2.28 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.04/2.28 inference(symmetry,[status(thm)],[6178])).
% 2.04/2.28 tff(6180,plain,
% 2.04/2.28 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[6144])).
% 2.04/2.28 tff(6181,plain,
% 2.04/2.28 (b(s(elem!1), s(s(z)))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[4218, 6180])).
% 2.04/2.28 tff(6182,plain,
% 2.04/2.28 (b(s(elem!1), s(s(elem!1)))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[6181, 6179])).
% 2.04/2.28 tff(6183,plain,
% 2.04/2.28 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[6142])).
% 2.04/2.29 tff(6184,plain,
% 2.04/2.29 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[6132, 6183])).
% 2.04/2.29 tff(6185,plain,
% 2.04/2.29 ((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))))))),
% 2.04/2.29 inference(commutativity,[status(thm)],[])).
% 2.04/2.29 tff(6186,plain,
% 2.04/2.29 ((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)))))),
% 2.04/2.29 inference(symmetry,[status(thm)],[6185])).
% 2.04/2.29 tff(6187,plain,
% 2.04/2.29 ((~(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))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[6186])).
% 2.04/2.29 tff(6188,assumption,(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.04/2.29 tff(6189,plain,
% 2.04/2.29 (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))),
% 2.04/2.29 inference(symmetry,[status(thm)],[6188])).
% 2.04/2.29 tff(6190,plain,
% 2.04/2.29 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[1393, 6189])).
% 2.04/2.29 tff(6191,plain,
% 2.04/2.29 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 2.04/2.29 inference(symmetry,[status(thm)],[6190])).
% 2.04/2.29 tff(6192,plain,
% 2.04/2.29 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(z))) = s(s(s(s(s(elem!1)))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[6191])).
% 2.04/2.29 tff(6193,plain,
% 2.04/2.29 (~(s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[472, 6192])).
% 2.04/2.29 tff(6194,plain,
% 2.04/2.29 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[6188])).
% 2.04/2.29 tff(6195,plain,
% 2.04/2.29 (s(s(s(z))) = s(s(s(s(s(elem!1)))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[1393, 271, 6194, 6167, 6188])).
% 2.04/2.29 tff(6196,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6195, 6193])).
% 2.04/2.29 tff(6197,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~(s(s(s(z))) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(6198,plain,
% 2.04/2.29 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6197, 6127, 6050])).
% 2.04/2.29 tff(6199,plain,
% 2.04/2.29 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[6198, 6187])).
% 2.04/2.29 tff(6200,plain,
% 2.04/2.29 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[6158])).
% 2.04/2.29 tff(6201,plain,
% 2.04/2.29 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.04/2.29 inference(symmetry,[status(thm)],[6200])).
% 2.04/2.29 tff(6202,plain,
% 2.04/2.29 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[6134, 6201])).
% 2.04/2.29 tff(6203,plain,
% 2.04/2.29 (~b(s(s(s(s(elem!1)))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3055, 255, 550, 61])).
% 2.04/2.29 tff(6204,plain,
% 2.04/2.29 (r(s(s(s(s(elem!1)))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[842, 6203])).
% 2.04/2.29 tff(6205,plain,
% 2.04/2.29 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3267, 255, 535, 339])).
% 2.04/2.29 tff(6206,plain,
% 2.04/2.29 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[452, 6205])).
% 2.04/2.29 tff(6207,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2905, 6206, 6204, 535, 61, 87])).
% 2.04/2.29 tff(6208,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(6209,plain,
% 2.04/2.29 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6208, 6132, 61, 87, 4218, 550])).
% 2.04/2.29 tff(6210,plain,
% 2.04/2.29 (r(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[280, 6209])).
% 2.04/2.29 tff(6211,plain,
% 2.04/2.29 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1909, 6210, 6050])).
% 2.04/2.29 tff(6212,plain,
% 2.04/2.29 (r(s(s(s(s(s(elem!1))))), s(elem!1)) <=> r(s(s(s(s(s(elem!1))))), s(z))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[1411])).
% 2.04/2.29 tff(6213,plain,
% 2.04/2.29 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.04/2.29 inference(symmetry,[status(thm)],[6212])).
% 2.04/2.29 tff(6214,assumption,(s(s(s(s(s(elem!1))))) = s(z)), introduced(assumption)).
% 2.04/2.29 tff(6215,plain,
% 2.04/2.29 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 2.04/2.29 inference(transitivity,[status(thm)],[6214, 24, 1400, 29])).
% 2.04/2.29 tff(6216,plain,
% 2.04/2.29 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[6215])).
% 2.04/2.29 tff(6217,plain,
% 2.04/2.29 (s(s(s(s(elem!1)))) = elem!1),
% 2.04/2.29 inference(transitivity,[status(thm)],[6168, 6216, 85])).
% 2.04/2.29 tff(6218,plain,
% 2.04/2.29 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.04/2.29 inference(monotonicity,[status(thm)],[1444])).
% 2.04/2.29 tff(6219,plain,
% 2.04/2.29 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[6218])).
% 2.04/2.29 tff(6220,plain,
% 2.04/2.29 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[837, 6219])).
% 2.04/2.29 tff(6221,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6220, 6217])).
% 2.04/2.29 tff(6222,plain,((~(s(s(s(s(s(elem!1))))) = s(z))) | (~(s(s(s(z))) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(6223,plain,
% 2.04/2.29 (~(s(s(s(s(s(elem!1))))) = s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6222, 1393])).
% 2.04/2.29 tff(6224,plain,
% 2.04/2.29 (b(s(s(s(s(s(elem!1))))), s(elem!1)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[1411])).
% 2.04/2.29 tff(6225,plain,
% 2.04/2.29 ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) <=> (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[6224])).
% 2.04/2.29 tff(6226,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 2.04/2.29 tff(6227,assumption,(b(s(s(s(s(s(elem!1))))), s(s(elem!1)))), introduced(assumption)).
% 2.04/2.29 tff(6228,plain,
% 2.04/2.29 (((~![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(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(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(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(6229,plain,
% 2.04/2.29 (((~b(s(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(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(6230,plain,
% 2.04/2.29 (((~![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(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(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(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(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[6229])).
% 2.04/2.29 tff(6231,plain,
% 2.04/2.29 (((~![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(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(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(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(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[6230, 6228])).
% 2.04/2.29 tff(6232,plain,
% 2.04/2.29 ((~![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(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(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(6233,plain,
% 2.04/2.29 ((~![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(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[6232, 6231])).
% 2.04/2.29 tff(6234,plain,
% 2.04/2.29 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6233, 97, 1633, 6227, 6226])).
% 2.04/2.29 tff(6235,plain,
% 2.04/2.29 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[6234, 6225])).
% 2.04/2.29 tff(6236,plain,
% 2.04/2.29 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(z)) | b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(z)) | b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z)))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(6237,plain,
% 2.04/2.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(z)) | b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z)))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(6238,plain,
% 2.04/2.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(z)) | b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[6237, 6236])).
% 2.04/2.29 tff(6239,plain,
% 2.04/2.29 ((s(s(s(s(s(elem!1))))) = s(z)) | b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6238, 53])).
% 2.04/2.29 tff(6240,plain,
% 2.04/2.29 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6239, 6235, 6223])).
% 2.04/2.29 tff(6241,plain,
% 2.04/2.29 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[6240, 6213])).
% 2.04/2.29 tff(6242,assumption,(r(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 2.04/2.29 tff(6243,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.04/2.29 tff(6244,plain,
% 2.04/2.29 (((~![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(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(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(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(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(6245,plain,
% 2.04/2.29 (((~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(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(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(6246,plain,
% 2.04/2.29 (((~![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(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(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(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[6245])).
% 2.04/2.29 tff(6247,plain,
% 2.04/2.29 (((~![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(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(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(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[6246, 6244])).
% 2.04/2.29 tff(6248,plain,
% 2.04/2.29 ((~![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(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)))))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(6249,plain,
% 2.04/2.29 ((~![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(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(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[6248, 6247])).
% 2.04/2.29 tff(6250,plain,
% 2.04/2.29 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6249, 97, 1545, 1633, 6227])).
% 2.04/2.29 tff(6251,plain,
% 2.04/2.29 (((~![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))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(6252,plain,
% 2.04/2.29 ((~![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))))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(6253,plain,
% 2.04/2.29 ((~![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)))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[6252, 6251])).
% 2.04/2.29 tff(6254,plain,
% 2.04/2.29 ((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)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6253, 53])).
% 2.04/2.29 tff(6255,plain,
% 2.04/2.29 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6254, 6250, 6243])).
% 2.04/2.29 tff(6256,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(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)))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(6257,plain,
% 2.04/2.29 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(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))))))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~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)))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(6258,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(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))))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[6257])).
% 2.04/2.29 tff(6259,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(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)))))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[6258, 6256])).
% 2.04/2.29 tff(6260,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~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)))))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(6261,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[6260, 6259])).
% 2.04/2.29 tff(6262,plain,
% 2.04/2.29 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6261, 155, 1912, 6255, 6242])).
% 2.04/2.29 tff(6263,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6262, 6241])).
% 2.04/2.29 tff(6264,plain,((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (s(s(s(s(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(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(6265,plain,
% 2.04/2.29 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6264, 6050, 6211, 6202, 6199, 6184, 6182, 6177])).
% 2.04/2.29 tff(6266,plain,
% 2.04/2.29 (((~![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))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(6267,plain,
% 2.04/2.29 ((~![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))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(6268,plain,
% 2.04/2.29 ((~![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)))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[6267, 6266])).
% 2.04/2.29 tff(6269,plain,
% 2.04/2.29 ((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)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6268, 53])).
% 2.04/2.29 tff(6270,plain,
% 2.04/2.29 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6269, 6265, 6173])).
% 2.04/2.29 tff(6271,plain,
% 2.04/2.29 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[1839])).
% 2.04/2.29 tff(6272,plain,
% 2.04/2.29 (b(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.04/2.29 inference(symmetry,[status(thm)],[6271])).
% 2.04/2.29 tff(6273,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(s(z))))), introduced(assumption)).
% 2.04/2.29 tff(6274,plain,
% 2.04/2.29 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[1839])).
% 2.04/2.29 tff(6275,plain,
% 2.04/2.29 ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[6274])).
% 2.04/2.29 tff(6276,assumption,(r(s(s(s(s(s(elem!1))))), s(s(elem!1)))), introduced(assumption)).
% 2.04/2.29 tff(6277,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 2.04/2.29 tff(6278,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(6279,plain,
% 2.04/2.29 (((~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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(6280,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[6279])).
% 2.04/2.29 tff(6281,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[6280, 6278])).
% 2.04/2.29 tff(6282,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(6283,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[6282, 6281])).
% 2.04/2.29 tff(6284,plain,
% 2.04/2.29 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6283, 155, 4497, 6277, 6276])).
% 2.04/2.29 tff(6285,plain,
% 2.04/2.29 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[6284, 6275])).
% 2.04/2.29 tff(6286,plain,
% 2.04/2.29 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) | b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(z)))) | b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(6287,plain,
% 2.04/2.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) | b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(6288,plain,
% 2.04/2.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(z)))) | b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[6287, 6286])).
% 2.04/2.29 tff(6289,plain,
% 2.04/2.29 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) | b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6288, 53])).
% 2.04/2.30 tff(6290,plain,
% 2.04/2.30 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[6289, 6285, 6273])).
% 2.04/2.30 tff(6291,plain,
% 2.04/2.30 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.04/2.30 inference(modus_ponens,[status(thm)],[6290, 6272])).
% 2.04/2.30 tff(6292,plain,
% 2.04/2.30 ((s(s(s(s(s(elem!1))))) = elem!1) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 2.04/2.30 inference(commutativity,[status(thm)],[])).
% 2.04/2.30 tff(6293,plain,
% 2.04/2.30 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.04/2.30 inference(symmetry,[status(thm)],[6292])).
% 2.04/2.30 tff(6294,plain,
% 2.04/2.30 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.04/2.30 inference(monotonicity,[status(thm)],[1444])).
% 2.04/2.30 tff(6295,plain,
% 2.04/2.30 ((s(s(s(s(s(elem!1))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 2.04/2.30 inference(transitivity,[status(thm)],[6294, 6292])).
% 2.04/2.30 tff(6296,plain,
% 2.04/2.30 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.04/2.30 inference(transitivity,[status(thm)],[6295, 6293])).
% 2.04/2.30 tff(6297,plain,
% 2.04/2.30 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.04/2.30 inference(monotonicity,[status(thm)],[6296])).
% 2.04/2.30 tff(6298,plain,
% 2.04/2.30 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(elem!1))))) = z))),
% 2.04/2.30 inference(quant_inst,[status(thm)],[])).
% 2.04/2.30 tff(6299,plain,
% 2.04/2.30 (~(s(s(s(s(s(elem!1))))) = z)),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[6298, 38])).
% 2.04/2.30 tff(6300,plain,
% 2.04/2.30 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.04/2.30 inference(modus_ponens,[status(thm)],[6299, 6297])).
% 2.04/2.30 tff(6301,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 2.04/2.30 tff(6302,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 2.04/2.30 tff(6303,plain,
% 2.04/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.04/2.30 inference(rewrite,[status(thm)],[])).
% 2.04/2.30 tff(6304,plain,
% 2.04/2.30 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.04/2.30 inference(rewrite,[status(thm)],[])).
% 2.04/2.30 tff(6305,plain,
% 2.04/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.04/2.30 inference(monotonicity,[status(thm)],[6304])).
% 2.04/2.30 tff(6306,plain,
% 2.04/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.04/2.30 inference(transitivity,[status(thm)],[6305, 6303])).
% 2.04/2.30 tff(6307,plain,
% 2.04/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(6308,plain,
% 2.14/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[6307, 6306])).
% 2.14/2.30 tff(6309,plain,
% 2.14/2.30 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6308, 155, 6302, 6301, 6276])).
% 2.14/2.30 tff(6310,plain,
% 2.14/2.30 (((~![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))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(6311,plain,
% 2.14/2.30 ((~![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))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(6312,plain,
% 2.14/2.30 ((~![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)),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[6311, 6310])).
% 2.14/2.30 tff(6313,plain,
% 2.14/2.30 ((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)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6312, 53])).
% 2.14/2.30 tff(6314,plain,
% 2.14/2.30 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6313, 6309, 6300])).
% 2.14/2.30 tff(6315,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 2.14/2.30 tff(6316,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 2.14/2.30 tff(6317,plain,
% 2.14/2.30 (((~![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(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(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(6318,plain,
% 2.14/2.30 (((~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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(6319,plain,
% 2.14/2.30 (((~![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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[6318])).
% 2.14/2.30 tff(6320,plain,
% 2.14/2.30 (((~![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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[6319, 6317])).
% 2.14/2.30 tff(6321,plain,
% 2.14/2.30 ((~![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))))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(6322,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[6321, 6320])).
% 2.14/2.30 tff(6323,plain,
% 2.14/2.30 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6322, 97, 6316, 6315, 6314])).
% 2.14/2.30 tff(6324,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6323, 6291])).
% 2.14/2.30 tff(6325,plain,((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (s(s(s(s(s(elem!1))))) = s(s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(6326,plain,
% 2.14/2.30 (s(s(s(s(s(elem!1))))) = s(s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6325, 6270, 6050, 6156, 6154, 6152, 6148, 6141, 6138])).
% 2.14/2.30 tff(6327,plain,
% 2.14/2.30 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 2.14/2.30 inference(transitivity,[status(thm)],[6326, 6050])).
% 2.14/2.30 tff(6328,plain,
% 2.14/2.30 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(elem!1))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[6327])).
% 2.14/2.30 tff(6329,plain,
% 2.14/2.30 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.14/2.30 inference(transitivity,[status(thm)],[6168, 6328, 19])).
% 2.14/2.30 tff(6330,plain,
% 2.14/2.30 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[6142])).
% 2.14/2.30 tff(6331,plain,
% 2.14/2.30 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.14/2.30 inference(transitivity,[status(thm)],[6330, 1428])).
% 2.14/2.30 tff(6332,plain,
% 2.14/2.30 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[6331])).
% 2.14/2.30 tff(6333,plain,
% 2.14/2.30 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[331, 6332])).
% 2.14/2.30 tff(6334,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6333, 6329])).
% 2.14/2.30 tff(6335,plain,((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | r(z, s(s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(6336,plain,
% 2.14/2.30 (~b(s(s(z)), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6335, 585, 61, 550, 126, 1960, 1961, 82])).
% 2.14/2.30 tff(6337,plain,
% 2.14/2.30 (r(s(s(z)), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[122, 6336])).
% 2.14/2.30 tff(6338,plain,
% 2.14/2.30 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1273, 6337, 494, 4214])).
% 2.14/2.30 tff(6339,plain,
% 2.14/2.30 (b(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[143, 6338])).
% 2.14/2.30 tff(6340,plain,
% 2.14/2.30 (~b(s(s(z)), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[4987, 6339, 126, 3008])).
% 2.14/2.30 tff(6341,plain,
% 2.14/2.30 (r(s(s(z)), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[625, 6340])).
% 2.14/2.30 tff(6342,plain,
% 2.14/2.30 (((~![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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(6343,plain,
% 2.14/2.30 (((~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(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(6344,plain,
% 2.14/2.30 (((~![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))), 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(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[6343])).
% 2.14/2.30 tff(6345,plain,
% 2.14/2.30 (((~![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))), 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(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[6344, 6342])).
% 2.14/2.30 tff(6346,plain,
% 2.14/2.30 ((~![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))), 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)))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(6347,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[6346, 6345])).
% 2.14/2.30 tff(6348,plain,
% 2.14/2.30 (~b(z, s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6347, 97, 126, 3008, 6339])).
% 2.14/2.30 tff(6349,plain,
% 2.14/2.30 (r(z, s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[222, 6348])).
% 2.14/2.30 tff(6350,plain,
% 2.14/2.30 (~r(s(s(s(z))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2693, 155, 6349, 6341, 1960])).
% 2.14/2.30 tff(6351,plain,
% 2.14/2.30 (b(s(s(s(z))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[402, 6350])).
% 2.14/2.30 tff(6352,plain,
% 2.14/2.30 (~r(z, s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1969, 6349, 1961, 1960])).
% 2.14/2.30 tff(6353,plain,
% 2.14/2.30 (b(z, s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1318, 6352])).
% 2.14/2.30 tff(6354,plain,
% 2.14/2.30 (~b(s(z), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2615, 6351, 61, 6353])).
% 2.14/2.30 tff(6355,plain,
% 2.14/2.30 (r(s(z), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[253, 6354])).
% 2.14/2.30 tff(6356,plain,
% 2.14/2.30 (~r(s(s(s(z))), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2940, 6355, 1961, 6337])).
% 2.14/2.30 tff(6357,plain,
% 2.14/2.30 (b(s(s(s(z))), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1358, 6356])).
% 2.14/2.30 tff(6358,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[3419, 97, 550, 61, 6357, 6351])).
% 2.14/2.30 tff(6359,plain,(r(z, s(s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(6360,plain,
% 2.14/2.30 (r(z, s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6359, 1961, 61, 550, 2591, 4206, 82])).
% 2.14/2.30 tff(6361,assumption,(~r(z, s(s(s(z))))), introduced(assumption)).
% 2.14/2.30 tff(6362,plain,
% 2.14/2.30 (b(z, s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1318, 6361])).
% 2.14/2.30 tff(6363,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[3391, 97, 550, 61, 1360, 1330])).
% 2.14/2.30 tff(6364,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(6365,plain,
% 2.14/2.30 (~b(s(s(s(z))), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6364, 6362, 61, 550])).
% 2.14/2.30 tff(6366,plain,
% 2.14/2.30 (r(s(s(s(z))), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1358, 6365])).
% 2.14/2.30 tff(6367,plain,
% 2.14/2.30 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5757, 6366, 4214, 125])).
% 2.14/2.30 tff(6368,plain,
% 2.14/2.30 ((~(s(s(s(elem!1))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(elem!1)))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[2679])).
% 2.14/2.30 tff(6369,plain,
% 2.14/2.30 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[2508])).
% 2.14/2.30 tff(6370,plain,
% 2.14/2.30 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 2.14/2.30 inference(symmetry,[status(thm)],[6369])).
% 2.14/2.30 tff(6371,plain,
% 2.14/2.30 ((~r(z, s(s(s(z))))) <=> (~r(z, s(s(s(elem!1)))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[6370])).
% 2.14/2.30 tff(6372,plain,
% 2.14/2.30 (~r(z, s(s(s(elem!1))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[6361, 6371])).
% 2.14/2.30 tff(6373,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[570, 6372])).
% 2.14/2.30 tff(6374,plain,((~(s(s(s(elem!1))) = s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | r(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(6375,plain,
% 2.14/2.30 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6374, 6361, 570])).
% 2.14/2.30 tff(6376,plain,
% 2.14/2.30 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[6375, 6368])).
% 2.14/2.30 tff(6377,plain,
% 2.14/2.30 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[3089, 6376, 6367])).
% 2.14/2.30 tff(6378,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[3413, 97, 61, 126, 1216, 1702])).
% 2.14/2.30 tff(6379,plain,((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(6380,plain,
% 2.14/2.30 (~b(s(s(s(z))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6379, 6377, 126, 61])).
% 2.14/2.30 tff(6381,plain,
% 2.14/2.30 (r(s(s(s(z))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[402, 6380])).
% 2.14/2.30 tff(6382,plain,
% 2.14/2.30 (~b(s(s(z)), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[3004, 6366, 1960, 550, 61])).
% 2.14/2.30 tff(6383,plain,
% 2.14/2.30 (r(s(s(z)), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[625, 6382])).
% 2.14/2.30 tff(6384,plain,
% 2.14/2.30 (~r(s(z), s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2984, 6366, 1961, 550, 1960, 61])).
% 2.14/2.30 tff(6385,plain,
% 2.14/2.30 (b(s(z), s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[548, 6384])).
% 2.14/2.30 tff(6386,plain,
% 2.14/2.30 (~r(s(z), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2940, 2, 1961, 2597])).
% 2.14/2.30 tff(6387,plain,
% 2.14/2.30 (~b(s(z), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2952, 2, 61, 1960, 1961, 570, 125, 645, 535])).
% 2.14/2.30 tff(6388,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[253, 6387, 6386])).
% 2.14/2.30 tff(6389,plain,((~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(6390,plain,
% 2.14/2.30 (~r(s(s(z)), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6389, 6383, 1960, 1961, 570, 125, 61, 6385, 6366])).
% 2.14/2.30 tff(6391,plain,
% 2.14/2.30 (b(s(s(z)), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[122, 6390])).
% 2.14/2.30 tff(6392,plain,
% 2.14/2.30 (~b(z, s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[3966, 6391, 550, 6385])).
% 2.14/2.30 tff(6393,plain,
% 2.14/2.30 (r(z, s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[222, 6392])).
% 2.14/2.30 tff(6394,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2625, 155, 6393, 6383, 1960, 6381])).
% 2.14/2.30 tff(6395,plain,(r(z, s(s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(6396,plain,
% 2.14/2.30 (r(z, s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6395, 1961, 550, 2591, 6360, 494, 61, 4206])).
% 2.14/2.30 tff(6397,plain,
% 2.14/2.30 (~r(z, s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1969, 6396, 1961, 2591])).
% 2.14/2.30 tff(6398,plain,
% 2.14/2.30 (b(z, s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[222, 6397])).
% 2.14/2.30 tff(6399,plain,
% 2.14/2.30 (~b(s(z), s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[4212, 97, 550, 61, 4206])).
% 2.14/2.30 tff(6400,plain,
% 2.14/2.30 (r(s(z), s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[181, 6399])).
% 2.14/2.30 tff(6401,plain,
% 2.14/2.30 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1390, 83, 126, 61])).
% 2.14/2.30 tff(6402,plain,
% 2.14/2.30 (r(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[58, 6401])).
% 2.14/2.30 tff(6403,plain,
% 2.14/2.30 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[135, 83, 61, 126])).
% 2.14/2.30 tff(6404,plain,
% 2.14/2.30 (r(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[143, 6403])).
% 2.14/2.30 tff(6405,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5875, 4077, 6404, 6402, 225])).
% 2.14/2.30 tff(6406,plain,((~b(s(s(z)), z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(6407,plain,
% 2.14/2.30 (~b(s(s(z)), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6406, 6400, 4206, 61, 6398])).
% 2.14/2.30 tff(6408,plain,
% 2.14/2.30 (r(s(s(z)), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[625, 6407])).
% 2.14/2.30 tff(6409,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[4047, 155, 645, 1300, 1961, 386])).
% 2.14/2.30 tff(6410,plain,((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(6411,plain,
% 2.14/2.30 (~r(s(s(s(z))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6410, 6408, 6396, 1961])).
% 2.14/2.30 tff(6412,plain,
% 2.14/2.30 (b(s(s(s(z))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[402, 6411])).
% 2.14/2.30 tff(6413,plain,
% 2.14/2.30 (~b(s(s(s(z))), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[3419, 97, 550, 61, 6412])).
% 2.14/2.30 tff(6414,plain,
% 2.14/2.30 (r(s(s(s(z))), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1358, 6413])).
% 2.14/2.30 tff(6415,plain,
% 2.14/2.30 (~r(s(z), s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2984, 6414, 1961, 550, 2591, 61])).
% 2.14/2.30 tff(6416,plain,
% 2.14/2.30 (b(s(z), s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[548, 6415])).
% 2.14/2.30 tff(6417,plain,
% 2.14/2.30 (((~![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(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))))) | (~b(s(s(s(z))), z)))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(6418,plain,
% 2.14/2.30 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(6419,plain,
% 2.14/2.30 (((~![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(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))))) | (~b(s(s(s(z))), z))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[6418])).
% 2.14/2.30 tff(6420,plain,
% 2.14/2.30 (((~![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(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))))) | (~b(s(s(s(z))), z)))),
% 2.14/2.31 inference(transitivity,[status(thm)],[6419, 6417])).
% 2.14/2.31 tff(6421,plain,
% 2.14/2.31 ((~![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(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(6422,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[6421, 6420])).
% 2.14/2.31 tff(6423,plain,
% 2.14/2.31 (~b(s(z), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6422, 97, 550, 61, 6412])).
% 2.14/2.31 tff(6424,plain,
% 2.14/2.31 (r(s(z), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[253, 6423])).
% 2.14/2.31 tff(6425,plain,
% 2.14/2.31 (~r(s(s(z)), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2940, 6424, 1961, 6414])).
% 2.14/2.31 tff(6426,plain,
% 2.14/2.31 (b(s(s(z)), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[122, 6425])).
% 2.14/2.31 tff(6427,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3966, 6426, 6416, 550, 6398])).
% 2.14/2.31 tff(6428,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | b(s(s(s(elem!1))), s(z)) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(6429,plain,
% 2.14/2.31 (~r(s(s(z)), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6428, 2590, 61, 82, 550])).
% 2.14/2.31 tff(6430,plain,
% 2.14/2.31 (b(s(s(z)), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[437, 6429])).
% 2.14/2.31 tff(6431,plain,
% 2.14/2.31 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2313, 3002, 125, 2994])).
% 2.14/2.31 tff(6432,plain,
% 2.14/2.31 (b(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[58, 6431])).
% 2.14/2.31 tff(6433,plain,
% 2.14/2.31 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2677, 6432, 2590])).
% 2.14/2.31 tff(6434,plain,
% 2.14/2.31 (~r(s(s(s(z))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3004, 83, 2591, 550, 61])).
% 2.14/2.31 tff(6435,plain,
% 2.14/2.31 (b(s(s(s(z))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1358, 6434])).
% 2.14/2.31 tff(6436,plain,
% 2.14/2.31 (~b(s(s(s(z))), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3383, 97, 550, 61, 6435])).
% 2.14/2.31 tff(6437,plain,
% 2.14/2.31 (r(s(s(s(z))), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[402, 6436])).
% 2.14/2.31 tff(6438,plain,
% 2.14/2.31 (~b(s(s(s(elem!1))), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1390, 6432, 83, 61])).
% 2.14/2.31 tff(6439,plain,
% 2.14/2.31 (r(s(s(s(elem!1))), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[246, 6438])).
% 2.14/2.31 tff(6440,plain,
% 2.14/2.31 (~b(z, s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[306, 6432, 124, 83])).
% 2.14/2.31 tff(6441,plain,
% 2.14/2.31 (r(z, s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[222, 6440])).
% 2.14/2.31 tff(6442,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(6443,plain,
% 2.14/2.31 (((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(6444,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[6443])).
% 2.14/2.31 tff(6445,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[6444, 6442])).
% 2.14/2.31 tff(6446,plain,
% 2.14/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(6447,plain,
% 2.14/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[6446, 6445])).
% 2.14/2.31 tff(6448,plain,
% 2.14/2.31 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6447, 155, 6441, 6439, 2591, 6437])).
% 2.14/2.31 tff(6449,plain,
% 2.14/2.31 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3089, 6448, 6433])).
% 2.14/2.31 tff(6450,plain,
% 2.14/2.31 (~b(s(z), s(s(s(elem!1))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[201, 6432, 61, 124])).
% 2.14/2.31 tff(6451,plain,
% 2.14/2.31 (r(s(z), s(s(s(elem!1))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[181, 6450])).
% 2.14/2.31 tff(6452,plain,
% 2.14/2.31 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1273, 6451, 125, 2994])).
% 2.14/2.31 tff(6453,plain,
% 2.14/2.31 (b(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[143, 6452])).
% 2.14/2.31 tff(6454,plain,
% 2.14/2.31 (((~![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(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(6455,plain,
% 2.14/2.31 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~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(s(elem!1))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(6456,plain,
% 2.14/2.31 (((~![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(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~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(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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[6455])).
% 2.14/2.31 tff(6457,plain,
% 2.14/2.31 (((~![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(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~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(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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[6456, 6454])).
% 2.14/2.31 tff(6458,plain,
% 2.14/2.31 ((~![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(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~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(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(6459,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[6458, 6457])).
% 2.14/2.31 tff(6460,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6459, 97, 6432, 1361, 6453, 6449])).
% 2.14/2.31 tff(6461,plain,((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(z))), s(s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(6462,plain,
% 2.14/2.31 (~b(s(s(z)), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6461, 3008, 494, 61, 6430, 2590, 550])).
% 2.14/2.31 tff(6463,plain,
% 2.14/2.31 (r(s(s(z)), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[625, 6462])).
% 2.14/2.31 tff(6464,plain,
% 2.14/2.31 (~b(s(s(s(z))), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3383, 97, 550, 61, 1360])).
% 2.14/2.31 tff(6465,plain,
% 2.14/2.31 (r(s(s(s(z))), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[402, 6464])).
% 2.14/2.31 tff(6466,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2625, 155, 226, 645, 1960, 386])).
% 2.14/2.31 tff(6467,plain,((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(6468,plain,
% 2.14/2.31 (~r(z, s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6467, 6465, 1960, 645])).
% 2.14/2.31 tff(6469,plain,
% 2.14/2.31 (b(z, s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[222, 6468])).
% 2.14/2.31 tff(6470,plain,
% 2.14/2.31 (~b(s(z), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3997, 6469, 550, 1361])).
% 2.14/2.31 tff(6471,plain,
% 2.14/2.31 (r(s(z), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[548, 6470])).
% 2.14/2.31 tff(6472,plain,
% 2.14/2.31 (((~![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(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(6473,plain,
% 2.14/2.31 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(6474,plain,
% 2.14/2.31 (((~![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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[6473])).
% 2.14/2.31 tff(6475,plain,
% 2.14/2.31 (((~![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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[6474, 6472])).
% 2.14/2.31 tff(6476,plain,
% 2.14/2.31 ((~![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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(6477,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[6476, 6475])).
% 2.14/2.31 tff(6478,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6477, 97, 124, 204, 60, 1361])).
% 2.14/2.31 tff(6479,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(6480,plain,
% 2.14/2.31 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6479, 6469, 1361, 124])).
% 2.14/2.31 tff(6481,plain,
% 2.14/2.31 (r(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[58, 6480])).
% 2.14/2.31 tff(6482,plain,
% 2.14/2.31 (~r(s(s(z)), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2313, 6481, 125, 6471])).
% 2.14/2.31 tff(6483,plain,
% 2.14/2.31 (b(s(s(z)), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[122, 6482])).
% 2.14/2.31 tff(6484,plain,
% 2.14/2.31 (((~![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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(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(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(6485,plain,
% 2.14/2.31 (((~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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(6486,plain,
% 2.14/2.31 (((~![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(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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[6485])).
% 2.14/2.31 tff(6487,plain,
% 2.14/2.31 (((~![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(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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[6486, 6484])).
% 2.14/2.31 tff(6488,plain,
% 2.14/2.31 ((~![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(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))))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(6489,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[6488, 6487])).
% 2.14/2.31 tff(6490,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6489, 97, 550, 6483, 1361, 1360])).
% 2.14/2.31 tff(6491,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(6492,plain,
% 2.14/2.31 (~b(s(s(s(z))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6491, 3008, 6430, 494, 550, 2591, 6463, 61])).
% 2.14/2.31 tff(6493,plain,
% 2.14/2.31 (r(s(s(s(z))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1358, 6492])).
% 2.14/2.31 tff(6494,plain,
% 2.14/2.31 (~b(s(s(s(z))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6364, 1330, 61, 550])).
% 2.14/2.31 tff(6495,plain,
% 2.14/2.31 (r(s(s(s(z))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1358, 6494])).
% 2.14/2.31 tff(6496,plain,
% 2.14/2.31 (~r(s(s(z)), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2930, 3, 6495, 2591])).
% 2.14/2.31 tff(6497,plain,
% 2.14/2.31 (b(s(s(z)), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[122, 6496])).
% 2.14/2.31 tff(6498,plain,
% 2.14/2.31 (~b(z, s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2603, 97, 550, 61, 6497])).
% 2.14/2.31 tff(6499,plain,
% 2.14/2.31 (r(z, s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[222, 6498])).
% 2.14/2.31 tff(6500,plain,
% 2.14/2.31 (~b(z, s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6039, 1961, 5829, 1, 3, 1960, 2597, 125])).
% 2.14/2.31 tff(6501,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1318, 6500, 4293])).
% 2.14/2.31 tff(6502,plain,((~r(s(s(z)), s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(6503,plain,
% 2.14/2.31 (~r(s(s(z)), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6502, 3, 1, 1960, 2597, 125, 226])).
% 2.14/2.31 tff(6504,plain,
% 2.14/2.31 (b(s(s(z)), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[437, 6503])).
% 2.14/2.31 tff(6505,plain,
% 2.14/2.31 (~b(s(z), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[4249, 6504, 1960, 5865, 2597])).
% 2.14/2.31 tff(6506,plain,
% 2.14/2.31 (r(s(z), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[253, 6505])).
% 2.14/2.31 tff(6507,plain,
% 2.14/2.31 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2638, 6506, 2597, 125])).
% 2.14/2.31 tff(6508,plain,
% 2.14/2.31 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2687, 6507, 4228])).
% 2.14/2.31 tff(6509,plain,
% 2.14/2.31 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6049, 125, 1960, 1, 2597, 226])).
% 2.14/2.31 tff(6510,plain,
% 2.14/2.31 (b(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[58, 6509])).
% 2.14/2.31 tff(6511,plain,
% 2.14/2.31 (((~![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(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(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(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(6512,plain,
% 2.14/2.31 (((~b(s(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(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~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(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(6513,plain,
% 2.14/2.31 (((~![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(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[6512])).
% 2.14/2.31 tff(6514,plain,
% 2.14/2.31 (((~![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(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[6513, 6511])).
% 2.14/2.31 tff(6515,plain,
% 2.14/2.31 ((~![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(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(6516,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[6515, 6514])).
% 2.14/2.31 tff(6517,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6516, 97, 6510, 6504, 5865, 6508])).
% 2.14/2.31 tff(6518,plain,((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(6519,plain,
% 2.14/2.31 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6518, 6499, 125, 2591, 3, 6495])).
% 2.14/2.31 tff(6520,plain,
% 2.14/2.31 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[6519])).
% 2.14/2.31 tff(6521,plain,
% 2.14/2.31 (s(s(z)) = s(s(elem!1))),
% 2.14/2.31 inference(transitivity,[status(thm)],[73, 6520, 19])).
% 2.14/2.31 tff(6522,plain,
% 2.14/2.31 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[6521])).
% 2.14/2.31 tff(6523,plain,
% 2.14/2.31 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.14/2.31 inference(symmetry,[status(thm)],[6522])).
% 2.14/2.31 tff(6524,plain,
% 2.14/2.31 (s(elem!1) = s(z)),
% 2.14/2.31 inference(transitivity,[status(thm)],[30, 6523, 23])).
% 2.14/2.31 tff(6525,plain,
% 2.14/2.31 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[6524])).
% 2.14/2.31 tff(6526,plain,
% 2.14/2.31 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.14/2.31 inference(symmetry,[status(thm)],[6525])).
% 2.14/2.31 tff(6527,plain,
% 2.14/2.31 (~b(s(s(z)), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3004, 6495, 2591, 550, 61])).
% 2.14/2.32 tff(6528,plain,
% 2.14/2.32 (r(s(s(z)), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[625, 6527])).
% 2.14/2.32 tff(6529,plain,
% 2.14/2.32 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2677, 6519, 2590])).
% 2.14/2.32 tff(6530,plain,
% 2.14/2.32 (r(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[58, 6529])).
% 2.14/2.32 tff(6531,plain,
% 2.14/2.32 (~r(s(s(s(elem!1))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2671, 6530, 6499, 6528])).
% 2.14/2.32 tff(6532,plain,
% 2.14/2.32 (b(s(s(s(elem!1))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[246, 6531])).
% 2.14/2.32 tff(6533,plain,
% 2.14/2.32 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[4260, 3, 6495, 2591, 125])).
% 2.14/2.32 tff(6534,plain,
% 2.14/2.32 (~b(s(z), s(s(s(elem!1))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3979, 6532, 61, 3008])).
% 2.14/2.32 tff(6535,plain,
% 2.14/2.32 (r(s(z), s(s(s(elem!1))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[181, 6534])).
% 2.14/2.32 tff(6536,plain,
% 2.14/2.32 (~b(z, s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6087, 6535, 3008, 6533, 125, 6532, 61, 550, 1330])).
% 2.14/2.32 tff(6537,plain,
% 2.14/2.32 (r(z, s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1093, 6536])).
% 2.14/2.32 tff(6538,plain,
% 2.14/2.32 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6519])).
% 2.14/2.32 tff(6539,plain,
% 2.14/2.32 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6538])).
% 2.14/2.32 tff(6540,plain,
% 2.14/2.32 (~r(s(s(s(z))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2693, 155, 6499, 6528, 2591])).
% 2.14/2.32 tff(6541,plain,
% 2.14/2.32 (b(s(s(s(z))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[402, 6540])).
% 2.14/2.32 tff(6542,plain,
% 2.14/2.32 (~b(s(s(s(s(z)))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2853, 6541, 61, 6495, 550])).
% 2.14/2.32 tff(6543,plain,
% 2.14/2.32 (r(s(s(s(s(z)))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2860, 6542])).
% 2.14/2.32 tff(6544,plain,
% 2.14/2.32 (r(s(s(s(s(elem!1)))), z)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[6543, 6539])).
% 2.14/2.32 tff(6545,plain,
% 2.14/2.32 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3326, 6544, 6519, 6528, 6537])).
% 2.14/2.32 tff(6546,plain,
% 2.14/2.32 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[336, 6545])).
% 2.14/2.32 tff(6547,plain,
% 2.14/2.32 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3240, 6546, 550, 6497])).
% 2.14/2.32 tff(6548,plain,
% 2.14/2.32 (r(s(s(s(s(elem!1)))), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[511, 6547])).
% 2.14/2.32 tff(6549,plain,
% 2.14/2.32 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3021, 6537, 585])).
% 2.14/2.32 tff(6550,plain,
% 2.14/2.32 (s(z) = s(elem!1)),
% 2.14/2.32 inference(transitivity,[status(thm)],[24, 6522, 29])).
% 2.14/2.32 tff(6551,plain,
% 2.14/2.32 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6550])).
% 2.14/2.32 tff(6552,plain,
% 2.14/2.32 (z = elem!1),
% 2.14/2.32 inference(transitivity,[status(thm)],[1443, 6551, 85])).
% 2.14/2.32 tff(6553,plain,
% 2.14/2.32 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6552, 6521])).
% 2.14/2.32 tff(6554,plain,
% 2.14/2.32 (r(elem!1, s(s(elem!1)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[6499, 6553])).
% 2.14/2.32 tff(6555,plain,
% 2.14/2.32 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6552])).
% 2.14/2.32 tff(6556,plain,
% 2.14/2.32 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6521])).
% 2.14/2.32 tff(6557,plain,
% 2.14/2.32 (r(s(s(elem!1)), z)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[6528, 6556])).
% 2.14/2.32 tff(6558,plain,
% 2.14/2.32 (r(s(s(elem!1)), elem!1)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[6557, 6555])).
% 2.14/2.32 tff(6559,plain,
% 2.14/2.32 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6552])).
% 2.14/2.32 tff(6560,plain,
% 2.14/2.32 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[6544, 6559])).
% 2.14/2.32 tff(6561,plain,
% 2.14/2.32 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6107, 155, 6560, 6558, 6554])).
% 2.14/2.32 tff(6562,plain,
% 2.14/2.32 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6521])).
% 2.14/2.32 tff(6563,plain,
% 2.14/2.32 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.14/2.32 inference(transitivity,[status(thm)],[6562, 1428])).
% 2.14/2.32 tff(6564,plain,
% 2.14/2.32 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6563])).
% 2.14/2.32 tff(6565,plain,
% 2.14/2.32 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[331, 6564])).
% 2.14/2.32 tff(6566,plain,
% 2.14/2.32 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1484, 6565, 6561])).
% 2.14/2.32 tff(6567,plain,
% 2.14/2.32 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5875, 6535, 3, 6530])).
% 2.14/2.32 tff(6568,plain,
% 2.14/2.32 (b(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[143, 6567])).
% 2.14/2.32 tff(6569,plain,
% 2.14/2.32 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2574, 6546, 6568, 6566])).
% 2.14/2.32 tff(6570,plain,
% 2.14/2.32 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[486, 6569, 6549])).
% 2.14/2.32 tff(6571,plain,
% 2.14/2.32 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[503, 6570, 125, 6548])).
% 2.14/2.32 tff(6572,plain,
% 2.14/2.32 (b(s(z), s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[280, 6571])).
% 2.14/2.32 tff(6573,plain,
% 2.14/2.32 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[6572, 6526])).
% 2.14/2.32 tff(6574,plain,
% 2.14/2.32 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.14/2.32 inference(symmetry,[status(thm)],[6520])).
% 2.14/2.32 tff(6575,plain,
% 2.14/2.32 (s(s(elem!1)) = s(s(z))),
% 2.14/2.32 inference(transitivity,[status(thm)],[167, 6574, 72])).
% 2.14/2.32 tff(6576,plain,
% 2.14/2.32 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(elem!1))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6575])).
% 2.14/2.32 tff(6577,plain,
% 2.14/2.32 (b(s(s(z)), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.14/2.32 inference(symmetry,[status(thm)],[6576])).
% 2.14/2.32 tff(6578,plain,
% 2.14/2.32 (b(s(s(z)), s(z)) <=> b(s(s(z)), s(elem!1))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6550])).
% 2.14/2.32 tff(6579,plain,
% 2.14/2.32 (b(s(s(z)), s(elem!1))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[6497, 6578])).
% 2.14/2.32 tff(6580,plain,
% 2.14/2.32 (b(s(s(elem!1)), s(elem!1))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[6579, 6577])).
% 2.14/2.32 tff(6581,plain,
% 2.14/2.32 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[6563, 1505])).
% 2.14/2.32 tff(6582,plain,
% 2.14/2.32 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6581])).
% 2.14/2.32 tff(6583,plain,
% 2.14/2.32 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[331, 6582])).
% 2.14/2.32 tff(6584,plain,
% 2.14/2.32 (r(z, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6552])).
% 2.14/2.32 tff(6585,plain,
% 2.14/2.32 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[6537, 6584])).
% 2.14/2.32 tff(6586,plain,
% 2.14/2.32 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(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)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(6587,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6586])).
% 2.14/2.32 tff(6588,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[6587, 3111])).
% 2.14/2.32 tff(6589,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(6590,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[6589, 6588])).
% 2.14/2.32 tff(6591,plain,
% 2.14/2.32 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6590, 155, 6560, 6558, 6585])).
% 2.14/2.32 tff(6592,plain,
% 2.14/2.32 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1631, 6591, 6583])).
% 2.14/2.32 tff(6593,plain,
% 2.14/2.32 (((~![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(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(6594,plain,
% 2.14/2.32 (((~b(s(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(s(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(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(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(6595,plain,
% 2.14/2.32 (((~![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(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(s(s(s(elem!1)))))) | (~b(s(elem!1), s(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(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6594])).
% 2.14/2.32 tff(6596,plain,
% 2.14/2.32 (((~![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(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(s(s(s(elem!1)))))) | (~b(s(elem!1), s(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(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[6595, 6593])).
% 2.14/2.32 tff(6597,plain,
% 2.14/2.32 ((~![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(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(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(6598,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[6597, 6596])).
% 2.14/2.32 tff(6599,plain,
% 2.14/2.32 ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6598, 97, 6566, 6592])).
% 2.14/2.32 tff(6600,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6599, 6580, 6573])).
% 2.14/2.32 tff(6601,plain,((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | r(z, s(s(s(elem!1)))) | (~b(z, s(s(s(z))))) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(6602,plain,
% 2.14/2.32 (~r(s(z), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6601, 1330, 550, 61, 585, 494, 2590])).
% 2.14/2.32 tff(6603,plain,
% 2.14/2.32 (b(s(z), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[548, 6602])).
% 2.14/2.32 tff(6604,plain,
% 2.14/2.32 (~b(z, s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3997, 6603, 550, 6430])).
% 2.14/2.32 tff(6605,plain,
% 2.14/2.32 (r(z, s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[222, 6604])).
% 2.14/2.32 tff(6606,plain,
% 2.14/2.32 (~r(s(s(s(elem!1))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3956, 6605, 550, 82, 585, 6528, 6603])).
% 2.14/2.32 tff(6607,plain,
% 2.14/2.32 (b(s(s(s(elem!1))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[246, 6606])).
% 2.14/2.32 tff(6608,plain,
% 2.14/2.32 (~b(s(z), s(s(s(elem!1))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3979, 6607, 61, 3008])).
% 2.14/2.32 tff(6609,plain,
% 2.14/2.32 (r(s(z), s(s(s(elem!1))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[181, 6608])).
% 2.14/2.32 tff(6610,plain,
% 2.14/2.32 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5757, 6609, 6495, 494])).
% 2.14/2.32 tff(6611,plain,
% 2.14/2.32 (~b(z, s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6087, 6609, 3008, 6610, 494, 6607, 61, 550, 1330])).
% 2.14/2.32 tff(6612,plain,
% 2.14/2.32 (r(z, s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1093, 6611])).
% 2.14/2.32 tff(6613,plain,
% 2.14/2.32 (r(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3954, 6605, 82, 550, 585, 6528, 6603])).
% 2.14/2.32 tff(6614,plain,
% 2.14/2.32 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6023, 6613, 2591, 494, 6430, 6495, 6605])).
% 2.14/2.32 tff(6615,plain,
% 2.14/2.32 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6614])).
% 2.14/2.32 tff(6616,plain,
% 2.14/2.32 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6615])).
% 2.14/2.32 tff(6617,plain,
% 2.14/2.32 (~r(s(s(s(z))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2693, 155, 6605, 6528, 2591])).
% 2.14/2.32 tff(6618,plain,
% 2.14/2.32 (b(s(s(s(z))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[402, 6617])).
% 2.14/2.32 tff(6619,plain,
% 2.14/2.32 (~b(s(s(s(s(z)))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2853, 6618, 61, 6495, 550])).
% 2.14/2.32 tff(6620,plain,
% 2.14/2.32 (r(s(s(s(s(z)))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2860, 6619])).
% 2.14/2.32 tff(6621,plain,
% 2.14/2.32 (r(s(s(s(s(elem!1)))), z)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[6620, 6616])).
% 2.14/2.32 tff(6622,plain,
% 2.14/2.32 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3326, 6621, 6614, 6528, 6612])).
% 2.14/2.32 tff(6623,plain,
% 2.14/2.32 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[1393])).
% 2.14/2.32 tff(6624,plain,
% 2.14/2.32 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 2.14/2.32 inference(symmetry,[status(thm)],[6623])).
% 2.14/2.32 tff(6625,plain,
% 2.14/2.32 ((~b(s(z), s(s(s(elem!1))))) <=> (~b(s(z), s(s(s(z)))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6624])).
% 2.14/2.32 tff(6626,plain,
% 2.14/2.32 (~b(s(z), s(s(s(z))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[176, 6625])).
% 2.14/2.32 tff(6627,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[86, 6626])).
% 2.14/2.32 tff(6628,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(6629,plain,
% 2.14/2.32 (~b(s(z), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6628, 6608, 6614])).
% 2.14/2.32 tff(6630,plain,
% 2.14/2.32 (r(s(z), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[253, 6629])).
% 2.14/2.32 tff(6631,plain,
% 2.14/2.32 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 2.14/2.32 inference(symmetry,[status(thm)],[2679])).
% 2.14/2.32 tff(6632,plain,
% 2.14/2.32 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[6614, 6631])).
% 2.14/2.32 tff(6633,plain,
% 2.14/2.32 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6125, 6632, 3008, 61, 494, 550, 6603, 6495, 6528, 6605, 6614, 6607, 6630])).
% 2.14/2.32 tff(6634,plain,
% 2.14/2.32 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3021, 6612, 585])).
% 2.14/2.32 tff(6635,plain,
% 2.14/2.32 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6614])).
% 2.14/2.32 tff(6636,plain,
% 2.14/2.32 (b(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[6430, 6635])).
% 2.14/2.32 tff(6637,plain,
% 2.14/2.32 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6615])).
% 2.14/2.32 tff(6638,plain,
% 2.14/2.32 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2881, 155, 6605, 6528, 6620])).
% 2.14/2.32 tff(6639,plain,
% 2.14/2.32 (b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2886, 6638, 80])).
% 2.14/2.32 tff(6640,plain,
% 2.14/2.32 (~b(s(s(s(s(z)))), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3250, 97, 6603, 6430, 6639])).
% 2.14/2.32 tff(6641,plain,
% 2.14/2.32 (r(s(s(s(s(z)))), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2807, 6640, 2795])).
% 2.14/2.32 tff(6642,plain,
% 2.14/2.32 (r(s(s(s(s(elem!1)))), s(z))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[6641, 6637])).
% 2.14/2.32 tff(6643,plain,
% 2.14/2.32 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1136, 6642, 494, 6609])).
% 2.14/2.32 tff(6644,plain,
% 2.14/2.32 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[4129, 6643, 6636, 6634, 6633])).
% 2.14/2.32 tff(6645,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[336, 6644, 6622])).
% 2.14/2.32 tff(6646,plain,((~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | r(z, s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(z)) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(6647,plain,
% 2.14/2.32 (~b(z, s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6646, 585, 550, 61, 82, 2590])).
% 2.14/2.32 tff(6648,plain,
% 2.14/2.32 (r(z, s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1318, 6647])).
% 2.14/2.32 tff(6649,plain,
% 2.14/2.32 ((~r(z, s(s(s(elem!1))))) <=> (~r(z, s(s(s(z)))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[1958])).
% 2.14/2.32 tff(6650,plain,
% 2.14/2.32 (~r(z, s(s(s(z))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[585, 6649])).
% 2.14/2.32 tff(6651,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1300, 6650])).
% 2.14/2.32 tff(6652,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(6653,plain,
% 2.14/2.32 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6652, 6648, 585])).
% 2.14/2.32 tff(6654,plain,
% 2.14/2.32 (~b(s(z), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6422, 97, 550, 61, 1216])).
% 2.14/2.32 tff(6655,plain,
% 2.14/2.32 (r(s(z), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[253, 6654])).
% 2.14/2.32 tff(6656,plain,
% 2.14/2.32 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2638, 6655, 2597, 125])).
% 2.14/2.32 tff(6657,plain,
% 2.14/2.32 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2687, 6656, 4228])).
% 2.14/2.32 tff(6658,plain,
% 2.14/2.32 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5819, 97, 1361, 1216, 6657])).
% 2.14/2.32 tff(6659,plain,
% 2.14/2.32 (r(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[58, 6658])).
% 2.14/2.32 tff(6660,plain,
% 2.14/2.32 (~r(z, s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6023, 6659, 1960, 125, 1361, 1, 2597])).
% 2.14/2.32 tff(6661,plain,
% 2.14/2.32 (b(z, s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[222, 6660])).
% 2.14/2.32 tff(6662,plain,
% 2.14/2.32 (~b(s(z), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3997, 6661, 550, 1361])).
% 2.14/2.32 tff(6663,plain,
% 2.14/2.32 (r(s(z), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[548, 6662])).
% 2.14/2.32 tff(6664,plain,
% 2.14/2.32 (~r(s(s(z)), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2930, 6663, 2597, 1960])).
% 2.14/2.32 tff(6665,plain,
% 2.14/2.32 (b(s(s(z)), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[122, 6664])).
% 2.14/2.32 tff(6666,plain,
% 2.14/2.32 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5811, 97, 1361, 1216, 6657])).
% 2.14/2.32 tff(6667,plain,
% 2.14/2.32 (r(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[143, 6666])).
% 2.14/2.32 tff(6668,plain,
% 2.14/2.32 (~r(s(z), s(s(s(elem!1))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5875, 6663, 6667, 6659])).
% 2.14/2.32 tff(6669,plain,
% 2.14/2.32 (b(s(z), s(s(s(elem!1))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[181, 6668])).
% 2.14/2.32 tff(6670,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2249, 6669, 6665, 61, 6661])).
% 2.14/2.32 tff(6671,plain,((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(6672,plain,
% 2.14/2.32 (~b(s(s(s(z))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6671, 6493, 61, 2591, 550, 6430, 494, 6653])).
% 2.14/2.32 tff(6673,plain,
% 2.14/2.32 (r(s(s(s(z))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[402, 6672])).
% 2.14/2.32 tff(6674,plain,
% 2.14/2.32 (~r(z, s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6467, 6673, 2591, 6463])).
% 2.14/2.32 tff(6675,plain,
% 2.14/2.32 (b(z, s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[222, 6674])).
% 2.14/2.32 tff(6676,plain,
% 2.14/2.32 (~b(s(z), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3997, 6675, 550, 6430])).
% 2.14/2.32 tff(6677,plain,
% 2.14/2.32 (r(s(z), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[548, 6676])).
% 2.14/2.32 tff(6678,plain,
% 2.14/2.32 (~r(s(s(z)), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2930, 6677, 6493, 2591])).
% 2.14/2.32 tff(6679,plain,
% 2.14/2.32 (b(s(s(z)), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[122, 6678])).
% 2.14/2.32 tff(6680,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2603, 97, 550, 61, 6675, 6679])).
% 2.14/2.32 tff(6681,plain,(r(z, s(s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | b(s(s(s(z))), s(s(z))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(6682,plain,
% 2.14/2.32 (r(z, s(s(s(elem!1))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6681, 2590, 61, 550, 82])).
% 2.14/2.32 tff(6683,plain,
% 2.14/2.32 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6671, 3477, 61, 2591, 550, 1361, 125, 1216])).
% 2.14/2.32 tff(6684,plain,
% 2.14/2.32 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6683])).
% 2.14/2.32 tff(6685,plain,
% 2.14/2.32 (s(s(z)) = s(s(elem!1))),
% 2.14/2.32 inference(transitivity,[status(thm)],[73, 6684, 19])).
% 2.14/2.32 tff(6686,plain,
% 2.14/2.32 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6685])).
% 2.14/2.32 tff(6687,plain,
% 2.14/2.32 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.14/2.32 inference(symmetry,[status(thm)],[6686])).
% 2.14/2.32 tff(6688,plain,
% 2.14/2.32 (s(elem!1) = s(z)),
% 2.14/2.32 inference(transitivity,[status(thm)],[30, 6687, 23])).
% 2.14/2.32 tff(6689,plain,
% 2.14/2.32 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6688])).
% 2.14/2.32 tff(6690,plain,
% 2.14/2.32 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(symmetry,[status(thm)],[6689])).
% 2.14/2.32 tff(6691,plain,
% 2.14/2.32 (r(s(s(s(z))), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1358, 1843])).
% 2.14/2.32 tff(6692,plain,
% 2.14/2.32 (~r(s(s(s(z))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[4368, 155, 729, 3, 2597, 1960])).
% 2.14/2.32 tff(6693,plain,
% 2.14/2.32 (b(s(s(s(z))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[402, 6692])).
% 2.14/2.32 tff(6694,plain,
% 2.14/2.32 (~r(z, s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[4590, 729, 570, 125, 3])).
% 2.14/2.32 tff(6695,plain,
% 2.14/2.32 (b(z, s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[222, 6694])).
% 2.14/2.32 tff(6696,plain,
% 2.14/2.32 (((~![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(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))))) | (~b(s(s(s(z))), z)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(6697,plain,
% 2.14/2.32 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(6698,plain,
% 2.14/2.32 (((~![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(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))))) | (~b(s(s(s(z))), z))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[6697])).
% 2.14/2.32 tff(6699,plain,
% 2.14/2.32 (((~![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(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))))) | (~b(s(s(s(z))), z)))),
% 2.14/2.32 inference(transitivity,[status(thm)],[6698, 6696])).
% 2.14/2.32 tff(6700,plain,
% 2.14/2.32 ((~![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(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(6701,plain,
% 2.14/2.32 ((~![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(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[6700, 6699])).
% 2.14/2.32 tff(6702,plain,
% 2.14/2.32 (~b(s(z), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6701, 97, 550, 6695, 6693])).
% 2.14/2.32 tff(6703,plain,
% 2.14/2.32 (r(s(z), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[253, 6702])).
% 2.14/2.32 tff(6704,plain,
% 2.14/2.32 (~r(z, s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5909, 155, 729, 6703, 2597])).
% 2.14/2.32 tff(6705,plain,
% 2.14/2.32 (b(z, s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1318, 6704])).
% 2.14/2.32 tff(6706,plain,
% 2.14/2.32 (~r(s(s(z)), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2641, 6703, 3, 1960])).
% 2.14/2.32 tff(6707,plain,
% 2.14/2.32 (b(s(s(z)), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[437, 6706])).
% 2.14/2.32 tff(6708,plain,
% 2.14/2.32 (~r(s(s(z)), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2930, 2597, 3, 1960])).
% 2.14/2.32 tff(6709,plain,
% 2.14/2.32 (b(s(s(z)), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[122, 6708])).
% 2.14/2.32 tff(6710,plain,
% 2.14/2.32 (((~![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(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(6711,plain,
% 2.14/2.32 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(6712,plain,
% 2.14/2.33 (((~![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(z))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[6711])).
% 2.14/2.33 tff(6713,plain,
% 2.14/2.33 (((~![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(z))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.14/2.33 inference(transitivity,[status(thm)],[6712, 6710])).
% 2.14/2.33 tff(6714,plain,
% 2.14/2.33 ((~![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(z))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(6715,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[6714, 6713])).
% 2.14/2.33 tff(6716,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[6715, 97, 550, 6695, 6709, 6707, 6705, 6693])).
% 2.14/2.33 tff(6717,plain,((~r(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(6718,plain,
% 2.14/2.33 (~r(z, s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[6717, 125, 2597, 3, 2591, 570, 550])).
% 2.14/2.33 tff(6719,plain,
% 2.14/2.33 (b(z, s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[723, 6718])).
% 2.14/2.33 tff(6720,plain,
% 2.14/2.33 (((~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(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(6721,plain,
% 2.14/2.33 (((~![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(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(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[6720])).
% 2.14/2.33 tff(6722,plain,
% 2.14/2.33 (((~![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(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(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.14/2.33 inference(transitivity,[status(thm)],[6721, 2987])).
% 2.14/2.33 tff(6723,plain,
% 2.14/2.33 ((~![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(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)))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(6724,plain,
% 2.14/2.33 ((~![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(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[6723, 6722])).
% 2.14/2.33 tff(6725,plain,
% 2.14/2.33 (~b(s(s(z)), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[6724, 97, 550, 61, 6709])).
% 2.14/2.33 tff(6726,plain,
% 2.14/2.33 (r(s(s(z)), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[625, 6725])).
% 2.14/2.33 tff(6727,plain,
% 2.14/2.33 (~b(z, s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2603, 97, 550, 61, 6709])).
% 2.14/2.33 tff(6728,plain,
% 2.14/2.33 (r(z, s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[222, 6727])).
% 2.14/2.33 tff(6729,plain,
% 2.14/2.33 (~r(s(s(s(z))), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2693, 155, 6728, 6726, 1960])).
% 2.14/2.33 tff(6730,plain,
% 2.14/2.33 (b(s(s(s(z))), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[402, 6729])).
% 2.14/2.33 tff(6731,plain,
% 2.14/2.33 (~b(s(z), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[6422, 97, 550, 61, 6730])).
% 2.14/2.33 tff(6732,plain,
% 2.14/2.33 (r(s(z), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[253, 6731])).
% 2.14/2.33 tff(6733,plain,
% 2.14/2.33 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2636, 155, 125, 6732, 2597])).
% 2.14/2.33 tff(6734,plain,
% 2.14/2.33 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2687, 6733, 2466])).
% 2.14/2.33 tff(6735,plain,
% 2.14/2.33 (~r(s(s(z)), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2641, 6732, 3, 1960])).
% 2.14/2.33 tff(6736,plain,
% 2.14/2.33 (b(s(s(z)), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[437, 6735])).
% 2.14/2.33 tff(6737,plain,
% 2.14/2.33 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5811, 97, 6736, 6730, 6734])).
% 2.14/2.33 tff(6738,plain,
% 2.14/2.33 (r(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[143, 6737])).
% 2.14/2.33 tff(6739,plain,
% 2.14/2.33 (~r(z, s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5949, 6738, 570, 1960, 6728])).
% 2.14/2.33 tff(6740,plain,
% 2.14/2.33 (b(z, s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1318, 6739])).
% 2.14/2.33 tff(6741,plain,
% 2.14/2.33 (((~![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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(6742,plain,
% 2.14/2.33 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(6743,plain,
% 2.14/2.33 (((~![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(z))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[6742])).
% 2.14/2.33 tff(6744,plain,
% 2.14/2.33 (((~![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(z))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[6743, 6741])).
% 2.14/2.33 tff(6745,plain,
% 2.14/2.33 ((~![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(z))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(6746,plain,
% 2.14/2.33 ((~![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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[6745, 6744])).
% 2.14/2.33 tff(6747,plain,
% 2.14/2.33 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[6746, 97, 550, 6709, 6736, 6730, 6734])).
% 2.14/2.33 tff(6748,plain,
% 2.14/2.33 (r(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[58, 6747])).
% 2.14/2.33 tff(6749,plain,
% 2.14/2.33 (~r(s(s(s(elem!1))), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2671, 6748, 6726, 6728])).
% 2.14/2.33 tff(6750,plain,
% 2.14/2.33 (b(s(s(s(elem!1))), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[246, 6749])).
% 2.14/2.33 tff(6751,plain,
% 2.14/2.33 (((~![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(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(6752,plain,
% 2.14/2.33 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(6753,plain,
% 2.14/2.33 (((~![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(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(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), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[6752])).
% 2.14/2.33 tff(6754,plain,
% 2.14/2.33 (((~![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(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(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), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[6753, 6751])).
% 2.14/2.33 tff(6755,plain,
% 2.14/2.33 ((~![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(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(6756,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[6755, 6754])).
% 2.14/2.33 tff(6757,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[6756, 97, 550, 61, 6750, 6740, 6730, 6734])).
% 2.14/2.33 tff(6758,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(6759,plain,
% 2.14/2.33 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[6758, 6719, 570, 2591, 550, 125, 2597, 3])).
% 2.14/2.33 tff(6760,plain,
% 2.14/2.33 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2682, 6759])).
% 2.14/2.33 tff(6761,plain,
% 2.14/2.33 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2677, 6760, 2590])).
% 2.14/2.33 tff(6762,plain,
% 2.14/2.33 (r(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[58, 6761])).
% 2.14/2.33 tff(6763,plain,
% 2.14/2.33 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[6760])).
% 2.14/2.33 tff(6764,plain,
% 2.14/2.33 (s(s(z)) = s(s(elem!1))),
% 2.14/2.33 inference(transitivity,[status(thm)],[73, 6763, 19])).
% 2.14/2.33 tff(6765,plain,
% 2.14/2.33 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[6764])).
% 2.14/2.33 tff(6766,plain,
% 2.14/2.33 (s(z) = s(elem!1)),
% 2.14/2.33 inference(transitivity,[status(thm)],[24, 6765, 29])).
% 2.14/2.33 tff(6767,plain,
% 2.14/2.33 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[6766])).
% 2.14/2.33 tff(6768,plain,
% 2.14/2.33 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 2.14/2.33 inference(symmetry,[status(thm)],[6767])).
% 2.14/2.33 tff(6769,plain,
% 2.14/2.33 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[6766])).
% 2.14/2.33 tff(6770,plain,
% 2.14/2.33 (z = elem!1),
% 2.14/2.33 inference(transitivity,[status(thm)],[1443, 6769, 85])).
% 2.14/2.33 tff(6771,plain,
% 2.14/2.33 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[6770, 6766])).
% 2.14/2.33 tff(6772,plain,
% 2.14/2.33 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.14/2.33 inference(transitivity,[status(thm)],[6771, 6768])).
% 2.14/2.33 tff(6773,plain,
% 2.14/2.33 (b(elem!1, s(z))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[6719, 6772])).
% 2.14/2.33 tff(6774,plain,
% 2.14/2.33 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.14/2.33 inference(monotonicity,[status(thm)],[6770])).
% 2.14/2.33 tff(6775,plain,
% 2.14/2.33 (b(s(z), elem!1)),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[550, 6774])).
% 2.14/2.33 tff(6776,plain,
% 2.14/2.33 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 2.14/2.33 inference(commutativity,[status(thm)],[])).
% 2.14/2.33 tff(6777,plain,
% 2.14/2.33 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.14/2.33 inference(symmetry,[status(thm)],[6776])).
% 2.14/2.33 tff(6778,plain,
% 2.14/2.33 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.14/2.33 inference(monotonicity,[status(thm)],[6770])).
% 2.14/2.33 tff(6779,plain,
% 2.14/2.33 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[6778, 6776])).
% 2.14/2.33 tff(6780,plain,
% 2.14/2.33 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.14/2.33 inference(transitivity,[status(thm)],[6779, 6777])).
% 2.14/2.33 tff(6781,plain,
% 2.14/2.33 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[6780])).
% 2.14/2.33 tff(6782,plain,
% 2.14/2.33 (~(s(s(s(elem!1))) = elem!1)),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[241, 6781])).
% 2.14/2.33 tff(6783,plain,
% 2.14/2.33 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.14/2.33 inference(symmetry,[status(thm)],[6763])).
% 2.14/2.33 tff(6784,plain,
% 2.14/2.33 (s(s(elem!1)) = s(s(z))),
% 2.14/2.33 inference(transitivity,[status(thm)],[167, 6783, 72])).
% 2.14/2.33 tff(6785,plain,
% 2.14/2.33 ((s(s(elem!1)) = elem!1) <=> (s(s(z)) = elem!1)),
% 2.14/2.33 inference(monotonicity,[status(thm)],[6784])).
% 2.14/2.33 tff(6786,plain,
% 2.14/2.33 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 2.14/2.33 inference(monotonicity,[status(thm)],[6770])).
% 2.14/2.33 tff(6787,plain,
% 2.14/2.33 ((s(s(elem!1)) = z) <=> (s(s(z)) = elem!1)),
% 2.14/2.33 inference(transitivity,[status(thm)],[6786, 6785])).
% 2.14/2.33 tff(6788,plain,
% 2.14/2.33 ((~(s(s(elem!1)) = z)) <=> (~(s(s(z)) = elem!1))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[6787])).
% 2.14/2.33 tff(6789,plain,
% 2.14/2.33 (~(s(s(z)) = elem!1)),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[170, 6788])).
% 2.14/2.33 tff(6790,plain,
% 2.14/2.33 (elem!1 = z),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1888, 6770])).
% 2.14/2.33 tff(6791,plain,
% 2.14/2.33 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.14/2.33 inference(symmetry,[status(thm)],[6765])).
% 2.14/2.33 tff(6792,plain,
% 2.14/2.33 (s(elem!1) = s(z)),
% 2.14/2.33 inference(transitivity,[status(thm)],[30, 6791, 23])).
% 2.14/2.33 tff(6793,plain,
% 2.14/2.33 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 2.14/2.33 inference(monotonicity,[status(thm)],[6792])).
% 2.14/2.33 tff(6794,plain,
% 2.14/2.33 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 2.14/2.33 inference(symmetry,[status(thm)],[6793])).
% 2.14/2.33 tff(6795,plain,
% 2.14/2.33 (b(s(elem!1), elem!1)),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[6775, 6794])).
% 2.14/2.33 tff(6796,plain,
% 2.14/2.33 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(elem!1))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[6784])).
% 2.14/2.33 tff(6797,plain,
% 2.14/2.33 (b(s(s(z)), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.14/2.33 inference(symmetry,[status(thm)],[6796])).
% 2.14/2.33 tff(6798,plain,
% 2.14/2.33 (b(s(s(z)), s(z)) <=> b(s(s(z)), s(elem!1))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[6766])).
% 2.14/2.33 tff(6799,plain,
% 2.14/2.33 (~r(s(s(z)), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2930, 2597, 3, 2591])).
% 2.14/2.33 tff(6800,plain,
% 2.14/2.33 (b(s(s(z)), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[122, 6799])).
% 2.14/2.33 tff(6801,plain,
% 2.14/2.33 (b(s(s(z)), s(elem!1))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[6800, 6798])).
% 2.14/2.33 tff(6802,plain,
% 2.14/2.33 (b(s(s(elem!1)), s(elem!1))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[6801, 6797])).
% 2.14/2.33 tff(6803,plain,
% 2.14/2.33 (b(elem!1, s(elem!1))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[6719, 6771])).
% 2.14/2.33 tff(6804,plain,
% 2.14/2.33 (((~![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(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(6805,plain,
% 2.14/2.33 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), 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)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(6806,plain,
% 2.14/2.33 (((~![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(s(elem!1), 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)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[6805])).
% 2.14/2.33 tff(6807,plain,
% 2.14/2.33 (((~![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(s(elem!1), 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)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.14/2.33 inference(transitivity,[status(thm)],[6806, 6804])).
% 2.14/2.34 tff(6808,plain,
% 2.14/2.34 ((~![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(elem!1), 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)))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(6809,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[6808, 6807])).
% 2.14/2.34 tff(6810,plain,
% 2.14/2.34 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6809, 97, 6803])).
% 2.14/2.34 tff(6811,plain,
% 2.14/2.34 (~b(s(s(elem!1)), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6810, 6802, 6795])).
% 2.14/2.34 tff(6812,plain,
% 2.14/2.34 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), z)),
% 2.14/2.34 inference(monotonicity,[status(thm)],[1974, 1972])).
% 2.14/2.34 tff(6813,plain,
% 2.14/2.34 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.14/2.34 inference(symmetry,[status(thm)],[6812])).
% 2.14/2.34 tff(6814,plain,
% 2.14/2.34 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 2.14/2.34 inference(monotonicity,[status(thm)],[1972])).
% 2.14/2.34 tff(6815,plain,
% 2.14/2.34 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.14/2.34 inference(transitivity,[status(thm)],[6814, 6813])).
% 2.14/2.34 tff(6816,plain,
% 2.14/2.34 (b(s(s(elem!1)), elem!1)),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[1548, 6815])).
% 2.14/2.34 tff(6817,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 2.14/2.34 tff(6818,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6817, 6816])).
% 2.14/2.34 tff(6819,plain,((~b(s(s(z)), elem!1)) | b(s(s(elem!1)), elem!1) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(6820,plain,
% 2.14/2.34 (~b(s(s(z)), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6819, 6811, 6790])).
% 2.14/2.34 tff(6821,plain,
% 2.14/2.34 (r(s(s(z)), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[1563, 6820, 6789])).
% 2.14/2.34 tff(6822,plain,
% 2.14/2.34 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.14/2.34 inference(commutativity,[status(thm)],[])).
% 2.14/2.34 tff(6823,plain,
% 2.14/2.34 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(z)))),
% 2.14/2.34 inference(symmetry,[status(thm)],[6822])).
% 2.14/2.34 tff(6824,plain,
% 2.14/2.34 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(z)))),
% 2.14/2.34 inference(transitivity,[status(thm)],[6786, 6785, 6823])).
% 2.14/2.34 tff(6825,plain,
% 2.14/2.34 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(z))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[6824])).
% 2.14/2.34 tff(6826,plain,
% 2.14/2.34 (~(elem!1 = s(s(z)))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[170, 6825])).
% 2.14/2.34 tff(6827,plain,
% 2.14/2.34 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[6764])).
% 2.14/2.34 tff(6828,plain,
% 2.14/2.34 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 2.14/2.34 inference(symmetry,[status(thm)],[6827])).
% 2.14/2.34 tff(6829,plain,
% 2.14/2.34 ((~b(elem!1, s(s(elem!1)))) <=> (~b(elem!1, s(s(z))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[6828])).
% 2.14/2.34 tff(6830,plain,
% 2.14/2.34 (((~![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(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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), elem!1)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(6831,plain,
% 2.14/2.34 (((~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(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(6832,plain,
% 2.14/2.34 (((~![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(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(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[6831])).
% 2.14/2.34 tff(6833,plain,
% 2.14/2.34 (((~![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(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(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 2.14/2.34 inference(transitivity,[status(thm)],[6832, 6830])).
% 2.14/2.34 tff(6834,plain,
% 2.14/2.34 ((~![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(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)))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(6835,plain,
% 2.14/2.34 ((~![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(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[6834, 6833])).
% 2.14/2.34 tff(6836,plain,
% 2.14/2.34 ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6835, 97, 6803])).
% 2.14/2.34 tff(6837,plain,
% 2.14/2.34 (~b(elem!1, s(s(elem!1)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6836, 6802, 6795])).
% 2.14/2.34 tff(6838,plain,
% 2.14/2.34 (~b(elem!1, s(s(z)))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[6837, 6829])).
% 2.14/2.34 tff(6839,plain,
% 2.14/2.34 (((~![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))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(6840,plain,
% 2.14/2.34 ((~![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))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(6841,plain,
% 2.14/2.34 ((~![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)))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[6840, 6839])).
% 2.14/2.34 tff(6842,plain,
% 2.14/2.34 ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6841, 53])).
% 2.14/2.34 tff(6843,plain,
% 2.14/2.34 (r(elem!1, s(s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6842, 6838, 6826])).
% 2.14/2.34 tff(6844,assumption,(r(elem!1, s(s(z)))), introduced(assumption)).
% 2.14/2.34 tff(6845,assumption,(r(s(s(z)), elem!1)), introduced(assumption)).
% 2.14/2.34 tff(6846,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(z)))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(6847,plain,
% 2.14/2.34 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(z)))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(6848,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(z))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[6847])).
% 2.14/2.34 tff(6849,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(z)))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[6848, 6846])).
% 2.14/2.34 tff(6850,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(6851,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(z))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[6850, 6849])).
% 2.14/2.34 tff(6852,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6851, 155, 6845, 6844, 1528, 145])).
% 2.14/2.34 tff(6853,plain,((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(6854,plain,
% 2.14/2.34 (~r(s(s(s(elem!1))), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6853, 6843, 6762, 6821])).
% 2.14/2.34 tff(6855,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 2.14/2.34 tff(6856,assumption,(~r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 2.14/2.34 tff(6857,assumption,(~b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 2.14/2.34 tff(6858,plain,
% 2.14/2.34 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(6859,plain,
% 2.14/2.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(6860,plain,
% 2.14/2.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[6859, 6858])).
% 2.14/2.34 tff(6861,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6860, 53, 6857, 6856, 6855])).
% 2.14/2.34 tff(6862,plain,(b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(6863,plain,
% 2.14/2.34 (b(s(s(s(elem!1))), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6862, 6854, 6782])).
% 2.14/2.34 tff(6864,plain,
% 2.14/2.34 (((~![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))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(6865,plain,
% 2.14/2.34 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(6866,plain,
% 2.14/2.34 (((~![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(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[6865])).
% 2.14/2.34 tff(6867,plain,
% 2.14/2.34 (((~![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(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[6866, 6864])).
% 2.14/2.34 tff(6868,plain,
% 2.14/2.34 ((~![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(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(6869,plain,
% 2.14/2.34 ((~![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))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[6868, 6867])).
% 2.14/2.34 tff(6870,plain,
% 2.14/2.34 ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6869, 97])).
% 2.14/2.34 tff(6871,plain,
% 2.14/2.34 (~b(s(z), s(s(s(elem!1))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6870, 6863, 6775, 6773])).
% 2.14/2.34 tff(6872,plain,
% 2.14/2.34 (r(s(z), s(s(s(elem!1))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[181, 6871])).
% 2.14/2.34 tff(6873,plain,
% 2.14/2.34 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[317, 6872, 3, 287, 6762])).
% 2.14/2.34 tff(6874,plain,
% 2.14/2.34 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[336, 6873])).
% 2.14/2.34 tff(6875,plain,
% 2.14/2.34 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[6760])).
% 2.14/2.34 tff(6876,plain,
% 2.14/2.34 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 2.14/2.34 inference(symmetry,[status(thm)],[6875])).
% 2.14/2.34 tff(6877,plain,
% 2.14/2.34 (r(z, s(s(s(z))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[570, 6876])).
% 2.14/2.34 tff(6878,plain,
% 2.14/2.34 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[6764])).
% 2.14/2.34 tff(6879,plain,
% 2.14/2.34 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 2.14/2.34 inference(symmetry,[status(thm)],[6878])).
% 2.14/2.34 tff(6880,plain,
% 2.14/2.34 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[6770])).
% 2.14/2.34 tff(6881,plain,
% 2.14/2.34 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 2.14/2.34 inference(symmetry,[status(thm)],[6880])).
% 2.14/2.34 tff(6882,plain,
% 2.14/2.34 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(z)))),
% 2.14/2.34 inference(transitivity,[status(thm)],[6881, 6879])).
% 2.14/2.34 tff(6883,plain,
% 2.14/2.34 ((~b(elem!1, s(s(elem!1)))) <=> (~b(z, s(s(z))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[6882])).
% 2.14/2.34 tff(6884,plain,
% 2.14/2.34 (~b(z, s(s(z)))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[6837, 6883])).
% 2.14/2.34 tff(6885,plain,
% 2.14/2.34 (r(z, s(s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[222, 6884])).
% 2.14/2.34 tff(6886,plain,
% 2.14/2.34 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5949, 6885, 570, 2591, 6877])).
% 2.14/2.34 tff(6887,plain,
% 2.14/2.34 (b(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[143, 6886])).
% 2.14/2.34 tff(6888,plain,
% 2.14/2.34 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[6760])).
% 2.14/2.34 tff(6889,plain,
% 2.14/2.34 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[6888, 1414])).
% 2.14/2.34 tff(6890,plain,
% 2.14/2.34 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[6889])).
% 2.14/2.34 tff(6891,plain,
% 2.14/2.34 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[286, 6890])).
% 2.14/2.34 tff(6892,plain,
% 2.14/2.34 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[3240, 6874, 550, 6800])).
% 2.14/2.34 tff(6893,plain,
% 2.14/2.34 (r(s(s(s(s(elem!1)))), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[511, 6892])).
% 2.14/2.34 tff(6894,plain,
% 2.14/2.34 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[503, 6893, 125, 287])).
% 2.14/2.34 tff(6895,plain,
% 2.14/2.34 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[1136, 6893, 125, 6872])).
% 2.14/2.34 tff(6896,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[4129, 6895, 6894, 6891, 6887, 6874])).
% 2.14/2.34 tff(6897,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | b(s(s(s(z))), s(s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(6898,plain,
% 2.14/2.34 (~r(s(s(s(elem!1))), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6897, 6691, 550, 3, 570, 2590, 287])).
% 2.14/2.34 tff(6899,plain,
% 2.14/2.34 (b(s(s(s(elem!1))), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[493, 6898])).
% 2.14/2.34 tff(6900,plain,
% 2.14/2.34 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[1846, 6899, 1843])).
% 2.14/2.34 tff(6901,plain,
% 2.14/2.34 (~r(s(s(z)), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2930, 6691, 3, 2591])).
% 2.14/2.34 tff(6902,plain,
% 2.14/2.34 (b(s(s(z)), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[122, 6901])).
% 2.14/2.34 tff(6903,plain,
% 2.14/2.34 (((~![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(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(6904,plain,
% 2.14/2.34 (((~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(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(6905,plain,
% 2.14/2.34 (((~![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(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(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[6904])).
% 2.14/2.34 tff(6906,plain,
% 2.14/2.34 (((~![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(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(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[6905, 6903])).
% 2.14/2.34 tff(6907,plain,
% 2.14/2.34 ((~![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(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))))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(6908,plain,
% 2.14/2.34 ((~![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(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[6907, 6906])).
% 2.14/2.34 tff(6909,plain,
% 2.14/2.34 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6908, 97, 6899, 550, 6902])).
% 2.14/2.34 tff(6910,plain,
% 2.14/2.34 (r(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[143, 6909])).
% 2.14/2.34 tff(6911,plain,
% 2.14/2.34 (((~![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(z), 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(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(6912,plain,
% 2.14/2.34 (((~b(s(z), z)) | (~b(s(z), z)) | (~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(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(6913,plain,
% 2.14/2.34 (((~![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(z), z)) | (~b(s(z), z)) | (~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(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[6912])).
% 2.14/2.34 tff(6914,plain,
% 2.14/2.34 (((~![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(z), z)) | (~b(s(z), z)) | (~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(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[6913, 6911])).
% 2.14/2.34 tff(6915,plain,
% 2.14/2.34 ((~![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(z), z)) | (~b(s(z), z)) | (~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)))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(6916,plain,
% 2.14/2.34 ((~![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(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[6915, 6914])).
% 2.14/2.34 tff(6917,plain,
% 2.14/2.34 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6916, 97, 6899, 550, 6902])).
% 2.14/2.35 tff(6918,plain,
% 2.14/2.35 (r(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[58, 6917])).
% 2.14/2.35 tff(6919,plain,
% 2.14/2.35 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[4382, 155, 6918, 6910, 2591])).
% 2.14/2.35 tff(6920,plain,
% 2.14/2.35 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[3089, 6919, 6900])).
% 2.14/2.35 tff(6921,plain,
% 2.14/2.35 (~r(s(z), s(s(s(elem!1))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5875, 6910, 3, 6918])).
% 2.14/2.35 tff(6922,plain,
% 2.14/2.35 (b(s(z), s(s(s(elem!1))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[181, 6921])).
% 2.14/2.35 tff(6923,plain,
% 2.14/2.35 (~b(s(z), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1710, 6920, 6899, 6922])).
% 2.14/2.35 tff(6924,plain,
% 2.14/2.35 (r(s(z), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[253, 6923])).
% 2.14/2.35 tff(6925,plain,
% 2.14/2.35 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~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(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(6926,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[6925])).
% 2.14/2.35 tff(6927,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[6926, 5177])).
% 2.14/2.35 tff(6928,plain,
% 2.14/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(6929,plain,
% 2.14/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[6928, 6927])).
% 2.14/2.35 tff(6930,plain,
% 2.14/2.35 (~r(z, s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[6929, 155, 570, 6918, 6910])).
% 2.14/2.35 tff(6931,plain,
% 2.14/2.35 (b(z, s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[222, 6930])).
% 2.14/2.35 tff(6932,plain,
% 2.14/2.35 (~b(z, s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2249, 6931, 6902, 6922])).
% 2.14/2.35 tff(6933,plain,
% 2.14/2.35 (r(z, s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[723, 6932])).
% 2.14/2.35 tff(6934,plain,
% 2.14/2.35 (~r(z, s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5909, 155, 6933, 6924, 6691])).
% 2.14/2.35 tff(6935,plain,
% 2.14/2.35 (b(z, s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1318, 6934])).
% 2.14/2.35 tff(6936,plain,
% 2.14/2.35 (~r(s(s(z)), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2641, 6924, 3, 2591])).
% 2.14/2.35 tff(6937,plain,
% 2.14/2.35 (b(s(s(z)), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[437, 6936])).
% 2.14/2.35 tff(6938,plain,
% 2.14/2.35 (((~![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(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(6939,plain,
% 2.14/2.35 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(6940,plain,
% 2.14/2.35 (((~![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(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[6939])).
% 2.14/2.35 tff(6941,plain,
% 2.14/2.35 (((~![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(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[6940, 6938])).
% 2.14/2.35 tff(6942,plain,
% 2.14/2.35 ((~![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(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(6943,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[6942, 6941])).
% 2.14/2.35 tff(6944,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[6943, 97, 6922, 6931, 6902, 6937, 6935, 6920])).
% 2.14/2.35 tff(6945,plain,(b(s(s(s(z))), s(z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), z)) | b(s(s(s(z))), s(s(z))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(6946,plain,
% 2.14/2.35 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[6945, 3476, 570, 550, 2590, 3])).
% 2.14/2.35 tff(6947,plain,
% 2.14/2.35 (b(s(z), s(s(s(s(elem!1)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[280, 6946])).
% 2.14/2.35 tff(6948,plain,
% 2.14/2.35 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[6947, 6690])).
% 2.14/2.35 tff(6949,plain,
% 2.14/2.35 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.14/2.35 inference(symmetry,[status(thm)],[6684])).
% 2.14/2.35 tff(6950,plain,
% 2.14/2.35 (s(s(elem!1)) = s(s(z))),
% 2.14/2.35 inference(transitivity,[status(thm)],[167, 6949, 72])).
% 2.14/2.35 tff(6951,plain,
% 2.14/2.35 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(elem!1))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[6950])).
% 2.14/2.35 tff(6952,plain,
% 2.14/2.35 (b(s(s(z)), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.14/2.35 inference(symmetry,[status(thm)],[6951])).
% 2.14/2.35 tff(6953,plain,
% 2.14/2.35 (s(z) = s(elem!1)),
% 2.14/2.35 inference(transitivity,[status(thm)],[24, 6686, 29])).
% 2.14/2.35 tff(6954,plain,
% 2.14/2.35 (b(s(s(z)), s(z)) <=> b(s(s(z)), s(elem!1))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[6953])).
% 2.14/2.35 tff(6955,plain,
% 2.14/2.35 (~r(s(s(z)), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2930, 3477, 3, 2591])).
% 2.14/2.35 tff(6956,plain,
% 2.14/2.35 (b(s(s(z)), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[122, 6955])).
% 2.14/2.35 tff(6957,plain,
% 2.14/2.35 (b(s(s(z)), s(elem!1))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[6956, 6954])).
% 2.14/2.35 tff(6958,plain,
% 2.14/2.35 (b(s(s(elem!1)), s(elem!1))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[6957, 6952])).
% 2.14/2.35 tff(6959,plain,
% 2.14/2.35 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[6685])).
% 2.14/2.35 tff(6960,plain,
% 2.14/2.35 (((~![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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, 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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(6961,plain,
% 2.14/2.35 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(6962,plain,
% 2.14/2.35 (((~![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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[6961])).
% 2.14/2.35 tff(6963,plain,
% 2.14/2.35 (((~![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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[6962, 6960])).
% 2.14/2.35 tff(6964,plain,
% 2.14/2.35 ((~![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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(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)))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(6965,plain,
% 2.14/2.35 ((~![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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[6964, 6963])).
% 2.14/2.35 tff(6966,plain,
% 2.14/2.35 (~b(z, s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[6965, 97, 61, 6947, 6956])).
% 2.14/2.35 tff(6967,plain,
% 2.14/2.35 (r(z, s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[222, 6966])).
% 2.14/2.35 tff(6968,plain,
% 2.14/2.35 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[6758, 3477, 61, 2591, 125, 570, 550, 3])).
% 2.14/2.35 tff(6969,plain,
% 2.14/2.35 (r(z, s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[6374, 6968, 570])).
% 2.14/2.35 tff(6970,plain,
% 2.14/2.35 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[6953])).
% 2.14/2.35 tff(6971,plain,
% 2.14/2.35 (z = elem!1),
% 2.14/2.35 inference(transitivity,[status(thm)],[1443, 6970, 85])).
% 2.14/2.35 tff(6972,plain,
% 2.14/2.35 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[6971, 6685])).
% 2.14/2.35 tff(6973,plain,
% 2.14/2.35 (r(elem!1, s(s(elem!1)))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[6967, 6972])).
% 2.14/2.35 tff(6974,plain,
% 2.14/2.35 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.14/2.35 inference(monotonicity,[status(thm)],[6971])).
% 2.14/2.35 tff(6975,plain,
% 2.14/2.35 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 2.14/2.35 inference(monotonicity,[status(thm)],[6685])).
% 2.14/2.35 tff(6976,plain,
% 2.14/2.35 (~b(s(s(z)), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[3004, 3477, 2591, 550, 61])).
% 2.14/2.35 tff(6977,plain,
% 2.14/2.35 (r(s(s(z)), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[625, 6976])).
% 2.14/2.35 tff(6978,plain,
% 2.14/2.35 (r(s(s(elem!1)), z)),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[6977, 6975])).
% 2.14/2.35 tff(6979,plain,
% 2.14/2.35 (r(s(s(elem!1)), elem!1)),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[6978, 6974])).
% 2.14/2.35 tff(6980,plain,
% 2.14/2.35 (~b(s(s(s(s(elem!1)))), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[3055, 6947, 550, 61])).
% 2.14/2.35 tff(6981,plain,
% 2.14/2.35 (r(s(s(s(s(elem!1)))), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[842, 6980])).
% 2.14/2.35 tff(6982,plain,
% 2.14/2.35 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[3107, 6981, 6683])).
% 2.14/2.35 tff(6983,plain,
% 2.14/2.35 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[6107, 155, 6982, 6979, 6973])).
% 2.14/2.35 tff(6984,plain,
% 2.14/2.35 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1822, 6983, 6683])).
% 2.14/2.35 tff(6985,plain,
% 2.14/2.35 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[452, 6984])).
% 2.14/2.35 tff(6986,plain,
% 2.14/2.35 (~b(z, s(s(s(s(elem!1)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1494, 6985, 61, 6947])).
% 2.14/2.35 tff(6987,plain,
% 2.14/2.35 (r(z, s(s(s(s(elem!1)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1093, 6986])).
% 2.14/2.35 tff(6988,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(6989,plain,
% 2.14/2.35 (((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(6990,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[6989])).
% 2.14/2.35 tff(6991,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[6990, 6988])).
% 2.14/2.35 tff(6992,plain,
% 2.14/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(6993,plain,
% 2.14/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[6992, 6991])).
% 2.14/2.35 tff(6994,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[6993, 155, 463, 309, 226, 1300, 1960])).
% 2.14/2.35 tff(6995,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(6996,plain,
% 2.14/2.35 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[6995, 6987, 6969, 2591, 6967])).
% 2.14/2.35 tff(6997,plain,
% 2.14/2.35 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[336, 6996])).
% 2.14/2.35 tff(6998,plain,
% 2.14/2.35 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[6997, 6959])).
% 2.14/2.35 tff(6999,plain,
% 2.14/2.35 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[6685])).
% 2.14/2.35 tff(7000,plain,
% 2.14/2.35 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.14/2.35 inference(transitivity,[status(thm)],[6999, 1428])).
% 2.14/2.35 tff(7001,plain,
% 2.14/2.35 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[7000])).
% 2.14/2.35 tff(7002,plain,
% 2.14/2.35 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[331, 7001])).
% 2.14/2.35 tff(7003,plain,
% 2.14/2.35 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1484, 7002, 6983])).
% 2.14/2.35 tff(7004,plain,
% 2.14/2.35 ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[6598, 97, 7003, 6998])).
% 2.14/2.35 tff(7005,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[7004, 6958, 6948])).
% 2.14/2.35 tff(7006,plain,((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(7007,plain,
% 2.14/2.35 (~b(s(s(s(z))), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[7006, 3, 550, 570, 125, 61, 1361, 2590])).
% 2.14/2.35 tff(7008,plain,
% 2.14/2.35 (r(s(s(s(z))), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[402, 7007])).
% 2.14/2.35 tff(7009,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[6489, 97, 550, 87, 1361, 1360])).
% 2.14/2.35 tff(7010,plain,((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(7011,plain,
% 2.14/2.35 (~b(s(s(z)), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[7010, 1360, 1361, 550])).
% 2.14/2.35 tff(7012,plain,
% 2.14/2.35 (r(s(s(z)), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[122, 7011])).
% 2.14/2.35 tff(7013,plain,
% 2.14/2.35 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2313, 7012, 125, 3])).
% 2.14/2.35 tff(7014,plain,
% 2.14/2.35 (b(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[58, 7013])).
% 2.14/2.35 tff(7015,plain,
% 2.14/2.35 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2677, 7014, 2590])).
% 2.14/2.35 tff(7016,plain,
% 2.14/2.35 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2682, 7015])).
% 2.14/2.35 tff(7017,plain,
% 2.14/2.35 (~b(z, s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[6364, 1360, 61, 550])).
% 2.14/2.35 tff(7018,plain,
% 2.14/2.35 (r(z, s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1318, 7017])).
% 2.14/2.35 tff(7019,plain,
% 2.14/2.35 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2313, 2994, 125, 3])).
% 2.14/2.35 tff(7020,plain,
% 2.14/2.35 (b(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[58, 7019])).
% 2.14/2.35 tff(7021,plain,
% 2.14/2.35 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2677, 7020, 2590])).
% 2.14/2.35 tff(7022,plain,
% 2.14/2.35 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2682, 7021])).
% 2.14/2.35 tff(7023,plain,
% 2.14/2.35 (~b(s(s(s(elem!1))), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1390, 7020, 83, 61])).
% 2.14/2.35 tff(7024,plain,
% 2.14/2.35 (r(s(s(s(elem!1))), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[246, 7023])).
% 2.14/2.35 tff(7025,plain,
% 2.14/2.35 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2488, 155, 7024, 7018, 386])).
% 2.14/2.35 tff(7026,plain,
% 2.14/2.35 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2687, 7025, 7022])).
% 2.14/2.35 tff(7027,plain,
% 2.14/2.35 (((~![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(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(7028,plain,
% 2.14/2.35 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(7029,plain,
% 2.14/2.35 (((~![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(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(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(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[7028])).
% 2.14/2.35 tff(7030,plain,
% 2.14/2.35 (((~![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(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(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(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[7029, 7027])).
% 2.14/2.35 tff(7031,plain,
% 2.14/2.35 ((~![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(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(7032,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[7031, 7030])).
% 2.14/2.35 tff(7033,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[7032, 97, 61, 7020, 83, 1361, 1360, 7026])).
% 2.14/2.35 tff(7034,plain,((~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | b(s(s(s(z))), s(s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(7035,plain,
% 2.14/2.35 (~b(s(s(z)), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[7034, 1360, 1361, 61, 7008, 2590, 125, 3, 550])).
% 2.14/2.35 tff(7036,plain,
% 2.14/2.35 (r(s(s(z)), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[625, 7035])).
% 2.14/2.36 tff(7037,plain,
% 2.14/2.36 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2253, 7012, 125, 570, 7036])).
% 2.14/2.36 tff(7038,plain,
% 2.14/2.36 (b(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[143, 7037])).
% 2.14/2.36 tff(7039,plain,
% 2.14/2.36 (~b(s(s(s(elem!1))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2261, 97, 204, 7014, 7038])).
% 2.14/2.36 tff(7040,plain,
% 2.14/2.36 (r(s(s(s(elem!1))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[246, 7039])).
% 2.14/2.36 tff(7041,plain,
% 2.14/2.36 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2488, 155, 7040, 7018, 7008])).
% 2.14/2.36 tff(7042,plain,
% 2.14/2.36 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2687, 7041, 7016])).
% 2.14/2.36 tff(7043,plain,
% 2.14/2.36 (((~![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(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(7044,plain,
% 2.14/2.36 (((~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(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(7045,plain,
% 2.14/2.36 (((~![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(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[7044])).
% 2.14/2.36 tff(7046,plain,
% 2.14/2.36 (((~![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(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[7045, 7043])).
% 2.14/2.36 tff(7047,plain,
% 2.14/2.36 ((~![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(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(7048,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[7047, 7046])).
% 2.14/2.36 tff(7049,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[7048, 97, 7014, 1361, 1360, 7042])).
% 2.14/2.36 tff(7050,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | b(s(s(s(z))), s(s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(7051,plain,
% 2.14/2.36 (~b(s(s(s(z))), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[7050, 204, 1361, 2590, 125, 570, 3, 550, 61])).
% 2.14/2.36 tff(7052,plain,
% 2.14/2.36 (r(s(s(s(z))), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1358, 7051])).
% 2.14/2.36 tff(7053,plain,
% 2.14/2.36 (~r(s(s(z)), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2930, 7052, 3, 2591])).
% 2.14/2.36 tff(7054,plain,
% 2.14/2.36 (b(s(s(z)), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[122, 7053])).
% 2.14/2.36 tff(7055,plain,
% 2.14/2.36 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[6945, 7051, 570, 550, 2590, 3])).
% 2.14/2.36 tff(7056,plain,
% 2.14/2.36 (b(s(z), s(s(s(s(elem!1)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[280, 7055])).
% 2.14/2.36 tff(7057,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[6965, 97, 61, 7056, 204, 7054])).
% 2.14/2.36 tff(7058,plain,((~b(z, s(s(z)))) | (~b(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), z)) | b(s(s(s(z))), s(s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(7059,plain,
% 2.14/2.36 (~b(z, s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[7058, 3, 61, 570, 550, 2590, 1361, 125])).
% 2.14/2.36 tff(7060,plain,
% 2.14/2.36 (r(z, s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[222, 7059])).
% 2.14/2.36 tff(7061,plain,
% 2.14/2.36 (~r(s(s(z)), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[6467, 7060, 2591, 7008])).
% 2.14/2.36 tff(7062,plain,
% 2.14/2.36 (b(s(s(z)), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[625, 7061])).
% 2.14/2.36 tff(7063,plain,
% 2.14/2.36 (~r(s(s(s(z))), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[3004, 7062, 2591, 550, 61])).
% 2.14/2.36 tff(7064,plain,
% 2.14/2.36 (~b(s(s(s(z))), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[7034, 7062, 1361, 61, 7008, 2590, 125, 3, 550])).
% 2.14/2.36 tff(7065,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1358, 7064, 7063])).
% 2.14/2.36 tff(7066,plain,((~r(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | b(s(s(s(z))), s(s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(7067,plain,
% 2.14/2.36 (~r(s(z), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[7066, 6430, 61, 2590, 494, 550, 6682])).
% 2.14/2.36 tff(7068,plain,
% 2.14/2.36 (b(s(z), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[548, 7067])).
% 2.14/2.36 tff(7069,plain,
% 2.14/2.36 (~b(z, s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[3997, 7068, 550, 6430])).
% 2.14/2.36 tff(7070,plain,
% 2.14/2.36 (r(z, s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[222, 7069])).
% 2.14/2.36 tff(7071,plain,
% 2.14/2.36 (~r(s(z), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[7066, 1361, 61, 2590, 125, 550, 570])).
% 2.14/2.36 tff(7072,plain,
% 2.14/2.36 (b(s(z), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[548, 7071])).
% 2.14/2.36 tff(7073,plain,
% 2.14/2.36 (~b(z, s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[3997, 7072, 550, 1361])).
% 2.14/2.36 tff(7074,plain,
% 2.14/2.36 (r(z, s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[222, 7073])).
% 2.14/2.36 tff(7075,plain,
% 2.14/2.36 (~r(s(s(s(z))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[6467, 3006, 2591, 7074])).
% 2.14/2.36 tff(7076,plain,
% 2.14/2.36 (b(s(s(s(z))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[402, 7075])).
% 2.14/2.36 tff(7077,plain,
% 2.14/2.36 (~b(s(z), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[4270, 7076, 1361, 7072])).
% 2.14/2.36 tff(7078,plain,
% 2.14/2.36 (r(s(z), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[253, 7077])).
% 2.14/2.36 tff(7079,plain,
% 2.14/2.36 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2638, 7078, 2597, 125])).
% 2.14/2.36 tff(7080,plain,
% 2.14/2.36 (~b(s(s(s(s(z)))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2853, 7076, 61, 2597, 550])).
% 2.14/2.36 tff(7081,plain,
% 2.14/2.36 (r(s(s(s(s(z)))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2860, 7080])).
% 2.14/2.36 tff(7082,plain,
% 2.14/2.36 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2881, 155, 7074, 3006, 7081])).
% 2.14/2.36 tff(7083,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2886, 7082, 80])).
% 2.14/2.36 tff(7084,assumption,(b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 2.14/2.36 tff(7085,plain,
% 2.14/2.36 (~b(s(s(s(s(z)))), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[3250, 97, 535, 1361, 7084])).
% 2.14/2.36 tff(7086,plain,
% 2.14/2.36 (r(s(s(s(s(z)))), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2807, 7085, 2795])).
% 2.14/2.36 tff(7087,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(7088,plain,
% 2.14/2.36 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(7089,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[7088])).
% 2.14/2.36 tff(7090,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 2.14/2.36 inference(transitivity,[status(thm)],[7089, 7087])).
% 2.14/2.36 tff(7091,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(7092,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[7091, 7090])).
% 2.14/2.36 tff(7093,plain,
% 2.14/2.36 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[7092, 155, 1300, 2597, 7086, 4153])).
% 2.14/2.36 tff(7094,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[4169, 7093])).
% 2.14/2.36 tff(7095,plain,
% 2.14/2.36 (((~![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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), 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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(7096,plain,
% 2.14/2.36 (((~b(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(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(7097,plain,
% 2.14/2.36 (((~![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(s(z))))) | (~b(s(s(z)), s(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(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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[7096])).
% 2.14/2.36 tff(7098,plain,
% 2.14/2.36 (((~![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(s(z))))) | (~b(s(s(z)), s(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(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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[7097, 7095])).
% 2.14/2.36 tff(7099,plain,
% 2.14/2.36 ((~![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(s(z))))) | (~b(s(s(z)), s(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(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(7100,plain,
% 2.14/2.36 ((~![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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[7099, 7098])).
% 2.14/2.36 tff(7101,plain,
% 2.14/2.36 (~b(s(z), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[7100, 97, 535, 1361, 7084])).
% 2.14/2.36 tff(7102,plain,
% 2.14/2.36 (r(s(z), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2844, 7101, 2833])).
% 2.14/2.36 tff(7103,plain,
% 2.14/2.36 (((~r(s(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)))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(7104,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[7103])).
% 2.14/2.36 tff(7105,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[7104, 2846])).
% 2.14/2.36 tff(7106,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(7107,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))))) | (~r(s(z), s(s(s(s(z))))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[7106, 7105])).
% 2.14/2.36 tff(7108,plain,
% 2.14/2.36 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[7107, 155, 2597, 7102, 7086])).
% 2.14/2.36 tff(7109,plain,
% 2.14/2.36 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2829, 7108])).
% 2.14/2.36 tff(7110,plain,
% 2.14/2.36 (((~![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(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), 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(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(7111,plain,
% 2.14/2.36 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(7112,plain,
% 2.14/2.36 (((~![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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(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(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[7111])).
% 2.14/2.36 tff(7113,plain,
% 2.14/2.36 (((~![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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(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(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[7112, 7110])).
% 2.14/2.36 tff(7114,plain,
% 2.14/2.36 ((~![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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(7115,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[7114, 7113])).
% 2.14/2.36 tff(7116,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[7115, 97, 1361, 7084, 7109, 7094])).
% 2.14/2.36 tff(7117,plain,((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(7118,plain,
% 2.14/2.36 (~r(z, s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[7117, 7083, 1361, 7072, 2597, 7081])).
% 2.14/2.36 tff(7119,plain,
% 2.14/2.36 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[6374, 7118, 570])).
% 2.14/2.36 tff(7120,plain,
% 2.14/2.36 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2687, 7119, 7079])).
% 2.14/2.36 tff(7121,plain,
% 2.14/2.36 (b(z, s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1318, 7118])).
% 2.14/2.36 tff(7122,plain,
% 2.14/2.36 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[6671, 7076, 61, 2591, 550, 1361, 125, 2597])).
% 2.14/2.36 tff(7123,plain,
% 2.14/2.36 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2677, 7122, 2590])).
% 2.14/2.36 tff(7124,plain,
% 2.14/2.36 (r(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[58, 7123])).
% 2.14/2.36 tff(7125,plain,
% 2.14/2.36 (~r(s(s(s(elem!1))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2671, 7124, 7074, 3006])).
% 2.14/2.36 tff(7126,plain,
% 2.14/2.36 (b(s(s(s(elem!1))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[246, 7125])).
% 2.14/2.36 tff(7127,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[6756, 97, 550, 61, 7126, 7121, 7076, 7120])).
% 2.14/2.36 tff(7128,plain,((~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(7129,plain,
% 2.14/2.36 (~r(s(s(s(z))), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[7128, 6682, 61, 550, 6430, 494, 2590])).
% 2.14/2.36 tff(7130,plain,
% 2.14/2.36 (b(s(s(s(z))), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1358, 7129])).
% 2.14/2.36 tff(7131,plain,
% 2.14/2.36 (~b(s(s(s(z))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[3383, 97, 550, 61, 7130])).
% 2.14/2.36 tff(7132,plain,
% 2.14/2.36 (r(s(s(s(z))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[402, 7131])).
% 2.14/2.36 tff(7133,plain,
% 2.14/2.36 (~r(s(s(z)), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[6467, 7132, 2591, 7070])).
% 2.14/2.36 tff(7134,plain,
% 2.14/2.36 (b(s(s(z)), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[625, 7133])).
% 2.14/2.36 tff(7135,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[3000, 97, 550, 61, 7134, 7068])).
% 2.14/2.36 tff(7136,plain,(b(s(s(s(z))), s(s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(7137,plain,
% 2.14/2.36 (b(s(s(s(z))), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[7136, 550, 61, 82])).
% 2.14/2.36 tff(7138,plain,
% 2.14/2.36 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2313, 2994, 494, 3])).
% 2.14/2.36 tff(7139,plain,
% 2.14/2.36 (b(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[58, 7138])).
% 2.14/2.36 tff(7140,plain,
% 2.14/2.36 (~b(s(s(s(elem!1))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1390, 7139, 83, 61])).
% 2.14/2.36 tff(7141,plain,
% 2.14/2.36 (r(s(s(s(elem!1))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[246, 7140])).
% 2.14/2.36 tff(7142,plain,
% 2.14/2.36 (((~![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)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(7143,plain,
% 2.14/2.36 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~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(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(7144,plain,
% 2.14/2.36 (((~![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)), z)) | (~b(s(s(z)), z)) | (~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(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(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[7143])).
% 2.14/2.37 tff(7145,plain,
% 2.14/2.37 (((~![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(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(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(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[7144, 7142])).
% 2.14/2.37 tff(7146,plain,
% 2.14/2.37 ((~![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(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(elem!1))), s(s(s(z))))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(7147,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[7146, 7145])).
% 2.14/2.37 tff(7148,plain,
% 2.14/2.37 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[7147, 97, 7139, 83, 7137])).
% 2.14/2.37 tff(7149,plain,
% 2.14/2.37 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2488, 155, 288, 7018, 6465])).
% 2.14/2.37 tff(7150,plain,
% 2.14/2.37 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2687, 7149, 2684])).
% 2.14/2.37 tff(7151,plain,
% 2.14/2.37 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7150])).
% 2.14/2.37 tff(7152,plain,
% 2.14/2.37 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.14/2.37 inference(symmetry,[status(thm)],[7151])).
% 2.14/2.37 tff(7153,plain,
% 2.14/2.37 (b(s(s(s(elem!1))), s(z))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[1360, 7152])).
% 2.14/2.37 tff(7154,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[82, 7153])).
% 2.14/2.37 tff(7155,plain,((~b(s(s(s(z))), s(z))) | b(s(s(s(elem!1))), s(z)) | b(s(s(s(elem!1))), s(s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(7156,plain,
% 2.14/2.37 (~b(s(s(s(z))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[7155, 7148, 82, 7141, 550, 61])).
% 2.14/2.37 tff(7157,plain,
% 2.14/2.37 (r(s(s(s(z))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1358, 7156])).
% 2.14/2.37 tff(7158,plain,
% 2.14/2.37 (~b(s(z), s(s(s(elem!1))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[201, 60, 124, 61])).
% 2.14/2.37 tff(7159,plain,
% 2.14/2.37 (r(s(z), s(s(s(elem!1))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[181, 7158])).
% 2.14/2.37 tff(7160,plain,
% 2.14/2.37 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[3015, 155, 125, 7159, 2597])).
% 2.14/2.37 tff(7161,plain,
% 2.14/2.37 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[3089, 7160, 1])).
% 2.14/2.37 tff(7162,plain,
% 2.14/2.37 (~b(s(s(z)), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[3662, 7161, 1331, 60])).
% 2.14/2.37 tff(7163,plain,
% 2.14/2.37 (r(s(s(z)), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[122, 7162])).
% 2.14/2.37 tff(7164,plain,
% 2.14/2.37 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1273, 7163, 125, 7159])).
% 2.14/2.37 tff(7165,plain,
% 2.14/2.37 (b(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[143, 7164])).
% 2.14/2.37 tff(7166,plain,
% 2.14/2.37 (((~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(z)), s(s(s(elem!1))))) | (~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))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(7167,plain,
% 2.14/2.37 (((~![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(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(z)), s(s(s(elem!1))))) | (~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)))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7166])).
% 2.14/2.37 tff(7168,plain,
% 2.14/2.37 (((~![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(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(z)), s(s(s(elem!1))))) | (~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))))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[7167, 2265])).
% 2.14/2.37 tff(7169,plain,
% 2.14/2.37 ((~![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(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)))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(7170,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[7169, 7168])).
% 2.14/2.37 tff(7171,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[7170, 97, 60, 1331, 7165, 7161])).
% 2.14/2.37 tff(7172,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(7173,plain,
% 2.14/2.37 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[7172, 124, 1331, 2597, 125, 60, 61])).
% 2.14/2.37 tff(7174,plain,
% 2.14/2.37 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7173])).
% 2.14/2.37 tff(7175,plain,
% 2.14/2.37 (s(s(z)) = s(s(elem!1))),
% 2.14/2.37 inference(transitivity,[status(thm)],[73, 7174, 19])).
% 2.14/2.37 tff(7176,plain,
% 2.14/2.37 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7175])).
% 2.14/2.37 tff(7177,plain,
% 2.14/2.37 (s(z) = s(elem!1)),
% 2.14/2.37 inference(transitivity,[status(thm)],[24, 7176, 29])).
% 2.14/2.37 tff(7178,plain,
% 2.14/2.37 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7177])).
% 2.14/2.37 tff(7179,plain,
% 2.14/2.37 (z = elem!1),
% 2.14/2.37 inference(transitivity,[status(thm)],[1443, 7178, 85])).
% 2.14/2.37 tff(7180,plain,
% 2.14/2.37 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7179])).
% 2.14/2.37 tff(7181,plain,
% 2.14/2.37 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7175])).
% 2.14/2.37 tff(7182,plain,
% 2.14/2.37 (b(s(s(elem!1)), z)),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[83, 7181])).
% 2.14/2.37 tff(7183,plain,
% 2.14/2.37 (b(s(s(elem!1)), elem!1)),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[7182, 7180])).
% 2.14/2.37 tff(7184,plain,
% 2.14/2.37 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.14/2.37 inference(symmetry,[status(thm)],[7174])).
% 2.14/2.37 tff(7185,plain,
% 2.14/2.37 (s(s(elem!1)) = s(s(z))),
% 2.14/2.37 inference(transitivity,[status(thm)],[167, 7184, 72])).
% 2.14/2.37 tff(7186,plain,
% 2.14/2.37 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7185])).
% 2.14/2.37 tff(7187,plain,
% 2.14/2.37 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.14/2.37 inference(symmetry,[status(thm)],[7186])).
% 2.14/2.37 tff(7188,plain,
% 2.14/2.37 (~b(s(z), s(s(s(elem!1))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[201, 124, 61, 60])).
% 2.14/2.37 tff(7189,plain,
% 2.14/2.37 (r(s(z), s(s(s(elem!1))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[181, 7188])).
% 2.14/2.37 tff(7190,plain,
% 2.14/2.37 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1273, 7189, 125, 2])).
% 2.14/2.37 tff(7191,plain,
% 2.14/2.37 (b(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[143, 7190])).
% 2.14/2.37 tff(7192,plain,
% 2.14/2.37 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[7191, 7187])).
% 2.14/2.37 tff(7193,plain,
% 2.14/2.37 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7185])).
% 2.14/2.37 tff(7194,plain,
% 2.14/2.37 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.14/2.37 inference(symmetry,[status(thm)],[7193])).
% 2.14/2.37 tff(7195,plain,
% 2.14/2.37 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[60, 7194])).
% 2.14/2.37 tff(7196,plain,
% 2.14/2.37 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7179])).
% 2.14/2.37 tff(7197,plain,
% 2.14/2.37 (b(elem!1, s(s(s(elem!1))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[124, 7196])).
% 2.14/2.37 tff(7198,plain,
% 2.14/2.37 (((~![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(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $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(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(7199,plain,
% 2.14/2.37 (((~b(s(s(s(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(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(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(7200,plain,
% 2.14/2.37 (((~![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(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(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(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7199])).
% 2.14/2.37 tff(7201,plain,
% 2.14/2.37 (((~![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(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(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(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.37 inference(transitivity,[status(thm)],[7200, 7198])).
% 2.14/2.37 tff(7202,plain,
% 2.14/2.37 ((~![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(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(7203,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[7202, 7201])).
% 2.14/2.37 tff(7204,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[7203, 97, 7197, 7195, 7192, 7183])).
% 2.14/2.37 tff(7205,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(7206,plain,
% 2.14/2.37 (~b(z, s(s(s(elem!1))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[7205, 83, 7139, 494, 2994, 61, 7137, 7157])).
% 2.14/2.37 tff(7207,plain,
% 2.14/2.37 (r(z, s(s(s(elem!1))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[590, 7206])).
% 2.14/2.37 tff(7208,plain,
% 2.14/2.37 (((~![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(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(7209,plain,
% 2.14/2.37 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(7210,plain,
% 2.14/2.37 (((~![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(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7209])).
% 2.14/2.37 tff(7211,plain,
% 2.14/2.37 (((~![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(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[7210, 7208])).
% 2.14/2.37 tff(7212,plain,
% 2.14/2.37 ((~![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(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(7213,plain,
% 2.14/2.37 ((~![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(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[7212, 7211])).
% 2.14/2.37 tff(7214,plain,
% 2.14/2.37 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[7213, 97, 7139, 83, 7137])).
% 2.14/2.37 tff(7215,plain,
% 2.14/2.37 (~r(z, s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5852, 1, 2684, 3087, 570])).
% 2.14/2.37 tff(7216,plain,
% 2.14/2.37 (b(z, s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1318, 7215])).
% 2.14/2.37 tff(7217,plain,
% 2.14/2.37 (~r(s(z), s(s(s(elem!1))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5757, 5841, 2597, 125])).
% 2.14/2.37 tff(7218,plain,
% 2.14/2.37 (b(s(z), s(s(s(elem!1))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[181, 7217])).
% 2.14/2.37 tff(7219,plain,
% 2.14/2.37 (~r(s(z), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2638, 5842, 2597, 125])).
% 2.14/2.37 tff(7220,plain,
% 2.14/2.37 (b(s(z), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[253, 7219])).
% 2.14/2.37 tff(7221,plain,
% 2.14/2.37 (((~![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(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(7222,plain,
% 2.14/2.37 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(7223,plain,
% 2.14/2.37 (((~![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(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(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(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7222])).
% 2.14/2.37 tff(7224,plain,
% 2.14/2.37 (((~![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(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(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(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[7223, 7221])).
% 2.14/2.37 tff(7225,plain,
% 2.14/2.37 ((~![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(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(7226,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[7225, 7224])).
% 2.14/2.37 tff(7227,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[7226, 97, 193, 61, 60, 1331, 86, 1330])).
% 2.14/2.37 tff(7228,plain,((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(7229,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[7228, 7220, 7218, 61, 1331, 60, 7216])).
% 2.14/2.37 tff(7230,plain,((s(s(s(z))) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | b(s(s(s(elem!1))), s(s(s(z)))) | b(s(s(s(z))), s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(7231,plain,
% 2.14/2.37 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[7230, 7139, 7137, 61, 7157, 494, 7148, 7214, 7207])).
% 2.14/2.37 tff(7232,plain,
% 2.14/2.37 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7231])).
% 2.14/2.37 tff(7233,plain,
% 2.14/2.37 (s(s(z)) = s(s(elem!1))),
% 2.14/2.37 inference(transitivity,[status(thm)],[73, 7232, 19])).
% 2.14/2.37 tff(7234,plain,
% 2.14/2.37 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7233])).
% 2.14/2.37 tff(7235,plain,
% 2.14/2.37 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.14/2.37 inference(transitivity,[status(thm)],[7234, 1428])).
% 2.14/2.37 tff(7236,plain,
% 2.14/2.37 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7235])).
% 2.14/2.37 tff(7237,plain,
% 2.14/2.37 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[331, 7236])).
% 2.14/2.37 tff(7238,plain,
% 2.14/2.37 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.14/2.37 inference(symmetry,[status(thm)],[7232])).
% 2.14/2.37 tff(7239,plain,
% 2.14/2.37 (s(s(elem!1)) = s(s(z))),
% 2.14/2.37 inference(transitivity,[status(thm)],[167, 7238, 72])).
% 2.14/2.37 tff(7240,plain,
% 2.14/2.37 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7239])).
% 2.14/2.37 tff(7241,plain,
% 2.14/2.37 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.14/2.37 inference(symmetry,[status(thm)],[7240])).
% 2.14/2.37 tff(7242,plain,
% 2.14/2.37 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7233])).
% 2.14/2.37 tff(7243,plain,
% 2.14/2.37 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.14/2.37 inference(symmetry,[status(thm)],[7242])).
% 2.14/2.37 tff(7244,plain,
% 2.14/2.37 (s(elem!1) = s(z)),
% 2.14/2.37 inference(transitivity,[status(thm)],[30, 7243, 23])).
% 2.14/2.37 tff(7245,plain,
% 2.14/2.37 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7244])).
% 2.14/2.37 tff(7246,plain,
% 2.14/2.37 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7245])).
% 2.14/2.37 tff(7247,plain,
% 2.14/2.37 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7231])).
% 2.14/2.37 tff(7248,plain,
% 2.14/2.37 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[7247, 1414])).
% 2.14/2.37 tff(7249,plain,
% 2.14/2.37 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[7248, 2507])).
% 2.14/2.37 tff(7250,plain,
% 2.14/2.37 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7249])).
% 2.14/2.37 tff(7251,plain,
% 2.14/2.37 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[286, 7250])).
% 2.14/2.37 tff(7252,plain,
% 2.14/2.37 (s(z) = s(elem!1)),
% 2.14/2.37 inference(transitivity,[status(thm)],[24, 7242, 29])).
% 2.14/2.37 tff(7253,plain,
% 2.14/2.37 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7252])).
% 2.14/2.37 tff(7254,plain,
% 2.14/2.37 (z = elem!1),
% 2.14/2.37 inference(transitivity,[status(thm)],[1443, 7253, 85])).
% 2.14/2.37 tff(7255,plain,
% 2.14/2.37 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7254])).
% 2.14/2.37 tff(7256,plain,
% 2.14/2.37 (r(elem!1, s(s(s(elem!1))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[7207, 7255])).
% 2.14/2.37 tff(7257,plain,
% 2.14/2.37 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7254])).
% 2.14/2.37 tff(7258,plain,
% 2.14/2.37 (r(s(s(s(elem!1))), elem!1)),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[7141, 7257])).
% 2.14/2.37 tff(7259,plain,
% 2.14/2.37 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7254])).
% 2.14/2.37 tff(7260,plain,
% 2.14/2.37 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7231])).
% 2.14/2.37 tff(7261,plain,
% 2.14/2.37 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 2.14/2.37 inference(monotonicity,[status(thm)],[7260])).
% 2.14/2.38 tff(7262,plain,
% 2.14/2.38 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.14/2.38 inference(transitivity,[status(thm)],[7261, 7259])).
% 2.14/2.38 tff(7263,plain,
% 2.14/2.38 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7254])).
% 2.14/2.38 tff(7264,plain,
% 2.14/2.38 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7233])).
% 2.14/2.38 tff(7265,plain,
% 2.14/2.38 (b(s(s(elem!1)), z)),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[83, 7264])).
% 2.14/2.38 tff(7266,plain,
% 2.14/2.38 (b(s(s(elem!1)), elem!1)),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[7265, 7263])).
% 2.14/2.38 tff(7267,plain,
% 2.14/2.38 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7233])).
% 2.14/2.38 tff(7268,plain,
% 2.14/2.38 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(z)))),
% 2.14/2.38 inference(symmetry,[status(thm)],[7267])).
% 2.14/2.38 tff(7269,plain,
% 2.14/2.38 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7252, 7233])).
% 2.14/2.38 tff(7270,plain,
% 2.14/2.38 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 2.14/2.38 inference(transitivity,[status(thm)],[7269, 7268])).
% 2.14/2.38 tff(7271,plain,
% 2.14/2.38 (r(s(elem!1), s(s(z)))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[3, 7270])).
% 2.14/2.38 tff(7272,plain,
% 2.14/2.38 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7233, 7252])).
% 2.14/2.38 tff(7273,plain,
% 2.14/2.38 (r(s(s(elem!1)), s(elem!1))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[2994, 7272])).
% 2.14/2.38 tff(7274,plain,
% 2.14/2.38 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[1444, 1401])).
% 2.14/2.38 tff(7275,plain,
% 2.14/2.38 (b(elem!1, s(elem!1))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[61, 7274])).
% 2.14/2.38 tff(7276,plain,
% 2.14/2.38 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.14/2.38 inference(monotonicity,[status(thm)],[1444])).
% 2.14/2.38 tff(7277,plain,
% 2.14/2.38 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[1393])).
% 2.14/2.38 tff(7278,plain,
% 2.14/2.38 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7277])).
% 2.14/2.38 tff(7279,plain,
% 2.14/2.38 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.14/2.38 inference(transitivity,[status(thm)],[7278, 7276])).
% 2.14/2.38 tff(7280,plain,
% 2.14/2.38 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[2796, 7279])).
% 2.14/2.38 tff(7281,plain,
% 2.14/2.38 (((~![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(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(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(7282,plain,
% 2.14/2.38 (((~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(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(7283,plain,
% 2.14/2.38 (((~![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(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(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7282])).
% 2.14/2.38 tff(7284,plain,
% 2.14/2.38 (((~![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(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(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[7283, 7281])).
% 2.14/2.38 tff(7285,plain,
% 2.14/2.38 ((~![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(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)))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(7286,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[7285, 7284])).
% 2.14/2.38 tff(7287,plain,
% 2.14/2.38 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[7286, 97, 7280, 1915, 7275])).
% 2.14/2.38 tff(7288,plain,
% 2.14/2.38 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1484, 7287, 1432])).
% 2.14/2.38 tff(7289,plain,
% 2.14/2.38 (b(s(s(s(s(elem!1)))), z)),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[2796, 7278])).
% 2.14/2.38 tff(7290,plain,
% 2.14/2.38 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2715, 7289, 550, 61])).
% 2.14/2.38 tff(7291,plain,
% 2.14/2.38 (r(s(s(s(s(elem!1)))), s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[511, 7290])).
% 2.14/2.38 tff(7292,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1816, 7291, 7288, 1812, 1393, 1520])).
% 2.14/2.38 tff(7293,plain,((~b(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(7294,plain,
% 2.14/2.38 (~b(s(s(s(s(z)))), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[7293, 7273, 7231, 7271, 550, 61, 7266])).
% 2.14/2.38 tff(7295,plain,
% 2.14/2.38 (r(s(s(s(s(z)))), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2860, 7294])).
% 2.14/2.38 tff(7296,plain,
% 2.14/2.38 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[7295, 7262])).
% 2.14/2.38 tff(7297,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(7298,plain,
% 2.14/2.38 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(7299,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7298])).
% 2.14/2.38 tff(7300,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.14/2.38 inference(transitivity,[status(thm)],[7299, 7297])).
% 2.14/2.38 tff(7301,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(7302,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[7301, 7300])).
% 2.14/2.38 tff(7303,plain,
% 2.14/2.38 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[7302, 155, 7296, 7258, 7256])).
% 2.14/2.38 tff(7304,plain,
% 2.14/2.38 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[821, 7303, 7251])).
% 2.14/2.38 tff(7305,plain,
% 2.14/2.38 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7239])).
% 2.14/2.38 tff(7306,plain,
% 2.14/2.38 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.14/2.38 inference(symmetry,[status(thm)],[7305])).
% 2.14/2.38 tff(7307,plain,
% 2.14/2.38 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[7139, 7306])).
% 2.14/2.38 tff(7308,plain,
% 2.14/2.38 ((~b(s(elem!1), s(s(s(s(elem!1)))))) <=> (~b(s(z), s(s(s(s(elem!1))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[1516])).
% 2.14/2.38 tff(7309,plain,
% 2.14/2.38 (((~![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(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(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(s(elem!1)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(7310,plain,
% 2.14/2.38 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(7311,plain,
% 2.14/2.38 (((~![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(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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(s(elem!1))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7310])).
% 2.14/2.38 tff(7312,plain,
% 2.14/2.38 (((~![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(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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(s(elem!1)))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[7311, 7309])).
% 2.14/2.38 tff(7313,plain,
% 2.14/2.38 ((~![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(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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(7314,plain,
% 2.14/2.38 ((~![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(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(s(elem!1))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[7313, 7312])).
% 2.14/2.38 tff(7315,plain,
% 2.14/2.38 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[7314, 97, 1529, 805, 1617])).
% 2.14/2.38 tff(7316,plain,
% 2.14/2.38 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[7315, 7308])).
% 2.14/2.38 tff(7317,plain,
% 2.14/2.38 (r(s(z), s(s(s(s(elem!1)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[280, 7316])).
% 2.14/2.38 tff(7318,plain,
% 2.14/2.38 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[1411])).
% 2.14/2.38 tff(7319,plain,
% 2.14/2.38 ((~b(s(s(s(s(elem!1)))), s(elem!1))) <=> (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7318])).
% 2.14/2.38 tff(7320,plain,
% 2.14/2.38 (((~![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(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(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(7321,plain,
% 2.14/2.38 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(7322,plain,
% 2.14/2.38 (((~![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(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(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7321])).
% 2.14/2.38 tff(7323,plain,
% 2.14/2.38 (((~![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(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(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[7322, 7320])).
% 2.14/2.38 tff(7324,plain,
% 2.14/2.38 ((~![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(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(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))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(7325,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[7324, 7323])).
% 2.14/2.38 tff(7326,plain,
% 2.14/2.38 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[7325, 97, 1529, 805, 1617])).
% 2.14/2.38 tff(7327,plain,
% 2.14/2.38 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[7326, 7319])).
% 2.14/2.38 tff(7328,plain,
% 2.14/2.38 (r(s(s(s(s(elem!1)))), s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[511, 7327])).
% 2.14/2.38 tff(7329,plain,
% 2.14/2.38 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[503, 7328, 125, 7317])).
% 2.14/2.38 tff(7330,plain,
% 2.14/2.38 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[486, 7329, 1418])).
% 2.14/2.38 tff(7331,plain,
% 2.14/2.38 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1816, 7328, 1812, 1393, 1520])).
% 2.14/2.38 tff(7332,plain,
% 2.14/2.38 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1484, 7331, 1432])).
% 2.14/2.38 tff(7333,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1586, 7332, 7330, 1529, 1528, 1527, 1523, 1444])).
% 2.14/2.38 tff(7334,plain,((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(7335,plain,
% 2.14/2.38 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[7334, 7307, 7258, 7256, 7273, 7231, 7271, 494, 7304])).
% 2.14/2.38 tff(7336,plain,
% 2.14/2.38 (~b(s(z), s(s(s(elem!1))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[7335, 7246])).
% 2.14/2.38 tff(7337,plain,
% 2.14/2.38 (r(s(z), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[181, 7336])).
% 2.14/2.38 tff(7338,plain,
% 2.14/2.38 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1273, 7337, 494, 2994])).
% 2.14/2.38 tff(7339,plain,
% 2.14/2.38 (b(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[143, 7338])).
% 2.14/2.38 tff(7340,plain,
% 2.14/2.38 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[7339, 7241])).
% 2.14/2.38 tff(7341,plain,
% 2.14/2.38 (((~![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(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(7342,plain,
% 2.14/2.38 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(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(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))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(7343,plain,
% 2.14/2.38 (((~![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(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(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))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7342])).
% 2.14/2.38 tff(7344,plain,
% 2.14/2.38 (((~![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(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(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)))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[7343, 7341])).
% 2.14/2.38 tff(7345,plain,
% 2.14/2.38 ((~![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(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(7346,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[7345, 7344])).
% 2.14/2.38 tff(7347,plain,
% 2.14/2.38 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[7346, 97, 7307, 7304, 7340])).
% 2.14/2.38 tff(7348,plain,
% 2.14/2.38 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1484, 7347, 7237])).
% 2.14/2.38 tff(7349,plain,
% 2.14/2.38 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.14/2.38 inference(symmetry,[status(thm)],[1818])).
% 2.14/2.38 tff(7350,plain,
% 2.14/2.38 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[1813, 7349])).
% 2.14/2.38 tff(7351,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[447, 7350])).
% 2.14/2.38 tff(7352,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(z))) | (~(s(s(s(z))) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(7353,plain,
% 2.14/2.38 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[7352, 7348, 7231])).
% 2.14/2.38 tff(7354,plain,
% 2.14/2.38 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[7213, 97, 7020, 83, 1331])).
% 2.14/2.38 tff(7355,plain,
% 2.14/2.38 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[7147, 97, 7020, 83, 1331])).
% 2.14/2.38 tff(7356,plain,
% 2.14/2.38 (~b(z, s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1339, 204, 1331, 83])).
% 2.14/2.38 tff(7357,plain,
% 2.14/2.38 (r(z, s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1318, 7356])).
% 2.14/2.38 tff(7358,plain,
% 2.14/2.38 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5852, 7357, 7355, 7354, 570])).
% 2.14/2.38 tff(7359,plain,
% 2.14/2.38 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7358])).
% 2.14/2.38 tff(7360,plain,
% 2.14/2.38 (s(s(z)) = s(s(elem!1))),
% 2.14/2.38 inference(transitivity,[status(thm)],[73, 7359, 19])).
% 2.14/2.38 tff(7361,plain,
% 2.14/2.38 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7360])).
% 2.14/2.38 tff(7362,plain,
% 2.14/2.38 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.14/2.38 inference(symmetry,[status(thm)],[7361])).
% 2.14/2.38 tff(7363,plain,
% 2.14/2.38 (s(elem!1) = s(z)),
% 2.14/2.38 inference(transitivity,[status(thm)],[30, 7362, 23])).
% 2.14/2.38 tff(7364,plain,
% 2.14/2.38 (b(s(s(s(s(s(elem!1))))), s(elem!1)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7363])).
% 2.14/2.38 tff(7365,plain,
% 2.14/2.38 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.14/2.38 inference(symmetry,[status(thm)],[7364])).
% 2.14/2.38 tff(7366,plain,
% 2.14/2.38 (~(s(s(s(s(s(elem!1))))) = s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[6222, 7358])).
% 2.14/2.38 tff(7367,plain,
% 2.14/2.38 (r(s(s(s(s(s(elem!1))))), s(elem!1)) <=> r(s(s(s(s(s(elem!1))))), s(z))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7363])).
% 2.14/2.38 tff(7368,plain,
% 2.14/2.38 ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) <=> (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7367])).
% 2.14/2.38 tff(7369,plain,
% 2.14/2.38 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(z))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7363])).
% 2.14/2.38 tff(7370,plain,
% 2.14/2.38 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(z) = s(s(s(s(elem!1)))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[7369, 265])).
% 2.14/2.38 tff(7371,plain,
% 2.14/2.38 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.14/2.38 inference(symmetry,[status(thm)],[7370])).
% 2.14/2.38 tff(7372,plain,
% 2.14/2.38 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7371])).
% 2.14/2.38 tff(7373,plain,
% 2.14/2.38 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[275, 7372])).
% 2.14/2.38 tff(7374,plain,
% 2.14/2.38 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[6172, 7373])).
% 2.14/2.38 tff(7375,plain,
% 2.14/2.38 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7358])).
% 2.14/2.38 tff(7376,plain,
% 2.14/2.38 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[7375, 1414])).
% 2.14/2.38 tff(7377,plain,
% 2.14/2.38 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[7376, 2507])).
% 2.14/2.38 tff(7378,plain,
% 2.14/2.38 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7377])).
% 2.14/2.38 tff(7379,plain,
% 2.14/2.38 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[286, 7378])).
% 2.14/2.38 tff(7380,plain,
% 2.14/2.38 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7360])).
% 2.14/2.38 tff(7381,plain,
% 2.14/2.38 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(z)))),
% 2.14/2.38 inference(symmetry,[status(thm)],[7380])).
% 2.14/2.38 tff(7382,plain,
% 2.14/2.38 (s(z) = s(elem!1)),
% 2.14/2.38 inference(transitivity,[status(thm)],[24, 7361, 29])).
% 2.14/2.38 tff(7383,plain,
% 2.14/2.38 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7382, 7360])).
% 2.14/2.38 tff(7384,plain,
% 2.14/2.38 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 2.14/2.38 inference(transitivity,[status(thm)],[7383, 7381])).
% 2.14/2.38 tff(7385,plain,
% 2.14/2.38 (r(s(elem!1), s(s(z)))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[3, 7384])).
% 2.14/2.38 tff(7386,plain,
% 2.14/2.38 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7360, 7382])).
% 2.14/2.38 tff(7387,plain,
% 2.14/2.38 (r(s(s(elem!1)), s(elem!1))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[2994, 7386])).
% 2.14/2.38 tff(7388,plain,
% 2.14/2.38 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[7358])).
% 2.14/2.39 tff(7389,plain,
% 2.14/2.39 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7388, 7360])).
% 2.14/2.39 tff(7390,plain,
% 2.14/2.39 (r(s(s(s(z))), z) <=> r(s(s(s(elem!1))), z)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7358])).
% 2.14/2.39 tff(7391,plain,
% 2.14/2.39 (r(s(s(s(elem!1))), z) <=> r(s(s(s(z))), z)),
% 2.14/2.39 inference(symmetry,[status(thm)],[7390])).
% 2.14/2.39 tff(7392,plain,
% 2.14/2.39 (r(s(s(s(z))), z)),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[7024, 7391])).
% 2.14/2.39 tff(7393,plain,
% 2.14/2.39 (((~![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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(7394,plain,
% 2.14/2.39 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(7395,plain,
% 2.14/2.39 (((~![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)), z)) | (~b(s(s(z)), z)) | (~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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7394])).
% 2.14/2.39 tff(7396,plain,
% 2.14/2.39 (((~![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)), z)) | (~b(s(s(z)), z)) | (~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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.39 inference(transitivity,[status(thm)],[7395, 7393])).
% 2.14/2.39 tff(7397,plain,
% 2.14/2.39 ((~![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)), z)) | (~b(s(s(z)), z)) | (~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)))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(7398,plain,
% 2.14/2.39 ((~![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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[7397, 7396])).
% 2.14/2.39 tff(7399,plain,
% 2.14/2.39 (~b(s(s(s(s(z)))), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[7398, 97, 204, 83, 7084])).
% 2.14/2.39 tff(7400,plain,
% 2.14/2.39 (r(s(s(s(s(z)))), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2860, 7399])).
% 2.14/2.39 tff(7401,plain,
% 2.14/2.39 (((~![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)), 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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(7402,plain,
% 2.14/2.39 (((~b(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(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(7403,plain,
% 2.14/2.39 (((~![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)), z)) | (~b(s(s(z)), z)) | (~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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7402])).
% 2.14/2.39 tff(7404,plain,
% 2.14/2.39 (((~![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)), z)) | (~b(s(s(z)), z)) | (~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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[7403, 7401])).
% 2.14/2.39 tff(7405,plain,
% 2.14/2.39 ((~![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)), z)) | (~b(s(s(z)), z)) | (~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)))))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(7406,plain,
% 2.14/2.39 ((~![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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[7405, 7404])).
% 2.14/2.39 tff(7407,plain,
% 2.14/2.39 (~b(z, s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[7406, 97, 204, 83, 7084])).
% 2.14/2.39 tff(7408,plain,
% 2.14/2.39 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 2.14/2.39 inference(commutativity,[status(thm)],[])).
% 2.14/2.39 tff(7409,plain,
% 2.14/2.39 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 2.14/2.39 inference(symmetry,[status(thm)],[7408])).
% 2.14/2.39 tff(7410,plain,
% 2.14/2.39 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7409])).
% 2.14/2.39 tff(7411,plain,
% 2.14/2.39 (~(z = s(s(s(s(z)))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[2856, 7410])).
% 2.14/2.39 tff(7412,plain,
% 2.14/2.39 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(7413,plain,
% 2.14/2.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(7414,plain,
% 2.14/2.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[7413, 7412])).
% 2.14/2.39 tff(7415,plain,
% 2.14/2.39 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[7414, 53])).
% 2.14/2.39 tff(7416,plain,
% 2.14/2.39 (b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[7415, 7411])).
% 2.14/2.39 tff(7417,plain,
% 2.14/2.39 (r(z, s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[7416, 7407])).
% 2.14/2.39 tff(7418,plain,
% 2.14/2.39 (((~![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)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), 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(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(7419,plain,
% 2.14/2.39 (((~b(s(s(z)), z)) | (~b(s(s(z)), 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(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(7420,plain,
% 2.14/2.39 (((~![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)), z)) | (~b(s(s(z)), 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(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(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7419])).
% 2.14/2.39 tff(7421,plain,
% 2.14/2.39 (((~![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)), z)) | (~b(s(s(z)), 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(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(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[7420, 7418])).
% 2.14/2.39 tff(7422,plain,
% 2.14/2.39 ((~![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)), z)) | (~b(s(s(z)), 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(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(7423,plain,
% 2.14/2.39 ((~![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)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[7422, 7421])).
% 2.14/2.39 tff(7424,plain,
% 2.14/2.39 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[7423, 97, 83, 1331, 7084])).
% 2.14/2.39 tff(7425,plain,
% 2.14/2.39 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2829, 7424])).
% 2.14/2.39 tff(7426,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(7427,plain,
% 2.14/2.39 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(7428,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7427])).
% 2.14/2.39 tff(7429,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[7428, 7426])).
% 2.14/2.39 tff(7430,plain,
% 2.14/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(7431,plain,
% 2.14/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[7430, 7429])).
% 2.14/2.39 tff(7432,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[7431, 155, 386, 7425, 7417, 7400])).
% 2.14/2.39 tff(7433,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(7434,plain,
% 2.14/2.39 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[7433, 7392, 1331, 204, 83])).
% 2.14/2.39 tff(7435,plain,
% 2.14/2.39 (r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2886, 7434, 80])).
% 2.14/2.39 tff(7436,plain,
% 2.14/2.39 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[7435, 7389])).
% 2.14/2.39 tff(7437,plain,
% 2.14/2.39 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1816, 7436, 7387, 7358, 7385])).
% 2.14/2.39 tff(7438,plain,
% 2.14/2.39 (b(s(s(s(s(elem!1)))), s(z))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[511, 7437])).
% 2.14/2.39 tff(7439,plain,
% 2.14/2.39 (~b(s(s(s(s(elem!1)))), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2715, 7438, 550, 61])).
% 2.14/2.39 tff(7440,plain,
% 2.14/2.39 (r(s(s(s(s(elem!1)))), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[842, 7439])).
% 2.14/2.39 tff(7441,plain,
% 2.14/2.39 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[832, 7440, 570, 7024])).
% 2.14/2.39 tff(7442,plain,
% 2.14/2.39 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[821, 7441, 7379])).
% 2.14/2.39 tff(7443,plain,
% 2.14/2.39 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.14/2.39 inference(symmetry,[status(thm)],[7359])).
% 2.14/2.39 tff(7444,plain,
% 2.14/2.39 (s(s(elem!1)) = s(s(z))),
% 2.14/2.39 inference(transitivity,[status(thm)],[167, 7443, 72])).
% 2.14/2.39 tff(7445,plain,
% 2.14/2.39 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7444])).
% 2.14/2.39 tff(7446,plain,
% 2.14/2.39 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.14/2.39 inference(symmetry,[status(thm)],[7445])).
% 2.14/2.39 tff(7447,plain,
% 2.14/2.39 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[7020, 7446])).
% 2.14/2.39 tff(7448,plain,
% 2.14/2.39 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7376])).
% 2.14/2.39 tff(7449,plain,
% 2.14/2.39 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[286, 7448])).
% 2.14/2.39 tff(7450,plain,
% 2.14/2.39 (~b(z, s(s(s(s(elem!1)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[558, 7438, 550, 61])).
% 2.14/2.39 tff(7451,plain,
% 2.14/2.39 (r(z, s(s(s(s(elem!1)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1093, 7450])).
% 2.14/2.39 tff(7452,plain,
% 2.14/2.39 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1872, 7451, 7024, 7440])).
% 2.14/2.39 tff(7453,plain,
% 2.14/2.39 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[486, 7452, 7449])).
% 2.14/2.39 tff(7454,plain,
% 2.14/2.39 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7382])).
% 2.14/2.39 tff(7455,plain,
% 2.14/2.39 (z = elem!1),
% 2.14/2.39 inference(transitivity,[status(thm)],[1443, 7454, 85])).
% 2.14/2.39 tff(7456,plain,
% 2.14/2.39 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7455])).
% 2.14/2.39 tff(7457,plain,
% 2.14/2.39 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7360])).
% 2.14/2.39 tff(7458,plain,
% 2.14/2.39 (b(z, s(s(elem!1)))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[204, 7457])).
% 2.14/2.39 tff(7459,plain,
% 2.14/2.39 (b(elem!1, s(s(elem!1)))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[7458, 7456])).
% 2.14/2.39 tff(7460,plain,
% 2.14/2.39 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7444])).
% 2.14/2.39 tff(7461,plain,
% 2.14/2.39 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.14/2.39 inference(symmetry,[status(thm)],[7460])).
% 2.14/2.39 tff(7462,plain,
% 2.14/2.39 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7363])).
% 2.14/2.39 tff(7463,plain,
% 2.14/2.39 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7462])).
% 2.14/2.39 tff(7464,plain,
% 2.14/2.39 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7455])).
% 2.14/2.39 tff(7465,plain,
% 2.14/2.39 (r(s(s(s(elem!1))), elem!1)),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[7024, 7464])).
% 2.14/2.39 tff(7466,plain,
% 2.14/2.39 (r(s(s(z)), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7360])).
% 2.14/2.39 tff(7467,plain,
% 2.14/2.39 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(elem!1))),
% 2.14/2.39 inference(symmetry,[status(thm)],[7466])).
% 2.14/2.39 tff(7468,plain,
% 2.14/2.39 (r(s(s(z)), s(z)) <=> r(s(s(z)), s(elem!1))),
% 2.14/2.39 inference(transitivity,[status(thm)],[7386, 7467])).
% 2.14/2.39 tff(7469,plain,
% 2.14/2.39 (r(s(s(z)), s(elem!1))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[2994, 7468])).
% 2.14/2.39 tff(7470,plain,
% 2.14/2.39 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7455])).
% 2.14/2.39 tff(7471,plain,
% 2.14/2.39 (r(elem!1, s(s(s(elem!1))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[570, 7470])).
% 2.14/2.39 tff(7472,plain,
% 2.14/2.39 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7360])).
% 2.14/2.39 tff(7473,plain,
% 2.14/2.39 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.14/2.39 inference(transitivity,[status(thm)],[7472, 1428])).
% 2.14/2.39 tff(7474,plain,
% 2.14/2.39 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[7473, 1505])).
% 2.14/2.39 tff(7475,plain,
% 2.14/2.39 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7474])).
% 2.14/2.39 tff(7476,plain,
% 2.14/2.39 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[331, 7475])).
% 2.14/2.39 tff(7477,plain,
% 2.14/2.39 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1641, 7453, 7447, 7438])).
% 2.14/2.39 tff(7478,plain,
% 2.14/2.39 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1631, 7477, 7476])).
% 2.14/2.39 tff(7479,plain,
% 2.14/2.39 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1626, 7478, 7453, 7471, 7469, 7385, 7447, 7465, 7358])).
% 2.14/2.39 tff(7480,plain,
% 2.14/2.39 (~b(s(z), s(s(s(elem!1))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[7479, 7463])).
% 2.14/2.39 tff(7481,plain,
% 2.14/2.39 (r(s(z), s(s(s(elem!1))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[181, 7480])).
% 2.14/2.39 tff(7482,plain,
% 2.14/2.39 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1273, 7481, 125, 2994])).
% 2.14/2.39 tff(7483,plain,
% 2.14/2.39 (b(s(s(z)), s(s(s(elem!1))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[143, 7482])).
% 2.14/2.39 tff(7484,plain,
% 2.14/2.39 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[7483, 7461])).
% 2.14/2.39 tff(7485,plain,
% 2.14/2.39 (r(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.14/2.39 inference(symmetry,[status(thm)],[6274])).
% 2.14/2.39 tff(7486,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(z)))), introduced(assumption)).
% 2.14/2.39 tff(7487,plain,
% 2.14/2.39 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 2.14/2.39 inference(transitivity,[status(thm)],[7486, 1393])).
% 2.14/2.39 tff(7488,plain,
% 2.14/2.39 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(elem!1))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[7487])).
% 2.14/2.39 tff(7489,plain,
% 2.14/2.39 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.14/2.39 inference(transitivity,[status(thm)],[6168, 7488, 19])).
% 2.14/2.39 tff(7490,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1432, 7489])).
% 2.14/2.39 tff(7491,plain,((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) | (~(s(s(s(z))) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(7492,plain,
% 2.14/2.39 (~(s(s(s(s(s(elem!1))))) = s(s(s(z))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[7491, 1393])).
% 2.14/2.39 tff(7493,plain,
% 2.14/2.39 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[6271])).
% 2.14/2.39 tff(7494,plain,
% 2.14/2.39 (((~![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(s(elem!1))), s(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(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(s(elem!1))), s(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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.14/2.40 inference(rewrite,[status(thm)],[])).
% 2.14/2.40 tff(7495,plain,
% 2.14/2.40 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.14/2.40 inference(rewrite,[status(thm)],[])).
% 2.14/2.40 tff(7496,plain,
% 2.14/2.40 (((~![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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.14/2.40 inference(monotonicity,[status(thm)],[7495])).
% 2.14/2.40 tff(7497,plain,
% 2.14/2.40 (((~![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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.14/2.40 inference(transitivity,[status(thm)],[7496, 7494])).
% 2.14/2.40 tff(7498,plain,
% 2.14/2.40 ((~![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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(7499,plain,
% 2.24/2.40 ((~![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(elem!1))), s(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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[7498, 7497])).
% 2.24/2.40 tff(7500,plain,
% 2.24/2.40 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[7499, 97, 473, 1529, 805, 2391, 6227])).
% 2.24/2.40 tff(7501,plain,
% 2.24/2.40 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[7500, 7493])).
% 2.24/2.40 tff(7502,plain,
% 2.24/2.40 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6289, 7501, 7492])).
% 2.24/2.40 tff(7503,plain,
% 2.24/2.40 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[7502, 7485])).
% 2.24/2.40 tff(7504,plain,
% 2.24/2.40 (((~![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(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))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $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(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(7505,plain,
% 2.24/2.40 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(7506,plain,
% 2.24/2.40 (((~![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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(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)), 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))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[7505])).
% 2.24/2.40 tff(7507,plain,
% 2.24/2.40 (((~![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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(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)), 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)))),
% 2.24/2.40 inference(transitivity,[status(thm)],[7506, 7504])).
% 2.24/2.40 tff(7508,plain,
% 2.24/2.40 ((~![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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(7509,plain,
% 2.24/2.40 ((~![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(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))))), elem!1))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[7508, 7507])).
% 2.24/2.40 tff(7510,plain,
% 2.24/2.40 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[7509, 97, 2391, 1914, 6227])).
% 2.24/2.40 tff(7511,plain,
% 2.24/2.40 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6313, 7510, 6300])).
% 2.24/2.40 tff(7512,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(7513,plain,
% 2.24/2.40 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(7514,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[7513])).
% 2.24/2.40 tff(7515,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.24/2.40 inference(transitivity,[status(thm)],[7514, 7512])).
% 2.24/2.40 tff(7516,plain,
% 2.24/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(7517,plain,
% 2.24/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[7516, 7515])).
% 2.24/2.40 tff(7518,plain,
% 2.24/2.40 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[7517, 155, 1528, 1523, 7511])).
% 2.24/2.40 tff(7519,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[7518, 7503])).
% 2.24/2.40 tff(7520,plain,((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(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(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(7521,plain,
% 2.24/2.40 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[7520, 7358, 7465, 7471, 7484, 7459, 7453, 7447, 7442])).
% 2.24/2.40 tff(7522,plain,
% 2.24/2.40 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6269, 7521, 7374])).
% 2.24/2.40 tff(7523,plain,
% 2.24/2.40 (r(s(elem!1), s(s(elem!1)))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[3, 7383])).
% 2.24/2.40 tff(7524,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(7525,plain,
% 2.24/2.40 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(7526,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[7525])).
% 2.24/2.40 tff(7527,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[7526, 7524])).
% 2.24/2.40 tff(7528,plain,
% 2.24/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(7529,plain,
% 2.24/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[7528, 7527])).
% 2.24/2.40 tff(7530,plain,
% 2.24/2.40 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[7529, 155, 7387, 7523, 7522])).
% 2.24/2.40 tff(7531,plain,
% 2.24/2.40 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[7530, 7368])).
% 2.24/2.40 tff(7532,plain,
% 2.24/2.40 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6239, 7531, 7366])).
% 2.24/2.40 tff(7533,plain,
% 2.24/2.40 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[7532, 7365])).
% 2.24/2.40 tff(7534,plain,
% 2.24/2.40 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[7363])).
% 2.24/2.40 tff(7535,plain,
% 2.24/2.40 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.24/2.40 inference(symmetry,[status(thm)],[7534])).
% 2.24/2.40 tff(7536,plain,
% 2.24/2.40 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[4669, 7478, 7358, 7385, 7436])).
% 2.24/2.40 tff(7537,plain,
% 2.24/2.40 (b(s(z), s(s(s(s(elem!1)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[280, 7536])).
% 2.24/2.40 tff(7538,plain,
% 2.24/2.40 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[7537, 7535])).
% 2.24/2.40 tff(7539,plain,
% 2.24/2.40 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6197, 7449, 7358])).
% 2.24/2.40 tff(7540,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 2.24/2.40 tff(7541,plain,
% 2.24/2.40 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[7540, 6185])).
% 2.24/2.40 tff(7542,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 2.24/2.40 tff(7543,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[7542, 7541])).
% 2.24/2.40 tff(7544,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,[]))).
% 2.24/2.40 tff(7545,plain,
% 2.24/2.40 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[7544, 7539])).
% 2.24/2.40 tff(7546,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(7547,plain,
% 2.24/2.40 (((~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(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(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)))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(7548,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[7547])).
% 2.24/2.40 tff(7549,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[7548, 7546])).
% 2.24/2.40 tff(7550,plain,
% 2.24/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(7551,plain,
% 2.24/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[7550, 7549])).
% 2.24/2.40 tff(7552,plain,
% 2.24/2.40 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[7551, 155, 7436, 7478, 7522])).
% 2.24/2.40 tff(7553,plain,
% 2.24/2.40 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6254, 7552, 7545])).
% 2.24/2.40 tff(7554,plain,
% 2.24/2.40 (((~![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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(7555,plain,
% 2.24/2.40 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), 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(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(7556,plain,
% 2.24/2.40 (((~![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(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[7555])).
% 2.24/2.40 tff(7557,plain,
% 2.24/2.40 (((~![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(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[7556, 7554])).
% 2.24/2.40 tff(7558,plain,
% 2.24/2.40 ((~![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(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(7559,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[7558, 7557])).
% 2.24/2.40 tff(7560,plain,
% 2.24/2.40 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[7559, 97, 7442, 7553, 7538])).
% 2.24/2.40 tff(7561,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[7560, 7533])).
% 2.24/2.40 tff(7562,plain,((~b(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(7563,plain,
% 2.24/2.40 (~b(z, s(s(z)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[7562, 7207, 494, 550, 61, 7137, 83, 3])).
% 2.24/2.40 tff(7564,plain,
% 2.24/2.40 (r(z, s(s(z)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[222, 7563])).
% 2.24/2.40 tff(7565,plain,
% 2.24/2.40 (r(s(s(s(s(elem!1)))), z)),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[7295, 7261])).
% 2.24/2.40 tff(7566,plain,
% 2.24/2.40 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[1816, 7348, 7273, 7231, 7271])).
% 2.24/2.40 tff(7567,plain,
% 2.24/2.40 (b(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[511, 7566])).
% 2.24/2.40 tff(7568,plain,
% 2.24/2.40 (~b(z, s(s(s(s(elem!1)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[558, 7567, 550, 61])).
% 2.24/2.40 tff(7569,plain,
% 2.24/2.40 (r(z, s(s(s(s(elem!1)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[1093, 7568])).
% 2.24/2.40 tff(7570,plain,
% 2.24/2.40 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[1872, 7569, 7141, 7565])).
% 2.24/2.40 tff(7571,plain,
% 2.24/2.40 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[3852, 7569, 7564, 7231, 7353])).
% 2.24/2.40 tff(7572,plain,
% 2.24/2.40 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[336, 7571])).
% 2.24/2.40 tff(7573,plain,
% 2.24/2.40 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[518, 340, 82])).
% 2.24/2.40 tff(7574,plain,
% 2.24/2.40 (r(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[511, 7573])).
% 2.24/2.40 tff(7575,plain,
% 2.24/2.40 (~r(s(s(s(s(elem!1)))), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[3278, 7574, 2, 226, 1170])).
% 2.24/2.40 tff(7576,plain,
% 2.24/2.40 (b(s(s(s(s(elem!1)))), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[842, 7575])).
% 2.24/2.40 tff(7577,plain,
% 2.24/2.40 (b(s(s(s(elem!1))), z)),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[7576, 3431])).
% 2.24/2.40 tff(7578,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[239, 7577])).
% 2.24/2.40 tff(7579,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), z) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(7580,plain,
% 2.24/2.40 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[7579, 1170, 2, 226, 239, 82])).
% 2.24/2.40 tff(7581,plain,
% 2.24/2.40 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[486, 7580, 1150])).
% 2.24/2.40 tff(7582,plain,
% 2.24/2.40 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[753, 7581, 1503, 339])).
% 2.24/2.40 tff(7583,plain,
% 2.24/2.40 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[4129, 7580, 127, 339, 1150])).
% 2.24/2.40 tff(7584,plain,
% 2.24/2.40 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[4115, 7583, 3, 494, 1170])).
% 2.24/2.40 tff(7585,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[511, 7584, 7582])).
% 2.24/2.40 tff(7586,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | b(s(s(s(elem!1))), z) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(7587,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[7586, 7572, 7570, 3, 2994, 7564, 7339, 7353, 7140, 82])).
% 2.24/2.41 tff(7588,plain,((~b(s(s(z)), z)) | (~r(s(z), s(s(z)))) | b(s(s(s(elem!1))), s(z)) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(7589,plain,
% 2.24/2.41 (~b(s(s(z)), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[7588, 3, 82, 550, 61])).
% 2.24/2.41 tff(7590,plain,
% 2.24/2.41 (r(s(s(z)), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[625, 7589])).
% 2.24/2.41 tff(7591,plain,
% 2.24/2.41 (~r(s(s(z)), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6410, 6465, 7590, 7018])).
% 2.24/2.41 tff(7592,plain,
% 2.24/2.41 (b(s(s(z)), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[437, 7591])).
% 2.24/2.41 tff(7593,plain,
% 2.24/2.41 (~b(s(s(z)), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[7010, 7592, 1360, 550])).
% 2.24/2.41 tff(7594,plain,
% 2.24/2.41 (r(s(s(z)), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[122, 7593])).
% 2.24/2.41 tff(7595,plain,
% 2.24/2.41 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2313, 7594, 494, 3])).
% 2.24/2.41 tff(7596,plain,
% 2.24/2.41 (b(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[58, 7595])).
% 2.24/2.41 tff(7597,plain,
% 2.24/2.41 (((~![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(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(7598,plain,
% 2.24/2.41 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(7599,plain,
% 2.24/2.41 (((~![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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~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(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(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[7598])).
% 2.24/2.41 tff(7600,plain,
% 2.24/2.41 (((~![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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~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(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(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[7599, 7597])).
% 2.24/2.41 tff(7601,plain,
% 2.24/2.41 ((~![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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~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(elem!1))), s(s(s(z))))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(7602,plain,
% 2.24/2.41 ((~![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(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[7601, 7600])).
% 2.24/2.41 tff(7603,plain,
% 2.24/2.41 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[7602, 97, 7596, 7592, 7137])).
% 2.24/2.41 tff(7604,plain,
% 2.24/2.41 (~r(s(s(s(elem!1))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[7155, 7603, 82, 1360, 550, 61])).
% 2.24/2.41 tff(7605,plain,
% 2.24/2.41 (b(s(s(s(elem!1))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[246, 7604])).
% 2.24/2.41 tff(7606,plain,
% 2.24/2.41 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3373, 97, 7596, 7592, 7137])).
% 2.24/2.41 tff(7607,plain,
% 2.24/2.41 (~r(z, s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5852, 7606, 1, 7018, 7603])).
% 2.24/2.41 tff(7608,plain,
% 2.24/2.41 (b(z, s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[590, 7607])).
% 2.24/2.41 tff(7609,plain,
% 2.24/2.41 (~b(s(z), s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3979, 7605, 61, 7608])).
% 2.24/2.41 tff(7610,plain,
% 2.24/2.41 (r(s(z), s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[181, 7609])).
% 2.24/2.41 tff(7611,plain,
% 2.24/2.41 (~b(z, s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6479, 7608, 7592, 7596])).
% 2.24/2.41 tff(7612,plain,
% 2.24/2.41 (r(z, s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[222, 7611])).
% 2.24/2.41 tff(7613,plain,
% 2.24/2.41 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2881, 155, 226, 645, 4153])).
% 2.24/2.41 tff(7614,plain,
% 2.24/2.41 (b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2886, 7613, 80])).
% 2.24/2.41 tff(7615,plain,
% 2.24/2.41 (~r(s(s(z)), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6410, 386, 645, 1300])).
% 2.24/2.41 tff(7616,plain,
% 2.24/2.41 (b(s(s(z)), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[437, 7615])).
% 2.24/2.41 tff(7617,plain,
% 2.24/2.41 (((~![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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(7618,plain,
% 2.24/2.41 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(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(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(7619,plain,
% 2.24/2.41 (((~![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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), 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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[7618])).
% 2.24/2.41 tff(7620,plain,
% 2.24/2.41 (((~![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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), 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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[7619, 7617])).
% 2.24/2.41 tff(7621,plain,
% 2.24/2.41 ((~![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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(7622,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[7621, 7620])).
% 2.24/2.41 tff(7623,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[7622, 97, 7616, 1331, 7614, 4170])).
% 2.24/2.41 tff(7624,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(7625,plain,
% 2.24/2.41 (~r(s(s(s(s(z)))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[7624, 7018, 7137, 6465, 7612, 7590])).
% 2.24/2.41 tff(7626,plain,
% 2.24/2.41 (b(s(s(s(s(z)))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2860, 7625])).
% 2.24/2.41 tff(7627,plain,
% 2.24/2.41 (((~![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(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(7628,plain,
% 2.24/2.41 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(7629,plain,
% 2.24/2.41 (((~![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(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[7628])).
% 2.24/2.41 tff(7630,plain,
% 2.24/2.41 (((~![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(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[7629, 7627])).
% 2.24/2.41 tff(7631,plain,
% 2.24/2.41 ((~![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(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(7632,plain,
% 2.24/2.41 ((~![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(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[7631, 7630])).
% 2.24/2.41 tff(7633,plain,
% 2.24/2.41 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[7632, 97, 61, 126, 2796])).
% 2.24/2.41 tff(7634,assumption,(~(s(s(s(s(z)))) = s(s(s(elem!1))))), introduced(assumption)).
% 2.24/2.41 tff(7635,plain,
% 2.24/2.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(7636,plain,
% 2.24/2.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(7637,plain,
% 2.24/2.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[7636, 7635])).
% 2.24/2.41 tff(7638,plain,
% 2.24/2.41 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[7637, 53, 7634, 7633])).
% 2.24/2.41 tff(7639,plain,
% 2.24/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(7640,plain,
% 2.24/2.41 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(7641,plain,
% 2.24/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[7640])).
% 2.24/2.41 tff(7642,plain,
% 2.24/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[7641, 7639])).
% 2.24/2.41 tff(7643,plain,
% 2.24/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(7644,plain,
% 2.24/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[7643, 7642])).
% 2.24/2.41 tff(7645,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[7644, 155, 125, 225, 2808, 7638])).
% 2.24/2.41 tff(7646,plain,((~b(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(7647,plain,
% 2.24/2.41 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[7646, 7626, 7610, 494, 61, 7605, 550])).
% 2.24/2.41 tff(7648,plain,
% 2.24/2.41 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[7647])).
% 2.24/2.41 tff(7649,plain,
% 2.24/2.41 (s(s(s(z))) = s(s(elem!1))),
% 2.24/2.41 inference(transitivity,[status(thm)],[2792, 7648, 19])).
% 2.24/2.41 tff(7650,plain,
% 2.24/2.41 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[7649])).
% 2.24/2.41 tff(7651,plain,
% 2.24/2.41 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[7650])).
% 2.24/2.41 tff(7652,plain,
% 2.24/2.41 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[286, 7651])).
% 2.24/2.41 tff(7653,plain,
% 2.24/2.41 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[349, 7652])).
% 2.24/2.41 tff(7654,plain,
% 2.24/2.41 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1273, 7610, 494, 7594])).
% 2.24/2.41 tff(7655,plain,
% 2.24/2.41 (b(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[143, 7654])).
% 2.24/2.41 tff(7656,plain,
% 2.24/2.41 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3290, 876, 124, 126])).
% 2.24/2.41 tff(7657,plain,
% 2.24/2.41 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3648, 876, 125, 550, 124])).
% 2.24/2.41 tff(7658,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[486, 7657, 7656, 472])).
% 2.24/2.41 tff(7659,plain,((~b(s(s(s(s(elem!1)))), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(7660,plain,
% 2.24/2.41 (~b(s(s(s(s(elem!1)))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[7659, 7653, 494, 550, 7605, 7608])).
% 2.24/2.41 tff(7661,plain,
% 2.24/2.41 (r(s(s(s(s(elem!1)))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[842, 7660])).
% 2.24/2.41 tff(7662,plain,
% 2.24/2.41 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3089, 7606, 1])).
% 2.24/2.41 tff(7663,plain,
% 2.24/2.41 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2687, 7603, 4228])).
% 2.24/2.41 tff(7664,plain,
% 2.24/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(7665,plain,
% 2.24/2.41 (((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(7666,plain,
% 2.24/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[7665])).
% 2.24/2.41 tff(7667,plain,
% 2.24/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[7666, 7664])).
% 2.24/2.42 tff(7668,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(7669,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[7668, 7667])).
% 2.24/2.42 tff(7670,plain,
% 2.24/2.42 (~r(s(z), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7669, 155, 7610, 7663, 7662])).
% 2.24/2.42 tff(7671,plain,
% 2.24/2.42 (b(s(z), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[253, 7670])).
% 2.24/2.42 tff(7672,plain,
% 2.24/2.42 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 2.24/2.42 inference(monotonicity,[status(thm)],[7649])).
% 2.24/2.42 tff(7673,plain,
% 2.24/2.42 (r(s(s(elem!1)), z)),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[6465, 7672])).
% 2.24/2.42 tff(7674,plain,
% 2.24/2.42 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[7649])).
% 2.24/2.42 tff(7675,plain,
% 2.24/2.42 (r(z, s(s(elem!1)))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[7018, 7674])).
% 2.24/2.42 tff(7676,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 2.24/2.42 tff(7677,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 2.24/2.42 tff(7678,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(elem!1)))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(7679,plain,
% 2.24/2.42 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(elem!1)))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(7680,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(elem!1))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[7679])).
% 2.24/2.42 tff(7681,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(elem!1)))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[7680, 7678])).
% 2.24/2.42 tff(7682,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(7683,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(elem!1))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[7682, 7681])).
% 2.24/2.42 tff(7684,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7683, 155, 1813, 824, 7677, 7676])).
% 2.24/2.42 tff(7685,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(7686,plain,
% 2.24/2.42 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7685, 7661, 7675, 7673])).
% 2.24/2.42 tff(7687,plain,
% 2.24/2.42 (~r(s(s(z)), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6410, 6465, 645, 7018])).
% 2.24/2.42 tff(7688,plain,
% 2.24/2.42 (b(s(s(z)), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[437, 7687])).
% 2.24/2.42 tff(7689,plain,
% 2.24/2.42 (((~![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(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(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(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(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(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(z))), s(s(z)))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(7690,plain,
% 2.24/2.42 (((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(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(z))), s(s(z)))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(7691,plain,
% 2.24/2.42 (((~![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), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(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(z))), s(s(z))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[7690])).
% 2.24/2.42 tff(7692,plain,
% 2.24/2.42 (((~![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), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(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(z))), s(s(z)))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[7691, 7689])).
% 2.24/2.42 tff(7693,plain,
% 2.24/2.42 ((~![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), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(7694,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[7693, 7692])).
% 2.24/2.42 tff(7695,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7694, 97, 513, 1361, 1360, 1331, 371, 86])).
% 2.24/2.42 tff(7696,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(7697,plain,
% 2.24/2.42 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7696, 513, 1360, 7688, 1331, 86])).
% 2.24/2.42 tff(7698,plain,
% 2.24/2.42 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2747, 7697])).
% 2.24/2.42 tff(7699,assumption,(s(s(s(s(z)))) = s(s(s(elem!1)))), introduced(assumption)).
% 2.24/2.42 tff(7700,plain,
% 2.24/2.42 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[7699])).
% 2.24/2.42 tff(7701,plain,
% 2.24/2.42 (s(s(s(z))) = s(s(elem!1))),
% 2.24/2.42 inference(transitivity,[status(thm)],[2792, 7700, 19])).
% 2.24/2.42 tff(7702,plain,
% 2.24/2.42 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[7701])).
% 2.24/2.42 tff(7703,plain,
% 2.24/2.42 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.24/2.42 inference(symmetry,[status(thm)],[7702])).
% 2.24/2.42 tff(7704,plain,
% 2.24/2.42 ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[7703])).
% 2.24/2.42 tff(7705,plain,
% 2.24/2.42 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[1820, 7704])).
% 2.24/2.42 tff(7706,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[387, 7705])).
% 2.24/2.42 tff(7707,plain,((~(s(s(s(s(z)))) = s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(7708,plain,
% 2.24/2.42 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7707, 7698, 1820])).
% 2.24/2.42 tff(7709,plain,
% 2.24/2.42 (~b(s(s(s(s(z)))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7646, 7708, 225, 125, 61, 126, 550])).
% 2.24/2.42 tff(7710,plain,
% 2.24/2.42 (r(s(s(s(s(z)))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2860, 7709])).
% 2.24/2.42 tff(7711,plain,
% 2.24/2.42 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[4163, 155, 7018, 6465, 7710])).
% 2.24/2.42 tff(7712,plain,
% 2.24/2.42 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[4169, 7711])).
% 2.24/2.42 tff(7713,plain,
% 2.24/2.42 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2881, 155, 226, 645, 7710])).
% 2.24/2.42 tff(7714,plain,
% 2.24/2.42 (b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2886, 7713, 80])).
% 2.24/2.42 tff(7715,plain,
% 2.24/2.42 (~b(z, s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[558, 513, 550, 61])).
% 2.24/2.42 tff(7716,plain,
% 2.24/2.42 (r(z, s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1093, 7715])).
% 2.24/2.42 tff(7717,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(7718,plain,
% 2.24/2.42 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(7719,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[7718])).
% 2.24/2.42 tff(7720,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[7719, 7717])).
% 2.24/2.42 tff(7721,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(7722,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[7721, 7720])).
% 2.24/2.42 tff(7723,plain,
% 2.24/2.42 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7722, 155, 463, 309, 645, 4153])).
% 2.24/2.42 tff(7724,plain,
% 2.24/2.42 (b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[4192, 7723, 2595])).
% 2.24/2.42 tff(7725,plain,
% 2.24/2.42 (((~![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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(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(z)))), s(s(s(z))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(7726,plain,
% 2.24/2.42 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(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(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(7727,plain,
% 2.24/2.42 (((~![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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), 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(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(z)))), s(s(s(z)))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[7726])).
% 2.24/2.42 tff(7728,plain,
% 2.24/2.42 (((~![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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), 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(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(z)))), s(s(s(z))))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[7727, 7725])).
% 2.24/2.42 tff(7729,plain,
% 2.24/2.42 ((~![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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(7730,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[7729, 7728])).
% 2.24/2.42 tff(7731,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7730, 97, 1331, 7614, 4170, 7724])).
% 2.24/2.42 tff(7732,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(7733,plain,
% 2.24/2.42 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7732, 7710, 7018, 6465, 226, 645, 7716, 1331])).
% 2.24/2.42 tff(7734,plain,
% 2.24/2.42 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[336, 7733])).
% 2.24/2.42 tff(7735,plain,
% 2.24/2.42 (((~![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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(7736,plain,
% 2.24/2.42 (((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), 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(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(7737,plain,
% 2.24/2.42 (((~![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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[7736])).
% 2.24/2.42 tff(7738,plain,
% 2.24/2.42 (((~![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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[7737, 7735])).
% 2.24/2.42 tff(7739,plain,
% 2.24/2.42 ((~![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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), 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))))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(7740,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[7739, 7738])).
% 2.24/2.42 tff(7741,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7740, 97, 7734, 1331, 7714, 7712])).
% 2.24/2.42 tff(7742,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | r(s(s(s(s(elem!1)))), s(s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(7743,plain,
% 2.24/2.42 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[7742, 7686, 7612, 7590, 7610, 494, 61, 7605, 550, 7137, 1360, 7671])).
% 2.24/2.42 tff(7744,plain,
% 2.24/2.42 (r(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[511, 7743])).
% 2.24/2.42 tff(7745,plain,
% 2.24/2.42 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3278, 7744, 7594, 7612, 7661])).
% 2.24/2.42 tff(7746,plain,
% 2.24/2.42 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[452, 7745])).
% 2.24/2.42 tff(7747,plain,
% 2.24/2.42 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[523, 7653])).
% 2.24/2.42 tff(7748,plain,
% 2.24/2.42 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1136, 7744, 494, 7610])).
% 2.24/2.42 tff(7749,plain,
% 2.24/2.42 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[821, 7748, 7747])).
% 2.24/2.42 tff(7750,plain,
% 2.24/2.42 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2741, 7749, 7746, 7655])).
% 2.24/2.42 tff(7751,plain,
% 2.24/2.42 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[486, 7750, 7653])).
% 2.24/2.42 tff(7752,plain,
% 2.24/2.42 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[7649])).
% 2.24/2.42 tff(7753,plain,
% 2.24/2.42 (s(s(z)) = s(elem!1)),
% 2.24/2.42 inference(transitivity,[status(thm)],[73, 7752, 29])).
% 2.24/2.42 tff(7754,plain,
% 2.24/2.42 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[7753])).
% 2.24/2.42 tff(7755,plain,
% 2.24/2.42 (s(z) = elem!1),
% 2.24/2.42 inference(transitivity,[status(thm)],[24, 7754, 85])).
% 2.24/2.42 tff(7756,plain,
% 2.24/2.42 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 2.24/2.42 inference(monotonicity,[status(thm)],[7755])).
% 2.24/2.42 tff(7757,plain,
% 2.24/2.42 (r(s(s(s(elem!1))), elem!1)),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[494, 7756])).
% 2.24/2.42 tff(7758,plain,
% 2.24/2.42 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 2.24/2.42 inference(symmetry,[status(thm)],[7648])).
% 2.24/2.42 tff(7759,plain,
% 2.24/2.42 (s(s(elem!1)) = s(s(s(z)))),
% 2.24/2.42 inference(transitivity,[status(thm)],[167, 7758, 63])).
% 2.24/2.42 tff(7760,plain,
% 2.24/2.42 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[7759])).
% 2.24/2.42 tff(7761,plain,
% 2.24/2.42 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.42 inference(symmetry,[status(thm)],[7760])).
% 2.24/2.42 tff(7762,plain,
% 2.24/2.42 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[7663, 7761])).
% 2.24/2.42 tff(7763,plain,
% 2.24/2.42 ((s(z) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[7755])).
% 2.24/2.42 tff(7764,plain,
% 2.24/2.42 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.24/2.42 inference(transitivity,[status(thm)],[7763, 1900])).
% 2.24/2.42 tff(7765,plain,
% 2.24/2.42 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[7764])).
% 2.24/2.42 tff(7766,plain,
% 2.24/2.42 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[275, 7765])).
% 2.24/2.42 tff(7767,plain,
% 2.24/2.42 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1484, 7686, 7652])).
% 2.24/2.43 tff(7768,plain,
% 2.24/2.43 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 2.24/2.43 inference(monotonicity,[status(thm)],[7649, 7755])).
% 2.24/2.43 tff(7769,plain,
% 2.24/2.43 (b(s(s(elem!1)), elem!1)),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[1360, 7768])).
% 2.24/2.43 tff(7770,plain,
% 2.24/2.43 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[503, 7751, 494, 7744])).
% 2.24/2.43 tff(7771,plain,
% 2.24/2.43 (b(s(z), s(s(s(s(elem!1)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[280, 7770])).
% 2.24/2.43 tff(7772,assumption,(s(z) = elem!1), introduced(assumption)).
% 2.24/2.43 tff(7773,plain,
% 2.24/2.43 (b(s(z), s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[7772])).
% 2.24/2.43 tff(7774,plain,
% 2.24/2.43 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.24/2.43 inference(symmetry,[status(thm)],[7773])).
% 2.24/2.43 tff(7775,plain,
% 2.24/2.43 ((~b(elem!1, s(s(s(s(elem!1)))))) <=> (~b(s(z), s(s(s(s(elem!1))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[7774])).
% 2.24/2.43 tff(7776,plain,
% 2.24/2.43 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[1925, 7775])).
% 2.24/2.43 tff(7777,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[255, 7776])).
% 2.24/2.43 tff(7778,plain,((~(s(z) = elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(7779,plain,
% 2.24/2.43 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7778, 7771, 7755])).
% 2.24/2.43 tff(7780,plain,
% 2.24/2.43 (((~![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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(7781,plain,
% 2.24/2.43 (((~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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(7782,plain,
% 2.24/2.43 (((~![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(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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[7781])).
% 2.24/2.43 tff(7783,plain,
% 2.24/2.43 (((~![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(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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[7782, 7780])).
% 2.24/2.43 tff(7784,plain,
% 2.24/2.43 ((~![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(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)))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(7785,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[7784, 7783])).
% 2.24/2.43 tff(7786,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7785, 97, 1545, 1458, 2392, 1915])).
% 2.24/2.43 tff(7787,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(7788,plain,
% 2.24/2.43 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7787, 7779, 7769, 7767])).
% 2.24/2.43 tff(7789,plain,
% 2.24/2.43 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1471, 7788, 7766])).
% 2.24/2.43 tff(7790,plain,
% 2.24/2.43 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[7650, 1505])).
% 2.24/2.43 tff(7791,plain,
% 2.24/2.43 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[7790])).
% 2.24/2.43 tff(7792,plain,
% 2.24/2.43 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[286, 7791])).
% 2.24/2.43 tff(7793,plain,
% 2.24/2.43 (((~![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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(7794,plain,
% 2.24/2.43 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(7795,plain,
% 2.24/2.43 (((~![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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[7794])).
% 2.24/2.43 tff(7796,plain,
% 2.24/2.43 (((~![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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[7795, 7793])).
% 2.24/2.43 tff(7797,plain,
% 2.24/2.43 ((~![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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(7798,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[7797, 7796])).
% 2.24/2.43 tff(7799,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7798, 97, 1545, 1633, 2392, 1915])).
% 2.24/2.43 tff(7800,plain,((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(7801,plain,
% 2.24/2.43 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7800, 7779, 7769, 7767])).
% 2.24/2.43 tff(7802,plain,
% 2.24/2.43 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1631, 7801, 7792])).
% 2.24/2.43 tff(7803,assumption,(r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 2.24/2.43 tff(7804,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[5271, 155, 1522, 488, 7803, 4497, 1528])).
% 2.24/2.43 tff(7805,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(7806,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7805, 7802, 7789, 7762, 7757, 7751])).
% 2.24/2.43 tff(7807,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(7808,plain,
% 2.24/2.43 (~b(s(s(s(z))), s(z))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7807, 1, 550, 61, 82, 3])).
% 2.24/2.43 tff(7809,plain,
% 2.24/2.43 (r(s(s(s(z))), s(z))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1358, 7808])).
% 2.24/2.43 tff(7810,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2603, 97, 550, 61, 204, 87])).
% 2.24/2.43 tff(7811,plain,((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(7812,plain,
% 2.24/2.43 (~b(s(s(z)), s(z))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7811, 204, 61, 550])).
% 2.24/2.43 tff(7813,plain,
% 2.24/2.43 (r(s(s(z)), s(z))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[122, 7812])).
% 2.24/2.43 tff(7814,plain,
% 2.24/2.43 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2313, 7813, 125, 3])).
% 2.24/2.43 tff(7815,plain,
% 2.24/2.43 (b(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[58, 7814])).
% 2.24/2.43 tff(7816,plain,
% 2.24/2.43 (~b(z, s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7172, 7815, 1331, 1, 125, 2597, 61])).
% 2.24/2.43 tff(7817,plain,
% 2.24/2.43 (r(z, s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[590, 7816])).
% 2.24/2.43 tff(7818,plain,
% 2.24/2.43 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2253, 7817, 125, 645, 7813])).
% 2.24/2.43 tff(7819,plain,
% 2.24/2.43 (b(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[143, 7818])).
% 2.24/2.43 tff(7820,plain,
% 2.24/2.43 (~b(s(z), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2286, 7819, 1331, 204, 7815, 61, 1])).
% 2.24/2.43 tff(7821,plain,
% 2.24/2.43 (r(s(z), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[181, 7820])).
% 2.24/2.43 tff(7822,plain,
% 2.24/2.43 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[5757, 7821, 2597, 125])).
% 2.24/2.43 tff(7823,plain,
% 2.24/2.43 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3089, 7822, 1])).
% 2.24/2.43 tff(7824,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7170, 97, 7815, 1331, 7819, 7823])).
% 2.24/2.43 tff(7825,plain,((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(7826,plain,
% 2.24/2.43 (~b(z, s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7825, 1, 7137, 7809, 494, 61, 7590, 3, 550])).
% 2.24/2.43 tff(7827,plain,
% 2.24/2.43 (r(z, s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[222, 7826])).
% 2.24/2.43 tff(7828,plain,
% 2.24/2.43 (((~![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), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(7829,plain,
% 2.24/2.43 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(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(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(7830,plain,
% 2.24/2.43 (((~![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(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(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(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[7829])).
% 2.24/2.43 tff(7831,plain,
% 2.24/2.43 (((~![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(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(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(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[7830, 7828])).
% 2.24/2.43 tff(7832,plain,
% 2.24/2.43 ((~![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(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(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)))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(7833,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[7832, 7831])).
% 2.24/2.43 tff(7834,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7833, 97, 550, 1331, 86, 1330])).
% 2.24/2.43 tff(7835,plain,((~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(7836,plain,
% 2.24/2.43 (~b(s(z), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7835, 1330, 1331, 550])).
% 2.24/2.43 tff(7837,plain,
% 2.24/2.43 (r(s(z), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[253, 7836])).
% 2.24/2.43 tff(7838,plain,
% 2.24/2.43 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2638, 7837, 2597, 125])).
% 2.24/2.43 tff(7839,plain,
% 2.24/2.43 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2687, 7838, 4228])).
% 2.24/2.43 tff(7840,plain,
% 2.24/2.43 (((~![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(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(7841,plain,
% 2.24/2.43 (((~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(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(7842,plain,
% 2.24/2.43 (((~![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(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(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))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[7841])).
% 2.24/2.43 tff(7843,plain,
% 2.24/2.43 (((~![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(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(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))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[7842, 7840])).
% 2.24/2.43 tff(7844,plain,
% 2.24/2.43 ((~![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(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(7845,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[7844, 7843])).
% 2.24/2.43 tff(7846,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7845, 97, 126, 1331, 1330, 5941])).
% 2.24/2.43 tff(7847,plain,((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(7848,plain,
% 2.24/2.43 (~b(s(s(s(elem!1))), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7847, 7839, 1331, 1330])).
% 2.24/2.43 tff(7849,plain,
% 2.24/2.43 (r(s(s(s(elem!1))), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[246, 7848])).
% 2.24/2.43 tff(7850,plain,
% 2.24/2.43 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2671, 7849, 645, 226])).
% 2.24/2.43 tff(7851,plain,
% 2.24/2.43 (b(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[58, 7850])).
% 2.24/2.43 tff(7852,plain,
% 2.24/2.43 (~b(z, s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7172, 7851, 1331, 1, 125, 2597, 61])).
% 2.24/2.43 tff(7853,plain,
% 2.24/2.43 (r(z, s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[590, 7852])).
% 2.24/2.43 tff(7854,plain,
% 2.24/2.43 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[735, 155, 7853, 7849, 645])).
% 2.24/2.43 tff(7855,plain,
% 2.24/2.43 (b(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[143, 7854])).
% 2.24/2.43 tff(7856,plain,
% 2.24/2.43 (((~![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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(7857,plain,
% 2.24/2.43 (((~b(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(elem!1))), s(s(s(z)))))) <=> ((~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)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(7858,plain,
% 2.24/2.43 (((~![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(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(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(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[7857])).
% 2.24/2.43 tff(7859,plain,
% 2.24/2.43 (((~![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(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(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(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[7858, 7856])).
% 2.24/2.43 tff(7860,plain,
% 2.24/2.43 ((~![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(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(elem!1))), s(s(s(z))))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(7861,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[7860, 7859])).
% 2.24/2.43 tff(7862,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7861, 97, 7851, 1331, 7855, 7839])).
% 2.24/2.43 tff(7863,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~r(z, s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(7864,plain,
% 2.24/2.43 (~b(z, s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7863, 1, 7590, 7137, 494, 7809, 61, 7827, 550])).
% 2.24/2.43 tff(7865,plain,
% 2.24/2.43 (r(z, s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1318, 7864])).
% 2.24/2.43 tff(7866,plain,
% 2.24/2.43 (~b(z, s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7825, 1, 1331, 2597, 125, 61, 645, 3, 550])).
% 2.24/2.43 tff(7867,plain,
% 2.24/2.43 (r(z, s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[222, 7866])).
% 2.24/2.43 tff(7868,plain,
% 2.24/2.43 (~b(z, s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7863, 1, 645, 1331, 125, 2597, 61, 7867, 550])).
% 2.24/2.43 tff(7869,plain,
% 2.24/2.43 (r(z, s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1318, 7868])).
% 2.24/2.43 tff(7870,plain,
% 2.24/2.43 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[7172, 124, 1331, 1, 125, 2597, 61])).
% 2.24/2.43 tff(7871,plain,
% 2.24/2.43 (r(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[58, 7870])).
% 2.24/2.44 tff(7872,plain,
% 2.24/2.44 (~r(s(s(s(elem!1))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2671, 7871, 645, 7867])).
% 2.24/2.44 tff(7873,plain,
% 2.24/2.44 (b(s(s(s(elem!1))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[246, 7872])).
% 2.24/2.44 tff(7874,plain,
% 2.24/2.44 (~b(s(s(s(elem!1))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[3979, 124, 61, 193])).
% 2.24/2.44 tff(7875,plain,
% 2.24/2.44 (r(s(s(s(elem!1))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[246, 7874])).
% 2.24/2.44 tff(7876,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2671, 7875, 7871, 645, 226])).
% 2.24/2.44 tff(7877,plain,((~b(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(7878,plain,
% 2.24/2.44 (~b(s(z), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7877, 124, 7867, 61, 645, 1331, 1, 125, 2597])).
% 2.24/2.44 tff(7879,plain,
% 2.24/2.44 (r(s(z), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[181, 7878])).
% 2.24/2.44 tff(7880,plain,
% 2.24/2.44 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[5757, 7879, 2597, 125])).
% 2.24/2.44 tff(7881,plain,
% 2.24/2.44 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[3089, 7880, 1])).
% 2.24/2.44 tff(7882,plain,
% 2.24/2.44 (~b(s(s(s(z))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6379, 7881, 7873, 61])).
% 2.24/2.44 tff(7883,plain,
% 2.24/2.44 (r(s(s(s(z))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[402, 7882])).
% 2.24/2.44 tff(7884,plain,
% 2.24/2.44 (~r(s(s(s(s(z)))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7624, 7883, 1331, 7869, 7867, 645])).
% 2.24/2.44 tff(7885,plain,
% 2.24/2.44 (b(s(s(s(s(z)))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2860, 7884])).
% 2.24/2.44 tff(7886,plain,
% 2.24/2.44 (~b(s(s(s(s(z)))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2802, 97, 550, 61, 7885])).
% 2.24/2.44 tff(7887,plain,
% 2.24/2.44 (r(s(s(s(s(z)))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2807, 7886, 2795])).
% 2.24/2.44 tff(7888,plain,
% 2.24/2.44 (~b(s(z), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2839, 97, 550, 61, 7885])).
% 2.24/2.44 tff(7889,plain,
% 2.24/2.44 (r(s(z), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2844, 7888, 2833])).
% 2.24/2.44 tff(7890,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(7891,plain,
% 2.24/2.44 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(7892,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[7891])).
% 2.24/2.44 tff(7893,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[7892, 7890])).
% 2.24/2.44 tff(7894,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(7895,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[7894, 7893])).
% 2.24/2.44 tff(7896,plain,
% 2.24/2.44 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7895, 155, 125, 7889, 7887])).
% 2.24/2.44 tff(7897,plain,
% 2.24/2.44 (((~![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(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(7898,plain,
% 2.24/2.44 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(7899,plain,
% 2.24/2.44 (((~![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(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[7898])).
% 2.24/2.44 tff(7900,plain,
% 2.24/2.44 (((~![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(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[7899, 7897])).
% 2.24/2.44 tff(7901,plain,
% 2.24/2.44 ((~![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(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(7902,plain,
% 2.24/2.44 ((~![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(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[7901, 7900])).
% 2.24/2.44 tff(7903,plain,
% 2.24/2.44 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7902, 97, 61, 7873, 7885])).
% 2.24/2.44 tff(7904,plain,
% 2.24/2.44 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(7905,plain,
% 2.24/2.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(7906,plain,
% 2.24/2.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[7905, 7904])).
% 2.24/2.44 tff(7907,plain,
% 2.24/2.44 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7906, 53, 7903, 7896])).
% 2.24/2.44 tff(7908,plain,
% 2.24/2.44 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[7907])).
% 2.24/2.44 tff(7909,plain,
% 2.24/2.44 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[5875, 7879, 3, 7871])).
% 2.24/2.44 tff(7910,plain,
% 2.24/2.44 (b(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[143, 7909])).
% 2.24/2.44 tff(7911,plain,
% 2.24/2.44 (b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[7910, 7908])).
% 2.24/2.44 tff(7912,plain,
% 2.24/2.44 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7107, 155, 2597, 7889, 7887])).
% 2.24/2.44 tff(7913,plain,
% 2.24/2.44 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2829, 7912])).
% 2.24/2.44 tff(7914,plain,
% 2.24/2.44 (~r(s(s(z)), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6410, 7883, 645, 7869])).
% 2.24/2.44 tff(7915,plain,
% 2.24/2.44 (b(s(s(z)), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[437, 7914])).
% 2.24/2.44 tff(7916,plain,
% 2.24/2.44 (((~![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(s(s(z))))) | (~b(s(s(z)), s(s(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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(7917,plain,
% 2.24/2.44 (((~b(s(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(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(7918,plain,
% 2.24/2.44 (((~![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(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[7917])).
% 2.24/2.44 tff(7919,plain,
% 2.24/2.44 (((~![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(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[7918, 7916])).
% 2.24/2.44 tff(7920,plain,
% 2.24/2.44 ((~![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(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(7921,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[7920, 7919])).
% 2.24/2.44 tff(7922,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7921, 97, 7915, 7913, 7911, 7885])).
% 2.24/2.44 tff(7923,plain,((~b(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(7924,plain,
% 2.24/2.44 (~b(z, s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7923, 7809, 494, 61, 550, 7590, 7137, 1, 3])).
% 2.24/2.44 tff(7925,plain,
% 2.24/2.44 (r(z, s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[590, 7924])).
% 2.24/2.44 tff(7926,plain,
% 2.24/2.44 (~r(s(s(s(elem!1))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2671, 145, 645, 7867])).
% 2.24/2.44 tff(7927,plain,
% 2.24/2.44 (b(s(s(s(elem!1))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[246, 7926])).
% 2.24/2.44 tff(7928,plain,
% 2.24/2.44 (~b(s(z), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[4212, 97, 550, 61, 7927])).
% 2.24/2.44 tff(7929,plain,
% 2.24/2.44 (r(s(z), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[181, 7928])).
% 2.24/2.44 tff(7930,plain,
% 2.24/2.44 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[5757, 7929, 2597, 125])).
% 2.24/2.44 tff(7931,plain,
% 2.24/2.44 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[3089, 7930, 1])).
% 2.24/2.44 tff(7932,plain,
% 2.24/2.44 (~b(s(s(s(z))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6379, 7931, 7927, 61])).
% 2.24/2.44 tff(7933,plain,
% 2.24/2.44 (r(s(s(s(z))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[402, 7932])).
% 2.24/2.44 tff(7934,plain,
% 2.24/2.44 (~r(s(s(s(s(z)))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7624, 7933, 1331, 7869, 7867, 645])).
% 2.24/2.44 tff(7935,plain,
% 2.24/2.44 (b(s(s(s(s(z)))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2860, 7934])).
% 2.24/2.44 tff(7936,plain,
% 2.24/2.44 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7646, 7935, 7929, 7927, 61, 125, 550])).
% 2.24/2.44 tff(7937,plain,
% 2.24/2.44 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[7936])).
% 2.24/2.44 tff(7938,plain,
% 2.24/2.44 (s(s(s(z))) = s(s(elem!1))),
% 2.24/2.44 inference(transitivity,[status(thm)],[2792, 7937, 19])).
% 2.24/2.44 tff(7939,plain,
% 2.24/2.44 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[7938])).
% 2.24/2.44 tff(7940,plain,
% 2.24/2.44 (s(s(z)) = s(elem!1)),
% 2.24/2.44 inference(transitivity,[status(thm)],[73, 7939, 29])).
% 2.24/2.44 tff(7941,plain,
% 2.24/2.44 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[7940, 7938])).
% 2.24/2.44 tff(7942,plain,
% 2.24/2.44 (~r(s(s(z)), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6410, 7933, 645, 7869])).
% 2.24/2.44 tff(7943,plain,
% 2.24/2.44 (b(s(s(z)), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[437, 7942])).
% 2.24/2.44 tff(7944,plain,
% 2.24/2.44 (b(s(elem!1), s(s(elem!1)))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[7943, 7941])).
% 2.24/2.44 tff(7945,plain,
% 2.24/2.44 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 2.24/2.44 inference(symmetry,[status(thm)],[7939])).
% 2.24/2.44 tff(7946,plain,
% 2.24/2.44 (s(elem!1) = s(s(z))),
% 2.24/2.44 inference(transitivity,[status(thm)],[30, 7945, 72])).
% 2.24/2.44 tff(7947,plain,
% 2.24/2.44 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[7946])).
% 2.24/2.44 tff(7948,plain,
% 2.24/2.44 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.44 inference(symmetry,[status(thm)],[7947])).
% 2.24/2.44 tff(7949,plain,
% 2.24/2.44 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[5875, 7929, 3, 145])).
% 2.24/2.44 tff(7950,plain,
% 2.24/2.44 (b(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[143, 7949])).
% 2.24/2.44 tff(7951,plain,
% 2.24/2.44 (b(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[7950, 7948])).
% 2.24/2.44 tff(7952,plain,
% 2.24/2.44 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 2.24/2.44 inference(symmetry,[status(thm)],[7937])).
% 2.24/2.44 tff(7953,plain,
% 2.24/2.44 (s(s(elem!1)) = s(s(s(z)))),
% 2.24/2.44 inference(transitivity,[status(thm)],[167, 7952, 63])).
% 2.24/2.44 tff(7954,plain,
% 2.24/2.44 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[7953])).
% 2.24/2.44 tff(7955,plain,
% 2.24/2.44 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.44 inference(symmetry,[status(thm)],[7954])).
% 2.24/2.44 tff(7956,plain,
% 2.24/2.44 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[7931, 7955])).
% 2.24/2.44 tff(7957,plain,
% 2.24/2.44 (((~![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(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(7958,plain,
% 2.24/2.44 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~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(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(7959,plain,
% 2.24/2.44 (((~![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(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~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(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(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[7958])).
% 2.24/2.44 tff(7960,plain,
% 2.24/2.44 (((~![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(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~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(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(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[7959, 7957])).
% 2.24/2.44 tff(7961,plain,
% 2.24/2.44 ((~![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(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~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(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(7962,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[7961, 7960])).
% 2.24/2.44 tff(7963,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7962, 97, 7927, 7956, 7951, 7944])).
% 2.24/2.44 tff(7964,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(7965,plain,
% 2.24/2.44 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7964, 1, 494, 550, 7590, 7137, 61, 3, 7809])).
% 2.24/2.44 tff(7966,plain,
% 2.24/2.44 (b(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[58, 7965])).
% 2.24/2.44 tff(7967,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(7968,plain,
% 2.24/2.44 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(7969,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[7968])).
% 2.24/2.44 tff(7970,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[7969, 7967])).
% 2.24/2.44 tff(7971,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(7972,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[7971, 7970])).
% 2.24/2.44 tff(7973,plain,
% 2.24/2.44 ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7972, 155, 125, 1300, 2597])).
% 2.24/2.44 tff(7974,plain,
% 2.24/2.44 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7973, 288])).
% 2.24/2.44 tff(7975,plain,
% 2.24/2.44 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2687, 7974, 2466])).
% 2.24/2.44 tff(7976,plain,
% 2.24/2.44 (b(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[143, 736])).
% 2.24/2.44 tff(7977,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7861, 97, 60, 1331, 7976, 7975])).
% 2.24/2.44 tff(7978,plain,((~r(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(7979,plain,
% 2.24/2.44 (~r(s(s(s(elem!1))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7978, 7966, 7137, 7925, 7590, 4228, 494, 7865, 7809])).
% 2.24/2.44 tff(7980,plain,
% 2.24/2.44 (b(s(s(s(elem!1))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[246, 7979])).
% 2.24/2.44 tff(7981,plain,
% 2.24/2.44 (~b(s(z), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[4212, 97, 550, 61, 7980])).
% 2.24/2.44 tff(7982,plain,
% 2.24/2.44 (r(s(z), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[181, 7981])).
% 2.24/2.44 tff(7983,plain,
% 2.24/2.44 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[5757, 7982, 7809, 494])).
% 2.24/2.44 tff(7984,plain,
% 2.24/2.44 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[3089, 7983, 1])).
% 2.24/2.44 tff(7985,plain,
% 2.24/2.44 (~b(s(s(s(z))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6379, 7984, 7980, 61])).
% 2.24/2.44 tff(7986,plain,
% 2.24/2.44 (r(s(s(s(z))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[402, 7985])).
% 2.24/2.44 tff(7987,plain,
% 2.24/2.44 (~r(s(s(z)), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6410, 7986, 7590, 7865])).
% 2.24/2.44 tff(7988,plain,
% 2.24/2.44 (b(s(s(z)), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[437, 7987])).
% 2.24/2.44 tff(7989,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[3373, 97, 7966, 7988, 7137, 7984])).
% 2.24/2.44 tff(7990,plain,((s(s(s(z))) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(z), s(s(z)))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(7991,plain,
% 2.24/2.44 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7990, 3, 550, 61, 82])).
% 2.24/2.44 tff(7992,plain,
% 2.24/2.44 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[7991])).
% 2.24/2.44 tff(7993,plain,
% 2.24/2.44 (s(s(z)) = s(s(elem!1))),
% 2.24/2.44 inference(transitivity,[status(thm)],[73, 7992, 19])).
% 2.24/2.44 tff(7994,plain,
% 2.24/2.44 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[7993])).
% 2.24/2.45 tff(7995,plain,
% 2.24/2.45 (b(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1995, 7991, 7137])).
% 2.24/2.45 tff(7996,plain,
% 2.24/2.45 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(elem!1))), s(s(s(elem!1))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[7991])).
% 2.24/2.45 tff(7997,plain,
% 2.24/2.45 (r(s(s(s(elem!1))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.24/2.45 inference(symmetry,[status(thm)],[7996])).
% 2.24/2.45 tff(7998,plain,
% 2.24/2.45 ((~r(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[7997])).
% 2.24/2.45 tff(7999,plain,
% 2.24/2.45 (^[X: $i] : refl((~r(X, X)) <=> (~r(X, X)))),
% 2.24/2.45 inference(bind,[status(th)],[])).
% 2.24/2.45 tff(8000,plain,
% 2.24/2.45 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 2.24/2.45 inference(quant_intro,[status(thm)],[7999])).
% 2.24/2.45 tff(8001,plain,
% 2.24/2.45 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(8002,axiom,(![X: $i] : (~r(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ri')).
% 2.24/2.45 tff(8003,plain,
% 2.24/2.45 (![X: $i] : (~r(X, X))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[8002, 8001])).
% 2.24/2.45 tff(8004,plain,(
% 2.24/2.45 ![X: $i] : (~r(X, X))),
% 2.24/2.45 inference(skolemize,[status(sab)],[8003])).
% 2.24/2.45 tff(8005,plain,
% 2.24/2.45 (![X: $i] : (~r(X, X))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[8004, 8000])).
% 2.24/2.45 tff(8006,plain,
% 2.24/2.45 ((~![X: $i] : (~r(X, X))) | (~r(s(s(s(elem!1))), s(s(s(elem!1)))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(8007,plain,
% 2.24/2.45 (~r(s(s(s(elem!1))), s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[8006, 8005])).
% 2.24/2.45 tff(8008,plain,
% 2.24/2.45 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[8007, 7998])).
% 2.24/2.45 tff(8009,plain,
% 2.24/2.45 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[7991])).
% 2.24/2.45 tff(8010,plain,
% 2.24/2.45 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.24/2.45 inference(monotonicity,[status(thm)],[8009])).
% 2.24/2.45 tff(8011,plain,
% 2.24/2.45 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[7993])).
% 2.24/2.45 tff(8012,plain,
% 2.24/2.45 (s(z) = s(elem!1)),
% 2.24/2.45 inference(transitivity,[status(thm)],[24, 8011, 29])).
% 2.24/2.45 tff(8013,plain,
% 2.24/2.45 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[8012])).
% 2.24/2.45 tff(8014,plain,
% 2.24/2.45 (z = elem!1),
% 2.24/2.45 inference(transitivity,[status(thm)],[1443, 8013, 85])).
% 2.24/2.45 tff(8015,plain,
% 2.24/2.45 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[8014])).
% 2.24/2.45 tff(8016,plain,
% 2.24/2.45 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[7993])).
% 2.24/2.45 tff(8017,plain,
% 2.24/2.45 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 2.24/2.45 inference(transitivity,[status(thm)],[8016, 8015])).
% 2.24/2.45 tff(8018,plain,
% 2.24/2.45 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[7993])).
% 2.24/2.45 tff(8019,plain,
% 2.24/2.45 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(z)))),
% 2.24/2.45 inference(symmetry,[status(thm)],[8018])).
% 2.24/2.45 tff(8020,plain,
% 2.24/2.45 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[8012, 7993])).
% 2.24/2.45 tff(8021,plain,
% 2.24/2.45 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 2.24/2.45 inference(transitivity,[status(thm)],[8020, 8019])).
% 2.24/2.45 tff(8022,plain,
% 2.24/2.45 (r(s(elem!1), s(s(z)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[3, 8021])).
% 2.24/2.45 tff(8023,plain,
% 2.24/2.45 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[1399, 1401])).
% 2.24/2.45 tff(8024,plain,
% 2.24/2.45 (r(s(s(elem!1)), s(elem!1))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[7813, 8023])).
% 2.24/2.45 tff(8025,plain,
% 2.24/2.45 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[1957, 1509])).
% 2.24/2.45 tff(8026,plain,
% 2.24/2.45 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[1393, 6631])).
% 2.24/2.45 tff(8027,plain,
% 2.24/2.45 (b(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1995, 1393, 1331])).
% 2.24/2.45 tff(8028,plain,
% 2.24/2.45 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[1393])).
% 2.24/2.45 tff(8029,plain,
% 2.24/2.45 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(z))), s(z))),
% 2.24/2.45 inference(symmetry,[status(thm)],[8028])).
% 2.24/2.45 tff(8030,plain,
% 2.24/2.45 (r(s(s(s(z))), s(z))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[125, 8029])).
% 2.24/2.45 tff(8031,plain,
% 2.24/2.45 (~r(z, s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6374, 6361, 2508])).
% 2.24/2.45 tff(8032,plain,
% 2.24/2.45 (b(z, s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[590, 8031])).
% 2.24/2.45 tff(8033,plain,
% 2.24/2.45 (~b(s(s(z)), s(s(s(z))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6479, 8032, 204, 60])).
% 2.24/2.45 tff(8034,plain,
% 2.24/2.45 (~b(s(z), s(s(s(z))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[7835, 6362, 1331, 550])).
% 2.24/2.45 tff(8035,plain,
% 2.24/2.45 (r(s(z), s(s(s(z))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[253, 8034])).
% 2.24/2.45 tff(8036,plain,
% 2.24/2.45 (~r(s(s(z)), s(s(s(z))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[2940, 8035, 2, 2597])).
% 2.24/2.45 tff(8037,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[437, 8036, 8033])).
% 2.24/2.45 tff(8038,plain,(r(z, s(s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), z)) | (~(s(s(s(elem!1))) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(8039,plain,
% 2.24/2.45 (r(z, s(s(s(z))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[8038, 7813, 8030, 204, 8027, 1331, 550, 8026])).
% 2.24/2.45 tff(8040,plain,
% 2.24/2.45 (r(elem!1, s(s(s(elem!1))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[8039, 8025])).
% 2.24/2.45 tff(8041,plain,
% 2.24/2.45 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[8027, 1501])).
% 2.24/2.45 tff(8042,plain,
% 2.24/2.45 (r(s(s(s(z))), z) <=> r(s(s(s(elem!1))), z)),
% 2.24/2.45 inference(monotonicity,[status(thm)],[1393])).
% 2.24/2.45 tff(8043,plain,
% 2.24/2.45 (r(s(s(s(z))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 2.24/2.45 inference(transitivity,[status(thm)],[8042, 1511])).
% 2.24/2.45 tff(8044,plain,
% 2.24/2.45 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[1393])).
% 2.24/2.45 tff(8045,plain,
% 2.24/2.45 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 2.24/2.45 inference(symmetry,[status(thm)],[8044])).
% 2.24/2.45 tff(8046,plain,
% 2.24/2.45 ((~r(s(s(z)), s(s(s(elem!1))))) <=> (~r(s(s(z)), s(s(s(z)))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[8045])).
% 2.24/2.45 tff(8047,plain,
% 2.24/2.45 (r(z, s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6652, 8039, 1393])).
% 2.24/2.45 tff(8048,plain,
% 2.24/2.45 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[2253, 8047, 125, 645, 7813])).
% 2.24/2.45 tff(8049,plain,
% 2.24/2.45 (~r(s(s(z)), s(s(s(z))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[8048, 8046])).
% 2.24/2.45 tff(8050,plain,
% 2.24/2.45 (b(s(s(z)), s(s(s(z))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[437, 8049])).
% 2.24/2.45 tff(8051,plain,
% 2.24/2.45 (~b(s(s(s(z))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[2205, 8050, 1331, 204])).
% 2.24/2.45 tff(8052,plain,
% 2.24/2.45 (r(s(s(s(z))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[402, 8051])).
% 2.24/2.45 tff(8053,plain,
% 2.24/2.45 (r(s(s(s(elem!1))), elem!1)),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[8052, 8043])).
% 2.24/2.45 tff(8054,plain,
% 2.24/2.45 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[486, 3443, 1418])).
% 2.24/2.45 tff(8055,plain,
% 2.24/2.45 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1816, 3438, 1812, 1393, 1520])).
% 2.24/2.45 tff(8056,plain,
% 2.24/2.45 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1484, 8055, 1432])).
% 2.24/2.45 tff(8057,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1586, 8056, 8054, 1529, 1528, 1527, 1523, 1444])).
% 2.24/2.45 tff(8058,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(8059,plain,
% 2.24/2.45 (~b(s(s(s(s(elem!1)))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[8058, 8053, 8041, 8040, 8024, 1393, 1520, 125, 550, 61])).
% 2.24/2.45 tff(8060,plain,
% 2.24/2.45 (r(s(s(s(s(elem!1)))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[842, 8059])).
% 2.24/2.45 tff(8061,plain,
% 2.24/2.45 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[1525, 1531])).
% 2.24/2.45 tff(8062,plain,
% 2.24/2.45 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[8061])).
% 2.24/2.45 tff(8063,plain,
% 2.24/2.45 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[43, 8062])).
% 2.24/2.45 tff(8064,plain,
% 2.24/2.45 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[1411])).
% 2.24/2.45 tff(8065,plain,
% 2.24/2.45 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.45 inference(symmetry,[status(thm)],[8064])).
% 2.24/2.45 tff(8066,plain,
% 2.24/2.45 (r(s(s(s(elem!1))), s(elem!1))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[125, 8065])).
% 2.24/2.45 tff(8067,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(8068,plain,
% 2.24/2.45 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(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(elem!1)), s(elem!1))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(8069,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[8068])).
% 2.24/2.45 tff(8070,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[8069, 8067])).
% 2.24/2.45 tff(8071,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(8072,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[8071, 8070])).
% 2.24/2.45 tff(8073,plain,
% 2.24/2.45 ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[8072, 155, 8040, 3321, 8024])).
% 2.24/2.45 tff(8074,plain,
% 2.24/2.45 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[8073, 8066])).
% 2.24/2.45 tff(8075,assumption,(~(s(s(elem!1)) = s(s(s(elem!1))))), introduced(assumption)).
% 2.24/2.45 tff(8076,assumption,(~r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 2.24/2.45 tff(8077,assumption,(~b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 2.24/2.45 tff(8078,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1576, 53, 8077, 8076, 8075])).
% 2.24/2.45 tff(8079,plain,(b(s(s(elem!1)), s(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,[]))).
% 2.24/2.45 tff(8080,plain,
% 2.24/2.45 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[8079, 8074, 8063])).
% 2.24/2.45 tff(8081,plain,
% 2.24/2.45 (r(s(s(s(elem!1))), z)),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[8052, 8042])).
% 2.24/2.45 tff(8082,plain,
% 2.24/2.45 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[832, 8060, 8047, 8081])).
% 2.24/2.45 tff(8083,plain,
% 2.24/2.45 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[821, 8082, 4451])).
% 2.24/2.45 tff(8084,plain,
% 2.24/2.45 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[7346, 97, 8041, 8083, 8080])).
% 2.24/2.45 tff(8085,plain,
% 2.24/2.45 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1484, 8084, 1432])).
% 2.24/2.45 tff(8086,plain,
% 2.24/2.45 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1816, 8085, 8024, 1393, 1520])).
% 2.24/2.45 tff(8087,plain,
% 2.24/2.45 (b(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[511, 8086])).
% 2.24/2.45 tff(8088,plain,
% 2.24/2.45 (~b(z, s(s(s(s(elem!1)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[558, 8087, 550, 61])).
% 2.24/2.45 tff(8089,plain,
% 2.24/2.45 (r(z, s(s(s(s(elem!1)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1093, 8088])).
% 2.24/2.45 tff(8090,plain,
% 2.24/2.45 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3326, 8089, 645, 1393, 8060])).
% 2.24/2.45 tff(8091,plain,
% 2.24/2.45 (b(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[143, 8048])).
% 2.24/2.45 tff(8092,plain,
% 2.24/2.45 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1872, 8089, 8081, 8060])).
% 2.24/2.45 tff(8093,plain,
% 2.24/2.45 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[4129, 8092, 8082, 1418, 8091])).
% 2.24/2.45 tff(8094,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[336, 8093, 8090])).
% 2.24/2.45 tff(8095,plain,((~b(z, s(s(z)))) | (~r(s(s(z)), z)) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(8096,plain,
% 2.24/2.45 (~b(z, s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[8095, 7590, 7991, 550, 61, 8022, 494, 7137])).
% 2.24/2.45 tff(8097,plain,
% 2.24/2.45 (r(z, s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[222, 8096])).
% 2.24/2.45 tff(8098,plain,
% 2.24/2.45 (r(elem!1, s(s(elem!1)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[8097, 8017])).
% 2.24/2.45 tff(8099,plain,
% 2.24/2.45 (r(s(elem!1), s(s(elem!1)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[3, 8020])).
% 2.24/2.45 tff(8100,plain,
% 2.24/2.45 (r(z, s(s(elem!1)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[8097, 8016])).
% 2.24/2.45 tff(8101,plain,
% 2.24/2.45 (~r(z, s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6374, 6361, 8026])).
% 2.24/2.45 tff(8102,plain,
% 2.24/2.45 (b(z, s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[590, 8101])).
% 2.24/2.45 tff(8103,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 2.24/2.45 tff(8104,plain,
% 2.24/2.45 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[1444])).
% 2.24/2.45 tff(8105,plain,
% 2.24/2.45 (b(z, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[1393])).
% 2.24/2.45 tff(8106,plain,
% 2.24/2.45 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[8105, 8104])).
% 2.24/2.45 tff(8107,plain,
% 2.24/2.45 (b(elem!1, s(s(s(elem!1))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[6362, 8106])).
% 2.24/2.45 tff(8108,plain,
% 2.24/2.45 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6172, 1612])).
% 2.24/2.45 tff(8109,plain,
% 2.24/2.45 (~b(s(s(s(s(elem!1)))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[7659, 126, 125, 550, 1418, 124])).
% 2.24/2.45 tff(8110,plain,
% 2.24/2.45 (r(s(s(s(s(elem!1)))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[842, 8109])).
% 2.24/2.45 tff(8111,plain,
% 2.24/2.45 (~b(z, s(s(s(s(elem!1)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6115, 126, 61, 4451, 125, 124, 7189, 550])).
% 2.24/2.45 tff(8112,plain,
% 2.24/2.45 (r(z, s(s(s(s(elem!1)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1093, 8111])).
% 2.24/2.45 tff(8113,plain,
% 2.24/2.45 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3326, 8112, 645, 1393, 8110])).
% 2.24/2.45 tff(8114,plain,
% 2.24/2.45 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[336, 8113])).
% 2.24/2.45 tff(8115,plain,
% 2.24/2.45 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[60, 1501])).
% 2.24/2.45 tff(8116,plain,
% 2.24/2.45 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[1399])).
% 2.24/2.45 tff(8117,plain,
% 2.24/2.45 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[8114, 8116])).
% 2.24/2.45 tff(8118,plain,
% 2.24/2.45 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[7685, 8110, 7676, 3320])).
% 2.24/2.45 tff(8119,plain,
% 2.24/2.45 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1484, 8118, 1432])).
% 2.24/2.45 tff(8120,plain,
% 2.24/2.45 (((~![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(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(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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)))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(8121,plain,
% 2.24/2.45 (((~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(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(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(elem!1)))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(8122,plain,
% 2.24/2.45 (((~![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(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(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(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(elem!1))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[8121])).
% 2.24/2.45 tff(8123,plain,
% 2.24/2.45 (((~![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(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(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(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(elem!1)))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[8122, 8120])).
% 2.24/2.45 tff(8124,plain,
% 2.24/2.45 ((~![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(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(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))))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(8125,plain,
% 2.24/2.45 ((~![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(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(elem!1))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[8124, 8123])).
% 2.24/2.45 tff(8126,plain,
% 2.24/2.45 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[8125, 97, 8119, 8117, 8115])).
% 2.24/2.45 tff(8127,plain,
% 2.24/2.45 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[821, 8126, 4451])).
% 2.24/2.45 tff(8128,plain,
% 2.24/2.45 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1136, 8127, 125, 7189])).
% 2.24/2.45 tff(8129,plain,
% 2.24/2.45 (b(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[511, 8128])).
% 2.24/2.45 tff(8130,plain,
% 2.24/2.45 (~b(s(s(z)), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3240, 8129, 550, 8114])).
% 2.24/2.45 tff(8131,plain,
% 2.24/2.45 (r(s(s(z)), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[122, 8130])).
% 2.24/2.45 tff(8132,plain,
% 2.24/2.45 (r(s(s(elem!1)), s(elem!1))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[8131, 8023])).
% 2.24/2.45 tff(8133,plain,
% 2.24/2.45 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 2.24/2.45 inference(monotonicity,[status(thm)],[1411])).
% 2.24/2.45 tff(8134,plain,
% 2.24/2.45 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 2.24/2.45 inference(symmetry,[status(thm)],[8133])).
% 2.24/2.45 tff(8135,plain,
% 2.24/2.45 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.24/2.45 inference(monotonicity,[status(thm)],[1444])).
% 2.24/2.45 tff(8136,plain,
% 2.24/2.45 (b(s(z), elem!1)),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[550, 8135])).
% 2.24/2.45 tff(8137,plain,
% 2.24/2.45 (b(s(elem!1), elem!1)),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[8136, 8134])).
% 2.24/2.45 tff(8138,plain,
% 2.24/2.45 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.24/2.45 inference(symmetry,[status(thm)],[6224])).
% 2.24/2.45 tff(8139,plain,
% 2.24/2.45 ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) <=> (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6212])).
% 2.24/2.45 tff(8140,plain,
% 2.24/2.45 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[7529, 155, 1812, 8103, 6276])).
% 2.24/2.45 tff(8141,plain,
% 2.24/2.45 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[8140, 8139])).
% 2.24/2.45 tff(8142,plain,
% 2.24/2.45 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6239, 8141, 6223])).
% 2.24/2.45 tff(8143,plain,
% 2.24/2.45 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[8142, 8138])).
% 2.24/2.45 tff(8144,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 2.24/2.45 tff(8145,plain,
% 2.24/2.45 (((~![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(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $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(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(8146,plain,
% 2.24/2.45 (((~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(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(8147,plain,
% 2.24/2.45 (((~![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(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(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[8146])).
% 2.24/2.45 tff(8148,plain,
% 2.24/2.45 (((~![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(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(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.24/2.45 inference(transitivity,[status(thm)],[8147, 8145])).
% 2.24/2.45 tff(8149,plain,
% 2.24/2.45 ((~![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(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))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(8150,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[8149, 8148])).
% 2.24/2.45 tff(8151,plain,
% 2.24/2.45 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[8150, 97, 6315, 6314, 8144])).
% 2.24/2.45 tff(8152,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[8151, 8143])).
% 2.24/2.45 tff(8153,plain,((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(8154,plain,
% 2.24/2.45 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[8153, 8137, 6315, 1393, 8132, 8103, 3321, 6301])).
% 2.24/2.45 tff(8155,plain,
% 2.24/2.45 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6269, 8154, 8108])).
% 2.24/2.45 tff(8156,plain,
% 2.24/2.45 (((~![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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(8157,plain,
% 2.24/2.45 (((~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(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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(8158,plain,
% 2.24/2.45 (((~![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(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(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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[8157])).
% 2.24/2.45 tff(8159,plain,
% 2.24/2.45 (((~![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(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(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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[8158, 8156])).
% 2.24/2.45 tff(8160,plain,
% 2.24/2.45 ((~![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(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(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))))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(8161,plain,
% 2.24/2.45 ((~![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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[8160, 8159])).
% 2.24/2.46 tff(8162,plain,
% 2.24/2.46 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[8161, 97, 8117, 8115, 8155])).
% 2.24/2.46 tff(8163,plain,
% 2.24/2.46 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[8162, 7493])).
% 2.24/2.46 tff(8164,plain,
% 2.24/2.46 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6289, 8163, 7492])).
% 2.24/2.46 tff(8165,plain,
% 2.24/2.46 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[8164, 7485])).
% 2.24/2.46 tff(8166,plain,
% 2.24/2.46 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6197, 1418, 1393])).
% 2.24/2.46 tff(8167,plain,
% 2.24/2.46 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[7544, 8166])).
% 2.24/2.46 tff(8168,plain,
% 2.24/2.46 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[1411])).
% 2.24/2.46 tff(8169,plain,
% 2.24/2.46 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.46 inference(symmetry,[status(thm)],[8168])).
% 2.24/2.46 tff(8170,plain,
% 2.24/2.46 (r(s(elem!1), s(s(s(elem!1))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[7189, 8169])).
% 2.24/2.46 tff(8171,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(8172,plain,
% 2.24/2.46 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(8173,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[8172])).
% 2.24/2.46 tff(8174,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[8173, 8171])).
% 2.24/2.46 tff(8175,plain,
% 2.24/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(8176,plain,
% 2.24/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[8175, 8174])).
% 2.24/2.46 tff(8177,plain,
% 2.24/2.46 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[8176, 155, 8127, 8170, 8066])).
% 2.24/2.46 tff(8178,plain,
% 2.24/2.46 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1615, 53, 1612, 8177])).
% 2.24/2.46 tff(8179,plain,
% 2.24/2.46 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1822, 8118, 1393])).
% 2.24/2.46 tff(8180,plain,
% 2.24/2.46 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[452, 8179])).
% 2.24/2.46 tff(8181,plain,
% 2.24/2.46 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3313, 8180, 60, 8114])).
% 2.24/2.46 tff(8182,plain,
% 2.24/2.46 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[486, 8181, 1418])).
% 2.24/2.46 tff(8183,plain,
% 2.24/2.46 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[924, 8127, 7189, 8182])).
% 2.24/2.46 tff(8184,plain,
% 2.24/2.46 (b(s(z), s(s(s(s(elem!1)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[280, 8183])).
% 2.24/2.46 tff(8185,plain,
% 2.24/2.46 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[8184, 1517])).
% 2.24/2.46 tff(8186,plain,
% 2.24/2.46 (((~![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(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)))))) | (~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(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(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(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(s(elem!1)))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(8187,plain,
% 2.24/2.46 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(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(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(8188,plain,
% 2.24/2.46 (((~![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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(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(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(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(s(elem!1))))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[8187])).
% 2.24/2.46 tff(8189,plain,
% 2.24/2.46 (((~![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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(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(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(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(s(elem!1)))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[8188, 8186])).
% 2.24/2.46 tff(8190,plain,
% 2.24/2.46 ((~![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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(8191,plain,
% 2.24/2.46 ((~![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(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)))))) | (~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(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[8190, 8189])).
% 2.24/2.46 tff(8192,plain,
% 2.24/2.46 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[8191, 97, 8119, 8117, 8155, 8185, 8178])).
% 2.24/2.46 tff(8193,plain,
% 2.24/2.46 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6254, 8192, 8167])).
% 2.24/2.46 tff(8194,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(8195,plain,
% 2.24/2.46 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(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))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(8196,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[8195])).
% 2.24/2.46 tff(8197,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[8196, 8194])).
% 2.24/2.46 tff(8198,plain,
% 2.24/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(8199,plain,
% 2.24/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[8198, 8197])).
% 2.24/2.46 tff(8200,plain,
% 2.24/2.46 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[8199, 155, 8182, 8127, 8193])).
% 2.24/2.46 tff(8201,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[8200, 8165])).
% 2.24/2.46 tff(8202,plain,((~b(s(s(s(elem!1))), z)) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(8203,plain,
% 2.24/2.46 (~b(s(s(s(elem!1))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[8202, 8107, 1393, 8103, 6301, 125, 550, 60, 645, 7676, 61, 8102])).
% 2.24/2.46 tff(8204,plain,
% 2.24/2.46 (r(s(s(s(elem!1))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[246, 8203])).
% 2.24/2.46 tff(8205,plain,
% 2.24/2.46 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[1396])).
% 2.24/2.46 tff(8206,plain,
% 2.24/2.46 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.46 inference(symmetry,[status(thm)],[8205])).
% 2.24/2.46 tff(8207,plain,
% 2.24/2.46 (~b(s(z), s(s(s(elem!1))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[201, 8102, 61, 60])).
% 2.24/2.46 tff(8208,plain,
% 2.24/2.46 (r(s(z), s(s(s(elem!1))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[181, 8207])).
% 2.24/2.46 tff(8209,plain,
% 2.24/2.46 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 2.24/2.46 inference(symmetry,[status(thm)],[4641])).
% 2.24/2.46 tff(8210,plain,
% 2.24/2.46 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 2.24/2.46 inference(transitivity,[status(thm)],[4639, 8209])).
% 2.24/2.46 tff(8211,plain,
% 2.24/2.46 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(z)), s(z)))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[8210])).
% 2.24/2.46 tff(8212,plain,
% 2.24/2.46 (~b(s(s(s(s(elem!1)))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3452, 8203, 125, 550, 8102, 61, 8208])).
% 2.24/2.46 tff(8213,plain,
% 2.24/2.46 (r(s(s(s(s(elem!1)))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[842, 8212])).
% 2.24/2.46 tff(8214,plain,
% 2.24/2.46 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[7685, 8213, 7676, 3320])).
% 2.24/2.46 tff(8215,plain,
% 2.24/2.46 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1484, 8214, 1432])).
% 2.24/2.46 tff(8216,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 2.24/2.46 tff(8217,plain,
% 2.24/2.46 (((~![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(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(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(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(elem!1)))), s(s(elem!1)))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(8218,plain,
% 2.24/2.46 (((~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(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(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(elem!1)))), s(s(elem!1)))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(8219,plain,
% 2.24/2.46 (((~![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(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(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(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(elem!1)))), s(s(elem!1))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[8218])).
% 2.24/2.46 tff(8220,plain,
% 2.24/2.46 (((~![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(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(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(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(elem!1)))), s(s(elem!1)))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[8219, 8217])).
% 2.24/2.46 tff(8221,plain,
% 2.24/2.46 ((~![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(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(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))))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(8222,plain,
% 2.24/2.46 ((~![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(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(elem!1)))), s(s(elem!1))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[8221, 8220])).
% 2.24/2.46 tff(8223,plain,
% 2.24/2.46 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[8222, 97, 1545, 1529])).
% 2.24/2.46 tff(8224,plain,
% 2.24/2.46 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[8223, 8216])).
% 2.24/2.46 tff(8225,plain,
% 2.24/2.46 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[821, 8224, 802])).
% 2.24/2.46 tff(8226,plain,
% 2.24/2.46 (((~![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(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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)))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(8227,plain,
% 2.24/2.46 (((~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(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)))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(8228,plain,
% 2.24/2.46 (((~![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(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(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))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[8227])).
% 2.24/2.46 tff(8229,plain,
% 2.24/2.46 (((~![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(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(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)))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[8228, 8226])).
% 2.24/2.46 tff(8230,plain,
% 2.24/2.46 ((~![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(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)))))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(8231,plain,
% 2.24/2.46 ((~![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(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))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[8230, 8229])).
% 2.24/2.46 tff(8232,plain,
% 2.24/2.46 ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[8231, 97, 1545, 1529])).
% 2.24/2.46 tff(8233,plain,
% 2.24/2.46 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[8232, 8216])).
% 2.24/2.46 tff(8234,plain,
% 2.24/2.46 (~r(z, s(s(s(s(elem!1)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3464, 8233, 585, 288, 824])).
% 2.24/2.46 tff(8235,plain,
% 2.24/2.46 (b(z, s(s(s(s(elem!1)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1093, 8234])).
% 2.24/2.46 tff(8236,plain,
% 2.24/2.46 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[701, 473, 372, 124])).
% 2.24/2.46 tff(8237,plain,
% 2.24/2.46 (r(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[509, 53, 8236, 274])).
% 2.24/2.46 tff(8238,plain,
% 2.24/2.46 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1190, 473, 372, 124])).
% 2.24/2.46 tff(8239,plain,
% 2.24/2.46 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[450, 53, 329, 8238])).
% 2.24/2.46 tff(8240,plain,
% 2.24/2.46 (~r(s(z), s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[4115, 8239, 823, 125, 8237])).
% 2.24/2.46 tff(8241,plain,
% 2.24/2.46 (b(s(z), s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[548, 8240])).
% 2.24/2.46 tff(8242,plain,
% 2.24/2.46 (~b(s(s(s(s(elem!1)))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3793, 473, 372, 124])).
% 2.24/2.46 tff(8243,plain,
% 2.24/2.46 (r(s(s(s(s(elem!1)))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[842, 8242])).
% 2.24/2.46 tff(8244,plain,
% 2.24/2.46 (~b(s(s(z)), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2905, 8243, 8239, 61, 8241])).
% 2.24/2.46 tff(8245,plain,
% 2.24/2.46 (r(s(s(z)), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[121, 8244, 117])).
% 2.24/2.46 tff(8246,plain,
% 2.24/2.46 (~r(z, s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3278, 8245, 8239, 8243, 8237])).
% 2.24/2.47 tff(8247,plain,
% 2.24/2.47 (b(z, s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[222, 8246])).
% 2.24/2.47 tff(8248,plain,
% 2.24/2.47 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(8249,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[8248])).
% 2.24/2.47 tff(8250,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[8249, 3157])).
% 2.24/2.47 tff(8251,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(8252,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[8251, 8250])).
% 2.24/2.47 tff(8253,plain,
% 2.24/2.47 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8252, 155, 287, 8245, 8237])).
% 2.24/2.47 tff(8254,plain,
% 2.24/2.47 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[336, 8253])).
% 2.24/2.47 tff(8255,plain,
% 2.24/2.47 (((~![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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(8256,plain,
% 2.24/2.47 (((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(8257,plain,
% 2.24/2.47 (((~![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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[8256])).
% 2.24/2.47 tff(8258,plain,
% 2.24/2.47 (((~![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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[8257, 8255])).
% 2.24/2.47 tff(8259,plain,
% 2.24/2.47 ((~![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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(8260,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[8259, 8258])).
% 2.24/2.47 tff(8261,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8260, 97, 61, 8254, 8247, 8241])).
% 2.24/2.47 tff(8262,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(8263,plain,
% 2.24/2.47 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8262, 287, 61, 372, 124, 823, 125])).
% 2.24/2.47 tff(8264,plain,
% 2.24/2.47 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[486, 8263, 472])).
% 2.24/2.47 tff(8265,plain,
% 2.24/2.47 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[503, 287, 125, 8264])).
% 2.24/2.47 tff(8266,plain,
% 2.24/2.47 (b(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[511, 8265])).
% 2.24/2.47 tff(8267,plain,
% 2.24/2.47 (~b(s(z), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[558, 8266, 372, 61])).
% 2.24/2.47 tff(8268,plain,
% 2.24/2.47 (r(s(z), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[568, 8267])).
% 2.24/2.47 tff(8269,plain,
% 2.24/2.47 (~b(s(z), s(s(s(elem!1))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[532, 8266, 372, 61])).
% 2.24/2.47 tff(8270,plain,
% 2.24/2.47 ((s(z) = s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[179, 53, 8269])).
% 2.24/2.47 tff(8271,plain,
% 2.24/2.47 (r(s(z), s(s(s(elem!1))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8270, 595])).
% 2.24/2.47 tff(8272,plain,
% 2.24/2.47 (~b(s(z), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[543, 8266, 372, 61])).
% 2.24/2.47 tff(8273,plain,
% 2.24/2.47 (r(s(z), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[548, 8272])).
% 2.24/2.47 tff(8274,plain,
% 2.24/2.47 (~r(s(s(z)), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[642, 8268, 8273, 124, 125, 61, 287, 8264])).
% 2.24/2.47 tff(8275,plain,
% 2.24/2.47 (b(s(s(z)), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[121, 8274, 117])).
% 2.24/2.47 tff(8276,plain,
% 2.24/2.47 (~r(z, s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[296, 8271, 288, 8273, 8268])).
% 2.24/2.47 tff(8277,plain,
% 2.24/2.47 (b(z, s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[222, 8276])).
% 2.24/2.47 tff(8278,plain,
% 2.24/2.47 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[212, 8277, 124, 8275])).
% 2.24/2.47 tff(8279,plain,
% 2.24/2.47 (r(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[58, 8278])).
% 2.24/2.47 tff(8280,plain,
% 2.24/2.47 (~r(s(s(z)), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[653, 8279, 8273, 8271, 8268])).
% 2.24/2.47 tff(8281,plain,
% 2.24/2.47 (b(s(s(z)), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[625, 8280])).
% 2.24/2.47 tff(8282,plain,
% 2.24/2.47 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[317, 8279, 8273, 8271, 287])).
% 2.24/2.47 tff(8283,plain,
% 2.24/2.47 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[336, 8282])).
% 2.24/2.47 tff(8284,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[669, 8283, 8281, 372, 8266])).
% 2.24/2.47 tff(8285,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(8286,plain,
% 2.24/2.47 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8285, 124, 372, 288, 61, 125, 472, 823])).
% 2.24/2.47 tff(8287,plain,
% 2.24/2.47 (b(s(z), s(s(s(s(elem!1)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[280, 8286])).
% 2.24/2.47 tff(8288,plain,
% 2.24/2.47 (((~![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(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(8289,plain,
% 2.24/2.47 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(8290,plain,
% 2.24/2.47 (((~![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(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(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(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[8289])).
% 2.24/2.47 tff(8291,plain,
% 2.24/2.47 (((~![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(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(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(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[8290, 8288])).
% 2.24/2.47 tff(8292,plain,
% 2.24/2.47 ((~![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(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(8293,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[8292, 8291])).
% 2.24/2.47 tff(8294,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8293, 97, 61, 255, 372, 513])).
% 2.24/2.47 tff(8295,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(8296,plain,
% 2.24/2.47 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8295, 8287, 61, 372])).
% 2.24/2.47 tff(8297,plain,
% 2.24/2.47 (r(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[511, 8296])).
% 2.24/2.47 tff(8298,plain,
% 2.24/2.47 (~r(s(z), s(s(s(elem!1))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1136, 8297, 823, 125])).
% 2.24/2.47 tff(8299,plain,
% 2.24/2.47 ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[179, 53, 8298])).
% 2.24/2.47 tff(8300,plain,
% 2.24/2.47 (b(s(z), s(s(s(elem!1))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8299, 595])).
% 2.24/2.47 tff(8301,plain,
% 2.24/2.47 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[201, 8300, 124, 61])).
% 2.24/2.47 tff(8302,plain,
% 2.24/2.47 (r(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[58, 8301])).
% 2.24/2.47 tff(8303,plain,
% 2.24/2.47 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[481, 8300, 61, 124])).
% 2.24/2.47 tff(8304,plain,
% 2.24/2.47 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[486, 8303, 472])).
% 2.24/2.47 tff(8305,plain,
% 2.24/2.47 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1494, 8287, 61, 372])).
% 2.24/2.47 tff(8306,plain,
% 2.24/2.47 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[452, 8305])).
% 2.24/2.47 tff(8307,plain,
% 2.24/2.47 (~r(s(z), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[4115, 8297, 823, 125, 8306])).
% 2.24/2.47 tff(8308,plain,
% 2.24/2.47 (b(s(z), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[548, 8307])).
% 2.24/2.47 tff(8309,plain,
% 2.24/2.47 (((~![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(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(8310,plain,
% 2.24/2.47 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(8311,plain,
% 2.24/2.47 (((~![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(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[8310])).
% 2.24/2.47 tff(8312,plain,
% 2.24/2.47 (((~![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(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[8311, 8309])).
% 2.24/2.47 tff(8313,plain,
% 2.24/2.47 ((~![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(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(8314,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[8313, 8312])).
% 2.24/2.47 tff(8315,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8314, 97, 61, 255, 372, 876])).
% 2.24/2.47 tff(8316,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(8317,plain,
% 2.24/2.47 (~b(s(s(s(s(elem!1)))), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8316, 8287, 61, 372])).
% 2.24/2.47 tff(8318,plain,
% 2.24/2.47 (r(s(s(s(s(elem!1)))), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[842, 8317])).
% 2.24/2.47 tff(8319,plain,
% 2.24/2.47 (~b(s(s(z)), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2905, 8318, 8306, 61, 8308])).
% 2.24/2.47 tff(8320,plain,
% 2.24/2.47 (r(s(s(z)), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[121, 8319, 117])).
% 2.24/2.47 tff(8321,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(8322,plain,
% 2.24/2.47 (((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~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(z)), s(z))) | (~r(s(s(s(elem!1))), 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(s(elem!1)))), s(s(z)))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(8323,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[8322])).
% 2.24/2.47 tff(8324,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[8323, 8321])).
% 2.24/2.47 tff(8325,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(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)))))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(8326,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[8325, 8324])).
% 2.24/2.47 tff(8327,plain,
% 2.24/2.47 ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8326, 155, 125, 8306, 8320])).
% 2.24/2.47 tff(8328,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[8327, 8304, 8302])).
% 2.24/2.47 tff(8329,plain,((~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(8330,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8329, 8235, 8225, 61, 3008, 125, 472, 288])).
% 2.24/2.48 tff(8331,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(8332,plain,
% 2.24/2.48 (~b(s(s(elem!1)), s(elem!1))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8331, 8204, 125, 1418, 61, 4451, 8101, 8213, 8215, 8115])).
% 2.24/2.48 tff(8333,plain,
% 2.24/2.48 (~b(s(s(z)), s(z))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[8332, 8211])).
% 2.24/2.48 tff(8334,plain,
% 2.24/2.48 (r(s(s(z)), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[122, 8333])).
% 2.24/2.48 tff(8335,plain,
% 2.24/2.48 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1273, 8334, 125, 8208])).
% 2.24/2.48 tff(8336,plain,
% 2.24/2.48 (b(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[143, 8335])).
% 2.24/2.48 tff(8337,plain,
% 2.24/2.48 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[8336, 8206])).
% 2.24/2.48 tff(8338,plain,
% 2.24/2.48 (((~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(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)))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(8339,plain,
% 2.24/2.48 (((~![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(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(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))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[8338])).
% 2.24/2.48 tff(8340,plain,
% 2.24/2.48 (((~![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(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(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)))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[8339, 7341])).
% 2.24/2.48 tff(8341,plain,
% 2.24/2.48 ((~![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(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))))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(8342,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[8341, 8340])).
% 2.24/2.48 tff(8343,plain,
% 2.24/2.48 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8342, 97, 8215, 8115, 8337])).
% 2.24/2.48 tff(8344,plain,
% 2.24/2.48 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[821, 8343, 4451])).
% 2.24/2.48 tff(8345,plain,
% 2.24/2.48 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1584, 97, 8215, 8115, 8337])).
% 2.24/2.48 tff(8346,plain,
% 2.24/2.48 (~r(z, s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[3464, 8345, 8101, 8204, 8213])).
% 2.24/2.48 tff(8347,plain,
% 2.24/2.48 (b(z, s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1093, 8346])).
% 2.24/2.48 tff(8348,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8329, 8347, 8344, 61, 8102, 125, 1418, 8204])).
% 2.24/2.48 tff(8349,plain,(r(z, s(s(s(z)))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~b(s(z), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(8350,plain,
% 2.24/2.48 (r(z, s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8349, 7991, 494, 61, 8100, 550, 8099, 8098, 7995, 7590])).
% 2.24/2.48 tff(8351,plain,
% 2.24/2.48 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[7991])).
% 2.24/2.48 tff(8352,plain,
% 2.24/2.48 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 2.24/2.48 inference(symmetry,[status(thm)],[8351])).
% 2.24/2.48 tff(8353,plain,
% 2.24/2.48 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(s(s(z))), z))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[8352])).
% 2.24/2.48 tff(8354,plain,
% 2.24/2.48 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.24/2.48 inference(symmetry,[status(thm)],[7992])).
% 2.24/2.48 tff(8355,plain,
% 2.24/2.48 (s(s(elem!1)) = s(s(z))),
% 2.24/2.48 inference(transitivity,[status(thm)],[167, 8354, 72])).
% 2.24/2.48 tff(8356,plain,
% 2.24/2.48 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[8355])).
% 2.24/2.48 tff(8357,plain,
% 2.24/2.48 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.48 inference(symmetry,[status(thm)],[8356])).
% 2.24/2.48 tff(8358,plain,
% 2.24/2.48 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[7995, 8357])).
% 2.24/2.48 tff(8359,plain,
% 2.24/2.48 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[1393])).
% 2.24/2.48 tff(8360,plain,
% 2.24/2.48 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(symmetry,[status(thm)],[8359])).
% 2.24/2.48 tff(8361,plain,
% 2.24/2.48 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[1444])).
% 2.24/2.48 tff(8362,plain,
% 2.24/2.48 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[1399])).
% 2.24/2.48 tff(8363,plain,
% 2.24/2.48 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 2.24/2.48 inference(transitivity,[status(thm)],[8362, 8361])).
% 2.24/2.48 tff(8364,plain,
% 2.24/2.48 (r(elem!1, s(s(elem!1)))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[226, 8363])).
% 2.24/2.48 tff(8365,plain,
% 2.24/2.48 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[7277])).
% 2.24/2.48 tff(8366,plain,
% 2.24/2.48 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.24/2.48 inference(transitivity,[status(thm)],[8365, 3103])).
% 2.24/2.48 tff(8367,plain,
% 2.24/2.48 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 2.24/2.48 inference(commutativity,[status(thm)],[])).
% 2.24/2.48 tff(8368,plain,
% 2.24/2.48 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[1393])).
% 2.24/2.48 tff(8369,plain,
% 2.24/2.48 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[8368, 8367])).
% 2.24/2.48 tff(8370,plain,
% 2.24/2.48 ((~(s(s(s(z))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[8369])).
% 2.24/2.48 tff(8371,plain,
% 2.24/2.48 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[2824, 8370])).
% 2.24/2.48 tff(8372,plain,
% 2.24/2.48 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[1401])).
% 2.24/2.48 tff(8373,plain,
% 2.24/2.48 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 2.24/2.48 inference(symmetry,[status(thm)],[8372])).
% 2.24/2.48 tff(8374,plain,
% 2.24/2.48 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.24/2.48 inference(transitivity,[status(thm)],[7274, 8373])).
% 2.24/2.48 tff(8375,plain,
% 2.24/2.48 (b(elem!1, s(z))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[61, 8374])).
% 2.24/2.48 tff(8376,plain,
% 2.24/2.48 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[1972])).
% 2.24/2.48 tff(8377,plain,
% 2.24/2.48 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.24/2.48 inference(symmetry,[status(thm)],[8376])).
% 2.24/2.48 tff(8378,plain,
% 2.24/2.48 (b(s(s(s(elem!1))), elem!1)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[126, 8377])).
% 2.24/2.48 tff(8379,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6857, 8378])).
% 2.24/2.48 tff(8380,plain,((~(elem!1 = z)) | b(s(s(s(elem!1))), elem!1) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(8381,plain,
% 2.24/2.48 (b(s(s(s(elem!1))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8380, 126, 1889])).
% 2.24/2.48 tff(8382,plain,
% 2.24/2.48 (~b(s(z), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6870, 8381, 8136, 8375])).
% 2.24/2.48 tff(8383,plain,
% 2.24/2.48 (r(s(z), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[181, 8382])).
% 2.24/2.48 tff(8384,plain,
% 2.24/2.48 (~b(s(s(s(s(z)))), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[7646, 8383, 126, 8371, 61, 125, 550])).
% 2.24/2.48 tff(8385,plain,
% 2.24/2.48 (r(s(s(s(s(z)))), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2860, 8384])).
% 2.24/2.48 tff(8386,plain,
% 2.24/2.48 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[8385, 8366])).
% 2.24/2.48 tff(8387,plain,
% 2.24/2.48 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6107, 155, 8386, 3321, 8364])).
% 2.24/2.48 tff(8388,plain,
% 2.24/2.48 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1484, 8387, 1432])).
% 2.24/2.48 tff(8389,plain,
% 2.24/2.48 (r(z, s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6652, 1300, 1393])).
% 2.24/2.48 tff(8390,plain,
% 2.24/2.48 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.24/2.48 inference(transitivity,[status(thm)],[4641, 4640])).
% 2.24/2.48 tff(8391,plain,
% 2.24/2.48 (~r(s(s(z)), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2253, 224, 125, 645, 570])).
% 2.24/2.48 tff(8392,plain,
% 2.24/2.48 (b(s(s(z)), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[122, 8391])).
% 2.24/2.48 tff(8393,plain,
% 2.24/2.48 (b(s(s(elem!1)), s(elem!1))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[8392, 8390])).
% 2.24/2.48 tff(8394,plain,
% 2.24/2.48 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8231, 97, 1545, 1529, 8393])).
% 2.24/2.48 tff(8395,plain,
% 2.24/2.48 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[486, 8394, 1418])).
% 2.24/2.48 tff(8396,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(8397,plain,
% 2.24/2.48 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~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(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(8398,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[8397])).
% 2.24/2.48 tff(8399,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[8398, 8396])).
% 2.24/2.48 tff(8400,plain,
% 2.24/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(8401,plain,
% 2.24/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[8400, 8399])).
% 2.24/2.48 tff(8402,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8401, 155, 570, 463, 488, 226, 224])).
% 2.24/2.48 tff(8403,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(8404,plain,
% 2.24/2.48 (~r(z, s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8403, 8395, 570, 224, 226])).
% 2.24/2.48 tff(8405,plain,
% 2.24/2.48 (b(z, s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1093, 8404])).
% 2.24/2.48 tff(8406,plain,
% 2.24/2.48 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8222, 97, 1545, 1529, 8393])).
% 2.24/2.48 tff(8407,plain,
% 2.24/2.48 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[821, 8406, 4451])).
% 2.24/2.48 tff(8408,plain,
% 2.24/2.48 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1136, 8407, 125, 225])).
% 2.24/2.48 tff(8409,plain,
% 2.24/2.48 (b(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[511, 8408])).
% 2.24/2.48 tff(8410,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[558, 8409, 8405, 550, 61])).
% 2.24/2.48 tff(8411,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(8412,plain,
% 2.24/2.48 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8411, 8383, 61, 125, 550, 8389, 226, 8388, 1529, 1393, 645])).
% 2.24/2.48 tff(8413,plain,
% 2.24/2.48 (b(s(s(z)), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[143, 8412])).
% 2.24/2.48 tff(8414,plain,
% 2.24/2.48 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[8413, 8206])).
% 2.24/2.48 tff(8415,plain,
% 2.24/2.48 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1584, 97, 8388, 1529, 8414])).
% 2.24/2.48 tff(8416,plain,
% 2.24/2.48 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[486, 8415, 1418])).
% 2.24/2.48 tff(8417,plain,
% 2.24/2.48 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[8416, 8360])).
% 2.24/2.48 tff(8418,plain,
% 2.24/2.48 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8342, 97, 8388, 1529, 8414])).
% 2.24/2.48 tff(8419,plain,
% 2.24/2.48 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[821, 8418, 4451])).
% 2.24/2.48 tff(8420,plain,
% 2.24/2.48 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2439, 8419, 1889])).
% 2.24/2.48 tff(8421,plain,
% 2.24/2.48 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1136, 8419, 125, 8383])).
% 2.24/2.48 tff(8422,plain,
% 2.24/2.48 (b(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[511, 8421])).
% 2.24/2.48 tff(8423,plain,
% 2.24/2.48 (~b(z, s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[558, 8422, 550, 61])).
% 2.24/2.48 tff(8424,plain,
% 2.24/2.48 (r(z, s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1093, 8423])).
% 2.24/2.48 tff(8425,plain,
% 2.24/2.48 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2449, 8424, 1300, 8420])).
% 2.24/2.48 tff(8426,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8425, 8417])).
% 2.24/2.48 tff(8427,plain,((~b(s(s(s(elem!1))), z)) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(8428,plain,
% 2.24/2.48 (~b(s(s(s(elem!1))), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8427, 7991, 8350, 550, 61, 494, 8358, 8097, 7590])).
% 2.24/2.48 tff(8429,plain,
% 2.24/2.48 (~b(s(s(s(z))), z)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[8428, 8353])).
% 2.24/2.48 tff(8430,plain,
% 2.24/2.48 (r(s(s(s(z))), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[402, 8429])).
% 2.24/2.48 tff(8431,plain,
% 2.24/2.48 (~r(s(s(s(s(z)))), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[7624, 8430, 7137, 8097, 8350, 7590])).
% 2.24/2.48 tff(8432,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2860, 8431])).
% 2.24/2.48 tff(8433,plain,
% 2.24/2.48 (b(s(s(s(s(elem!1)))), z)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[8432, 8010])).
% 2.24/2.48 tff(8434,plain,
% 2.24/2.48 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[7991])).
% 2.24/2.48 tff(8435,plain,
% 2.24/2.48 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[8434, 1414])).
% 2.24/2.48 tff(8436,plain,
% 2.24/2.48 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[8435])).
% 2.24/2.48 tff(8437,plain,
% 2.24/2.48 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[286, 8436])).
% 2.24/2.48 tff(8438,plain,
% 2.24/2.48 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[3055, 8433, 550, 61])).
% 2.24/2.48 tff(8439,plain,
% 2.24/2.48 (r(s(z), s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[280, 8438])).
% 2.24/2.48 tff(8440,plain,
% 2.24/2.48 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2715, 8433, 550, 61])).
% 2.24/2.48 tff(8441,plain,
% 2.24/2.48 (r(s(s(s(s(elem!1)))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[511, 8440])).
% 2.24/2.48 tff(8442,plain,
% 2.24/2.48 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[503, 8441, 494, 8439])).
% 2.24/2.48 tff(8443,plain,
% 2.24/2.48 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[486, 8442, 8437])).
% 2.24/2.48 tff(8444,plain,
% 2.24/2.48 (((~![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(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~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))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(8445,plain,
% 2.24/2.48 (((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(8446,plain,
% 2.24/2.48 (((~![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(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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)))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[8445])).
% 2.24/2.48 tff(8447,plain,
% 2.24/2.48 (((~![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(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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))))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[8446, 8444])).
% 2.24/2.48 tff(8448,plain,
% 2.24/2.48 ((~![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(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(8449,plain,
% 2.24/2.48 ((~![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(s(s(z)), s(s(s(s(elem!1)))))) | (~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)))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[8448, 8447])).
% 2.24/2.48 tff(8450,plain,
% 2.24/2.48 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8449, 97, 339, 60, 1331])).
% 2.24/2.48 tff(8451,plain,
% 2.24/2.48 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[3089, 8450, 1749])).
% 2.24/2.48 tff(8452,plain,
% 2.24/2.48 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[8451])).
% 2.24/2.48 tff(8453,plain,
% 2.24/2.48 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.24/2.48 inference(symmetry,[status(thm)],[8452])).
% 2.24/2.48 tff(8454,plain,
% 2.24/2.48 (s(s(elem!1)) = s(s(z))),
% 2.24/2.48 inference(transitivity,[status(thm)],[167, 8453, 72])).
% 2.24/2.48 tff(8455,plain,
% 2.24/2.48 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[8454])).
% 2.24/2.48 tff(8456,plain,
% 2.24/2.48 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.48 inference(symmetry,[status(thm)],[8455])).
% 2.24/2.48 tff(8457,plain,
% 2.24/2.48 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[60, 8456])).
% 2.24/2.48 tff(8458,plain,
% 2.24/2.48 (s(s(z)) = s(s(elem!1))),
% 2.24/2.48 inference(transitivity,[status(thm)],[73, 8452, 19])).
% 2.24/2.48 tff(8459,plain,
% 2.24/2.48 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[8458])).
% 2.24/2.48 tff(8460,plain,
% 2.24/2.48 (s(z) = s(elem!1)),
% 2.24/2.48 inference(transitivity,[status(thm)],[24, 8459, 29])).
% 2.24/2.48 tff(8461,plain,
% 2.24/2.48 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[8460])).
% 2.24/2.48 tff(8462,plain,
% 2.24/2.48 (z = elem!1),
% 2.24/2.48 inference(transitivity,[status(thm)],[1443, 8461, 85])).
% 2.24/2.48 tff(8463,plain,
% 2.24/2.48 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[8462])).
% 2.24/2.48 tff(8464,plain,
% 2.24/2.48 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[876, 8463])).
% 2.24/2.48 tff(8465,plain,
% 2.24/2.48 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[8458])).
% 2.24/2.48 tff(8466,plain,
% 2.24/2.48 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[339, 8465])).
% 2.24/2.48 tff(8467,plain,
% 2.24/2.48 (((~![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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(8468,plain,
% 2.24/2.48 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(8469,plain,
% 2.24/2.48 (((~![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(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[8468])).
% 2.24/2.48 tff(8470,plain,
% 2.24/2.48 (((~![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(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[8469, 8467])).
% 2.24/2.48 tff(8471,plain,
% 2.24/2.48 ((~![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(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(8472,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[8471, 8470])).
% 2.24/2.48 tff(8473,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8472, 97, 8466, 473, 8464, 8457])).
% 2.24/2.48 tff(8474,plain,((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(8475,plain,
% 2.24/2.48 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8474, 8443, 7137, 8433, 8008, 7995])).
% 2.24/2.48 tff(8476,plain,
% 2.24/2.48 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[336, 8475])).
% 2.24/2.48 tff(8477,plain,
% 2.24/2.48 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[8476, 7994])).
% 2.24/2.49 tff(8478,plain,
% 2.24/2.49 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[7993])).
% 2.24/2.49 tff(8479,plain,
% 2.24/2.49 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.24/2.49 inference(transitivity,[status(thm)],[8478, 1428])).
% 2.24/2.49 tff(8480,plain,
% 2.24/2.49 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[8479])).
% 2.24/2.49 tff(8481,plain,
% 2.24/2.49 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[331, 8480])).
% 2.24/2.49 tff(8482,plain,
% 2.24/2.49 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.24/2.49 inference(monotonicity,[status(thm)],[8014])).
% 2.24/2.49 tff(8483,plain,
% 2.24/2.49 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[8482, 6776])).
% 2.24/2.49 tff(8484,plain,
% 2.24/2.49 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.24/2.49 inference(transitivity,[status(thm)],[8483, 6777])).
% 2.24/2.49 tff(8485,plain,
% 2.24/2.49 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[8484])).
% 2.24/2.49 tff(8486,plain,
% 2.24/2.49 (~(s(s(s(elem!1))) = elem!1)),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[241, 8485])).
% 2.24/2.49 tff(8487,plain,
% 2.24/2.49 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.24/2.49 inference(monotonicity,[status(thm)],[8014])).
% 2.24/2.49 tff(8488,plain,
% 2.24/2.49 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[8487])).
% 2.24/2.49 tff(8489,plain,
% 2.24/2.49 (~b(s(s(s(elem!1))), elem!1)),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[8428, 8488])).
% 2.24/2.49 tff(8490,plain,
% 2.24/2.49 (r(s(s(s(elem!1))), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6860, 53, 8489, 8486])).
% 2.24/2.49 tff(8491,plain,
% 2.24/2.49 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[8355])).
% 2.24/2.49 tff(8492,plain,
% 2.24/2.49 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.24/2.49 inference(symmetry,[status(thm)],[8491])).
% 2.24/2.49 tff(8493,plain,
% 2.24/2.49 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[8492])).
% 2.24/2.49 tff(8494,plain,
% 2.24/2.49 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[43, 8493])).
% 2.24/2.49 tff(8495,plain,
% 2.24/2.49 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[8014])).
% 2.24/2.49 tff(8496,plain,
% 2.24/2.49 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[7991])).
% 2.24/2.49 tff(8497,plain,
% 2.24/2.49 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[8496, 8495])).
% 2.24/2.49 tff(8498,plain,
% 2.24/2.49 (r(elem!1, s(s(s(elem!1))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[8350, 8497])).
% 2.24/2.49 tff(8499,plain,
% 2.24/2.49 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1586, 8443, 8358, 8498, 8494, 8490, 8014])).
% 2.24/2.49 tff(8500,plain,
% 2.24/2.49 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1484, 8499, 8481])).
% 2.24/2.49 tff(8501,plain,
% 2.24/2.49 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[4669, 8500, 7991, 8022, 8439])).
% 2.24/2.49 tff(8502,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8501, 8477])).
% 2.24/2.49 tff(8503,plain,((~r(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(8504,plain,
% 2.24/2.49 (~r(s(z), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8503, 550, 61, 82])).
% 2.24/2.49 tff(8505,plain,
% 2.24/2.49 (b(s(z), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[548, 8504])).
% 2.24/2.49 tff(8506,plain,
% 2.24/2.49 (((~![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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(8507,plain,
% 2.24/2.49 (((~b(s(z), s(s(z)))) | (~b(s(z), 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(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(8508,plain,
% 2.24/2.49 (((~![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(z)))) | (~b(s(z), 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(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[8507])).
% 2.24/2.49 tff(8509,plain,
% 2.24/2.49 (((~![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(z)))) | (~b(s(z), 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(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.24/2.49 inference(transitivity,[status(thm)],[8508, 8506])).
% 2.24/2.49 tff(8510,plain,
% 2.24/2.49 ((~![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(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(8511,plain,
% 2.24/2.49 ((~![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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[8510, 8509])).
% 2.24/2.49 tff(8512,plain,
% 2.24/2.49 (~b(s(s(s(z))), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8511, 97, 61, 535, 1360])).
% 2.24/2.49 tff(8513,plain,
% 2.24/2.49 (r(s(s(s(z))), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[402, 8512])).
% 2.24/2.49 tff(8514,plain,
% 2.24/2.49 (((~![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(z))) | (~b(s(z), s(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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(8515,plain,
% 2.24/2.49 (((~b(s(z), s(s(z)))) | (~b(s(z), 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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(8516,plain,
% 2.24/2.49 (((~![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(z)))) | (~b(s(z), 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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[8515])).
% 2.24/2.49 tff(8517,plain,
% 2.24/2.49 (((~![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(z)))) | (~b(s(z), 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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[8516, 8514])).
% 2.24/2.49 tff(8518,plain,
% 2.24/2.49 ((~![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(z)))) | (~b(s(z), 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))))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(8519,plain,
% 2.24/2.49 ((~![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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[8518, 8517])).
% 2.24/2.49 tff(8520,plain,
% 2.24/2.49 (~b(z, s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8519, 97, 61, 535, 1360])).
% 2.24/2.49 tff(8521,plain,
% 2.24/2.49 (r(z, s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1318, 8520])).
% 2.24/2.49 tff(8522,plain,
% 2.24/2.49 (~r(s(s(z)), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[4047, 155, 8521, 3587, 8513])).
% 2.24/2.49 tff(8523,plain,
% 2.24/2.49 (b(s(s(z)), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[625, 8522])).
% 2.24/2.49 tff(8524,plain,
% 2.24/2.49 (((~![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(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(8525,plain,
% 2.24/2.49 (((~b(s(s(z)), z)) | (~b(s(s(z)), 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(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(8526,plain,
% 2.24/2.49 (((~![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)), z)) | (~b(s(s(z)), 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(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[8525])).
% 2.24/2.49 tff(8527,plain,
% 2.24/2.49 (((~![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)), z)) | (~b(s(s(z)), 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(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[8526, 8524])).
% 2.24/2.49 tff(8528,plain,
% 2.24/2.49 ((~![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)), z)) | (~b(s(s(z)), 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))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(8529,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[8528, 8527])).
% 2.24/2.49 tff(8530,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8529, 97, 8523, 535, 1360, 1331])).
% 2.24/2.49 tff(8531,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(8532,plain,
% 2.24/2.49 (~b(s(s(s(z))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8531, 8505, 61, 7137])).
% 2.24/2.49 tff(8533,plain,
% 2.24/2.49 (r(s(s(s(z))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1358, 8532])).
% 2.24/2.49 tff(8534,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[3000, 97, 550, 61, 83, 535])).
% 2.24/2.49 tff(8535,plain,((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(8536,plain,
% 2.24/2.49 (~b(s(s(z)), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8535, 8505, 61, 550])).
% 2.24/2.49 tff(8537,plain,
% 2.24/2.49 (r(s(s(z)), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[625, 8536])).
% 2.24/2.49 tff(8538,assumption,(~r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 2.24/2.49 tff(8539,plain,
% 2.24/2.49 (~b(s(s(s(z))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8531, 535, 61, 7137])).
% 2.24/2.49 tff(8540,plain,
% 2.24/2.49 (r(s(s(s(z))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1358, 8539])).
% 2.24/2.49 tff(8541,plain,
% 2.24/2.49 (~b(s(s(s(s(z)))), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2853, 1216, 61, 8540, 550])).
% 2.24/2.49 tff(8542,plain,
% 2.24/2.49 (r(s(s(s(s(z)))), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2860, 8541])).
% 2.24/2.49 tff(8543,plain,
% 2.24/2.49 (~b(s(s(z)), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2651, 87, 535, 61])).
% 2.24/2.49 tff(8544,plain,
% 2.24/2.49 (r(s(s(z)), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[625, 8543])).
% 2.24/2.49 tff(8545,plain,
% 2.24/2.49 (~b(z, s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[3966, 87, 550, 535])).
% 2.24/2.49 tff(8546,plain,
% 2.24/2.49 (r(z, s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[222, 8545])).
% 2.24/2.49 tff(8547,plain,
% 2.24/2.49 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2881, 155, 8546, 8544, 4153])).
% 2.24/2.49 tff(8548,plain,
% 2.24/2.49 (b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2886, 8547, 80])).
% 2.24/2.49 tff(8549,plain,
% 2.24/2.49 (((~![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), z)) | (~b(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(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(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(8550,plain,
% 2.24/2.49 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(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(s(s(s(z)))), s(z))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(8551,plain,
% 2.24/2.49 (((~![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(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(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(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[8550])).
% 2.24/2.49 tff(8552,plain,
% 2.24/2.49 (((~![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(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(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(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[8551, 8549])).
% 2.24/2.49 tff(8553,plain,
% 2.24/2.49 ((~![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(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(8554,plain,
% 2.24/2.49 ((~![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), z)) | (~b(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(s(s(s(z)))), s(z)))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[8553, 8552])).
% 2.24/2.49 tff(8555,plain,
% 2.24/2.49 (~b(s(s(s(s(z)))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8554, 97, 550, 61, 87, 535, 8548])).
% 2.24/2.49 tff(8556,plain,
% 2.24/2.49 (r(s(s(s(s(z)))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2807, 8555, 2795])).
% 2.24/2.49 tff(8557,plain,
% 2.24/2.49 (((~![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(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), 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(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(8558,plain,
% 2.24/2.49 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), 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(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(8559,plain,
% 2.24/2.49 (((~![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(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), 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(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[8558])).
% 2.24/2.49 tff(8560,plain,
% 2.24/2.49 (((~![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(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), 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(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[8559, 8557])).
% 2.24/2.49 tff(8561,plain,
% 2.24/2.49 ((~![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(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(8562,plain,
% 2.24/2.49 ((~![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(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[8561, 8560])).
% 2.24/2.49 tff(8563,plain,
% 2.24/2.49 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8562, 97, 87, 1331, 8548])).
% 2.24/2.49 tff(8564,plain,
% 2.24/2.49 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2829, 8563])).
% 2.24/2.49 tff(8565,plain,
% 2.24/2.49 (((~![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(z)))) | (~b(s(s(s(s(z)))), 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(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(8566,plain,
% 2.24/2.49 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(8567,plain,
% 2.24/2.49 (((~![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(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), 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(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[8566])).
% 2.24/2.49 tff(8568,plain,
% 2.24/2.49 (((~![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(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), 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(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[8567, 8565])).
% 2.24/2.50 tff(8569,plain,
% 2.24/2.50 ((~![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(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.24/2.50 inference(quant_inst,[status(thm)],[])).
% 2.24/2.50 tff(8570,plain,
% 2.24/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 2.24/2.50 inference(modus_ponens,[status(thm)],[8569, 8568])).
% 2.24/2.50 tff(8571,plain,
% 2.24/2.50 (~b(s(z), s(s(s(s(z)))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[8570, 97, 87, 535, 8548])).
% 2.24/2.50 tff(8572,plain,
% 2.24/2.50 (r(s(z), s(s(s(s(z)))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[2844, 8571, 2833])).
% 2.24/2.50 tff(8573,plain,
% 2.24/2.50 (~b(s(s(s(z))), s(z))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[8531, 535, 61, 1331])).
% 2.24/2.50 tff(8574,plain,
% 2.24/2.50 (r(s(s(s(z))), s(z))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[1358, 8573])).
% 2.24/2.50 tff(8575,plain,
% 2.24/2.50 ($false),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[2851, 155, 8574, 8572, 8564, 8556])).
% 2.24/2.50 tff(8576,plain,((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.50 tff(8577,plain,
% 2.24/2.50 (~b(s(s(z)), s(z))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[8576, 8542, 535, 550, 61, 7137])).
% 2.24/2.50 tff(8578,plain,
% 2.24/2.50 (r(s(s(z)), s(z))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[122, 8577])).
% 2.24/2.50 tff(8579,plain,
% 2.24/2.50 (~r(s(s(z)), s(s(s(z))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[2940, 8578, 6655, 8540])).
% 2.24/2.50 tff(8580,plain,
% 2.24/2.50 (b(s(s(z)), s(s(s(z))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[437, 8579])).
% 2.24/2.50 tff(8581,plain,
% 2.24/2.50 (~b(z, s(s(z)))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[2205, 8580, 7137, 1216])).
% 2.24/2.50 tff(8582,plain,
% 2.24/2.50 (r(z, s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[222, 8581])).
% 2.34/2.50 tff(8583,plain,
% 2.34/2.50 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7172, 1, 1331, 8574, 125, 124, 61])).
% 2.34/2.50 tff(8584,plain,
% 2.34/2.50 (r(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[58, 8583])).
% 2.34/2.50 tff(8585,plain,
% 2.34/2.50 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[5757, 225, 2597, 125])).
% 2.34/2.50 tff(8586,plain,
% 2.34/2.50 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3089, 8585, 1])).
% 2.34/2.50 tff(8587,plain,
% 2.34/2.50 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1273, 225, 125, 2])).
% 2.34/2.50 tff(8588,plain,
% 2.34/2.50 (b(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[143, 8587])).
% 2.34/2.50 tff(8589,plain,
% 2.34/2.50 (~b(z, s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2661, 8588, 535, 61])).
% 2.34/2.50 tff(8590,plain,
% 2.34/2.50 (r(z, s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[222, 8589])).
% 2.34/2.50 tff(8591,plain,
% 2.34/2.50 (~r(s(s(s(elem!1))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3987, 8590, 61, 125, 145, 535])).
% 2.34/2.50 tff(8592,plain,
% 2.34/2.50 (b(s(s(s(elem!1))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[246, 8591])).
% 2.34/2.50 tff(8593,plain,
% 2.34/2.50 (((~![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(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(8594,plain,
% 2.34/2.50 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), 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))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(8595,plain,
% 2.34/2.50 (((~![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(s(elem!1))), z)) | (~b(s(s(s(elem!1))), 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))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[8594])).
% 2.34/2.50 tff(8596,plain,
% 2.34/2.50 (((~![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(s(elem!1))), z)) | (~b(s(s(s(elem!1))), 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))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.34/2.50 inference(transitivity,[status(thm)],[8595, 8593])).
% 2.34/2.50 tff(8597,plain,
% 2.34/2.50 ((~![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(s(elem!1))), z)) | (~b(s(s(s(elem!1))), 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)))))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(8598,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[8597, 8596])).
% 2.34/2.50 tff(8599,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8598, 97, 8592, 1331, 8588, 8586])).
% 2.34/2.50 tff(8600,plain,((~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(8601,plain,
% 2.34/2.50 (~r(s(z), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8600, 8584, 125, 1331, 61, 535, 2, 1, 8574])).
% 2.34/2.50 tff(8602,plain,
% 2.34/2.50 (b(s(z), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[181, 8601])).
% 2.34/2.50 tff(8603,plain,
% 2.34/2.50 (~r(s(s(s(elem!1))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3987, 8584, 226, 125, 61, 535])).
% 2.34/2.50 tff(8604,plain,
% 2.34/2.50 (b(s(s(s(elem!1))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[246, 8603])).
% 2.34/2.50 tff(8605,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3979, 8604, 8602, 61, 124])).
% 2.34/2.50 tff(8606,plain,((s(s(s(z))) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(8607,plain,
% 2.34/2.50 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8606, 8582, 3008, 61, 494, 535, 7137, 8578])).
% 2.34/2.50 tff(8608,plain,
% 2.34/2.50 (b(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1995, 8607, 7137])).
% 2.34/2.50 tff(8609,plain,
% 2.34/2.50 (~b(s(z), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[201, 8608, 61, 3008])).
% 2.34/2.50 tff(8610,plain,
% 2.34/2.50 (r(s(z), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[181, 8609])).
% 2.34/2.50 tff(8611,plain,
% 2.34/2.50 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[5757, 8610, 8540, 494])).
% 2.34/2.50 tff(8612,plain,
% 2.34/2.50 (~r(z, s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6652, 8607, 585])).
% 2.34/2.50 tff(8613,plain,
% 2.34/2.50 (b(z, s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1318, 8612])).
% 2.34/2.50 tff(8614,plain,
% 2.34/2.50 (~b(s(s(z)), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2972, 8613, 550, 535])).
% 2.34/2.50 tff(8615,plain,
% 2.34/2.50 (r(s(s(z)), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[625, 8614])).
% 2.34/2.50 tff(8616,plain,
% 2.34/2.50 (~r(s(s(s(elem!1))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3956, 8615, 550, 82, 535, 585, 8582])).
% 2.34/2.50 tff(8617,plain,
% 2.34/2.50 (b(s(s(s(elem!1))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[246, 8616])).
% 2.34/2.50 tff(8618,plain,
% 2.34/2.50 (~b(z, s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6087, 8617, 3008, 8613, 494, 8611, 61, 550, 8610])).
% 2.34/2.50 tff(8619,plain,
% 2.34/2.50 (r(z, s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1093, 8618])).
% 2.34/2.50 tff(8620,plain,
% 2.34/2.50 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3021, 8619, 585])).
% 2.34/2.50 tff(8621,plain,
% 2.34/2.50 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2638, 6655, 8540, 494])).
% 2.34/2.50 tff(8622,plain,
% 2.34/2.50 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6096, 97, 61, 8617, 1216])).
% 2.34/2.50 tff(8623,plain,
% 2.34/2.50 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2687, 8622, 8621])).
% 2.34/2.50 tff(8624,plain,
% 2.34/2.50 (~b(s(s(s(s(elem!1)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3648, 488, 494, 550, 124])).
% 2.34/2.50 tff(8625,plain,
% 2.34/2.50 (r(s(s(s(s(elem!1)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[842, 8624])).
% 2.34/2.50 tff(8626,plain,
% 2.34/2.50 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3107, 8625, 1393])).
% 2.34/2.50 tff(8627,plain,
% 2.34/2.50 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6107, 155, 8626, 3321, 3843])).
% 2.34/2.50 tff(8628,plain,
% 2.34/2.50 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1822, 8627, 1393])).
% 2.34/2.50 tff(8629,plain,
% 2.34/2.50 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[452, 8628])).
% 2.34/2.50 tff(8630,plain,
% 2.34/2.50 (~b(z, s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6125, 488, 494, 535, 226, 645, 338, 2597, 550, 2508, 1393, 126, 124])).
% 2.34/2.50 tff(8631,plain,
% 2.34/2.50 (r(z, s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[723, 8630])).
% 2.34/2.50 tff(8632,plain,
% 2.34/2.50 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3267, 339, 535, 441])).
% 2.34/2.50 tff(8633,plain,
% 2.34/2.50 (r(s(z), s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[280, 8632])).
% 2.34/2.50 tff(8634,plain,
% 2.34/2.50 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[503, 8633, 494, 488])).
% 2.34/2.50 tff(8635,plain,
% 2.34/2.50 (b(s(s(s(s(elem!1)))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[511, 8634])).
% 2.34/2.50 tff(8636,plain,
% 2.34/2.50 (~b(s(s(z)), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3240, 8635, 550, 339])).
% 2.34/2.50 tff(8637,plain,
% 2.34/2.50 (r(s(s(z)), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[122, 8636])).
% 2.34/2.50 tff(8638,plain,
% 2.34/2.50 (~b(z, s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1083, 8635, 82, 8633])).
% 2.34/2.50 tff(8639,plain,
% 2.34/2.50 (r(z, s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1093, 8638])).
% 2.34/2.50 tff(8640,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3746, 8639, 8637, 226, 729, 8633])).
% 2.34/2.50 tff(8641,plain,((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(z, s(z))) | b(s(s(s(elem!1))), s(z)) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(8642,plain,
% 2.34/2.50 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8641, 8631, 226, 82, 550, 488, 535, 8629])).
% 2.34/2.50 tff(8643,plain,
% 2.34/2.50 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[336, 8642])).
% 2.34/2.50 tff(8644,plain,
% 2.34/2.50 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[8643, 3323])).
% 2.34/2.50 tff(8645,plain,
% 2.34/2.50 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.34/2.50 inference(transitivity,[status(thm)],[8044, 5365])).
% 2.34/2.50 tff(8646,plain,
% 2.34/2.50 (~r(z, s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3326, 8643, 645, 1393, 8625])).
% 2.34/2.50 tff(8647,plain,
% 2.34/2.50 (b(z, s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1093, 8646])).
% 2.34/2.50 tff(8648,plain,
% 2.34/2.50 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[914, 8647, 126, 124])).
% 2.34/2.50 tff(8649,plain,
% 2.34/2.50 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[821, 8648, 4451])).
% 2.34/2.50 tff(8650,plain,
% 2.34/2.50 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[924, 8649, 6112, 488])).
% 2.34/2.50 tff(8651,plain,
% 2.34/2.50 (b(s(z), s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[280, 8650])).
% 2.34/2.50 tff(8652,plain,
% 2.34/2.50 (~b(s(s(z)), s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3067, 8651, 535, 8629])).
% 2.34/2.50 tff(8653,plain,
% 2.34/2.50 (r(s(s(z)), s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[437, 8652])).
% 2.34/2.50 tff(8654,plain,
% 2.34/2.50 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[8653, 8645])).
% 2.34/2.50 tff(8655,plain,
% 2.34/2.50 ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3695, 155, 488, 8626, 3321])).
% 2.34/2.50 tff(8656,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8655, 8654, 8644])).
% 2.34/2.50 tff(8657,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | b(s(s(s(elem!1))), s(z)) | (~b(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~(s(s(s(elem!1))) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(8658,plain,
% 2.34/2.50 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8657, 8623, 535, 3008, 8607, 8615, 8582, 82, 550, 8617, 8540, 6655])).
% 2.34/2.50 tff(8659,plain,
% 2.34/2.50 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[486, 8658, 8620])).
% 2.34/2.50 tff(8660,plain,
% 2.34/2.50 (~b(s(s(s(s(elem!1)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3290, 8659, 3008, 8617])).
% 2.34/2.50 tff(8661,plain,
% 2.34/2.50 (r(s(s(s(s(elem!1)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[842, 8660])).
% 2.34/2.50 tff(8662,plain,
% 2.34/2.50 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3326, 8661, 8607, 8615, 8619])).
% 2.34/2.50 tff(8663,plain,
% 2.34/2.50 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3349, 8659, 8617, 535, 8611, 494, 8610, 8582, 61, 8608, 8615, 585, 7137])).
% 2.34/2.50 tff(8664,plain,
% 2.34/2.50 (b(s(s(s(s(elem!1)))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[511, 8663])).
% 2.34/2.50 tff(8665,plain,
% 2.34/2.50 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3253, 8664, 6655, 61, 550, 535, 8540, 8615, 8582, 8623])).
% 2.34/2.50 tff(8666,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[336, 8665, 8662])).
% 2.34/2.50 tff(8667,plain,((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | r(z, s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(8668,plain,
% 2.34/2.50 (~b(s(s(s(z))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8667, 585, 550, 535, 61, 82])).
% 2.34/2.50 tff(8669,plain,
% 2.34/2.50 (r(s(s(s(z))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[402, 8668])).
% 2.34/2.50 tff(8670,plain,
% 2.34/2.50 (~b(s(s(z)), s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3997, 204, 550, 535])).
% 2.34/2.50 tff(8671,plain,
% 2.34/2.50 (r(s(s(z)), s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[437, 8670])).
% 2.34/2.50 tff(8672,plain,
% 2.34/2.50 (~b(s(s(z)), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2962, 204, 61, 535])).
% 2.34/2.50 tff(8673,plain,
% 2.34/2.50 (r(s(s(z)), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[625, 8672])).
% 2.34/2.50 tff(8674,plain,
% 2.34/2.50 (~r(z, s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6410, 8671, 386, 8673])).
% 2.34/2.50 tff(8675,plain,
% 2.34/2.50 (b(z, s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1318, 8674])).
% 2.34/2.50 tff(8676,plain,
% 2.34/2.50 (~b(s(s(z)), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3966, 204, 550, 535])).
% 2.34/2.50 tff(8677,plain,
% 2.34/2.50 (r(s(s(z)), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[122, 8676])).
% 2.34/2.50 tff(8678,plain,
% 2.34/2.50 (~r(s(z), s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2940, 8677, 8671, 8574])).
% 2.34/2.50 tff(8679,plain,
% 2.34/2.50 (b(s(z), s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[253, 8678])).
% 2.34/2.50 tff(8680,plain,
% 2.34/2.50 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2661, 204, 61, 535])).
% 2.34/2.50 tff(8681,plain,
% 2.34/2.50 (r(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[143, 8680])).
% 2.34/2.50 tff(8682,plain,
% 2.34/2.50 (~r(s(z), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1273, 8681, 125, 8677])).
% 2.34/2.50 tff(8683,plain,
% 2.34/2.50 (b(s(z), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[181, 8682])).
% 2.34/2.50 tff(8684,plain,
% 2.34/2.50 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7228, 8683, 61, 1331, 8679, 8675])).
% 2.34/2.50 tff(8685,plain,
% 2.34/2.50 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1995, 8684, 1331])).
% 2.34/2.50 tff(8686,plain,
% 2.34/2.50 (r(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[58, 8684])).
% 2.34/2.50 tff(8687,plain,
% 2.34/2.50 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[4024, 8686, 585, 8683, 535, 550, 61, 8574])).
% 2.34/2.50 tff(8688,plain,
% 2.34/2.50 (~b(s(s(s(elem!1))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1147, 61, 535, 124])).
% 2.34/2.50 tff(8689,plain,
% 2.34/2.50 (~b(s(s(s(z))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8531, 61, 1331, 535])).
% 2.34/2.50 tff(8690,plain,
% 2.34/2.50 (r(s(s(s(z))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1358, 8689])).
% 2.34/2.50 tff(8691,plain,
% 2.34/2.50 (r(s(s(s(elem!1))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[493, 8688])).
% 2.34/2.50 tff(8692,plain,
% 2.34/2.50 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7172, 8690, 8691, 1, 1331, 124, 61])).
% 2.34/2.50 tff(8693,plain,
% 2.34/2.50 (r(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[58, 8692])).
% 2.34/2.50 tff(8694,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2895, 97, 61, 204, 87, 535])).
% 2.34/2.50 tff(8695,plain,((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(8696,plain,
% 2.34/2.50 (~b(s(s(z)), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8695, 204, 61, 535])).
% 2.34/2.50 tff(8697,plain,
% 2.34/2.50 (r(s(s(z)), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[122, 8696])).
% 2.34/2.50 tff(8698,plain,
% 2.34/2.50 (~r(s(z), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8600, 8697, 61, 8691, 8693, 535, 1, 1331, 8690])).
% 2.34/2.50 tff(8699,plain,
% 2.34/2.50 (b(s(z), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[181, 8698])).
% 2.34/2.50 tff(8700,plain,
% 2.34/2.50 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[481, 8699, 124, 61])).
% 2.34/2.50 tff(8701,plain,
% 2.34/2.50 (~b(s(s(s(elem!1))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3979, 8699, 61, 124])).
% 2.34/2.50 tff(8702,plain,
% 2.34/2.50 (r(s(s(s(elem!1))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[246, 8701])).
% 2.34/2.50 tff(8703,plain,
% 2.34/2.50 (r(s(z), s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[280, 1245])).
% 2.34/2.50 tff(8704,plain,
% 2.34/2.50 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1248, 8699, 1245])).
% 2.34/2.50 tff(8705,plain,
% 2.34/2.50 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[486, 8700, 8704])).
% 2.34/2.50 tff(8706,plain,
% 2.34/2.50 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[503, 8705, 8691, 8703])).
% 2.34/2.50 tff(8707,plain,
% 2.34/2.50 (b(s(s(s(s(elem!1)))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[511, 8706])).
% 2.34/2.50 tff(8708,plain,
% 2.34/2.50 (~b(s(s(z)), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2962, 204, 535, 61])).
% 2.34/2.50 tff(8709,plain,
% 2.34/2.50 (r(s(s(z)), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[625, 8708])).
% 2.34/2.50 tff(8710,plain,
% 2.34/2.50 (~r(s(z), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[5689, 8697, 8709, 8690, 1961])).
% 2.34/2.50 tff(8711,plain,
% 2.34/2.50 (b(s(z), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[568, 8710])).
% 2.34/2.50 tff(8712,plain,
% 2.34/2.50 (~b(s(s(s(s(elem!1)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3648, 8705, 8691, 8711, 124])).
% 2.34/2.50 tff(8713,plain,
% 2.34/2.50 (r(s(s(s(s(elem!1)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[842, 8712])).
% 2.34/2.50 tff(8714,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2723, 8713, 8707, 535, 61, 8702, 8700, 8688])).
% 2.34/2.50 tff(8715,plain,((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(8716,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8715, 8687, 8685, 61, 1331, 3008, 535, 204, 8671])).
% 2.34/2.50 tff(8717,plain,((~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | r(z, s(s(s(elem!1)))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(8718,plain,
% 2.34/2.50 (~b(z, s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8717, 585, 7137, 535, 61, 550, 494, 8669])).
% 2.34/2.50 tff(8719,plain,
% 2.34/2.50 (r(z, s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[222, 8718])).
% 2.34/2.50 tff(8720,plain,
% 2.34/2.50 (~b(s(s(z)), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2651, 83, 535, 61])).
% 2.34/2.50 tff(8721,plain,
% 2.34/2.50 (r(s(s(z)), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[122, 8720])).
% 2.34/2.50 tff(8722,plain,
% 2.34/2.50 (~b(z, s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2972, 83, 550, 535])).
% 2.34/2.50 tff(8723,plain,
% 2.34/2.50 (r(z, s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1318, 8722])).
% 2.34/2.50 tff(8724,plain,
% 2.34/2.50 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6652, 8723, 585])).
% 2.34/2.50 tff(8725,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8606, 8724, 8721, 3008, 61, 125, 535, 1331, 226])).
% 2.34/2.50 tff(8726,plain,((~b(s(s(z)), z)) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | r(z, s(s(s(elem!1)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(8727,plain,
% 2.34/2.50 (~b(s(s(z)), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8726, 8719, 494, 535, 7137, 61, 585, 550])).
% 2.34/2.50 tff(8728,plain,
% 2.34/2.50 (r(s(s(z)), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[625, 8727])).
% 2.34/2.50 tff(8729,plain,
% 2.34/2.50 (r(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3954, 8728, 82, 550, 535, 585, 8719])).
% 2.34/2.50 tff(8730,plain,
% 2.34/2.50 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[1393])).
% 2.34/2.50 tff(8731,plain,
% 2.34/2.50 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(z))), s(s(z)))),
% 2.34/2.50 inference(symmetry,[status(thm)],[8730])).
% 2.34/2.50 tff(8732,plain,
% 2.34/2.50 (r(s(s(s(z))), s(s(z)))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[145, 8731])).
% 2.34/2.50 tff(8733,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8538, 8732])).
% 2.34/2.50 tff(8734,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | r(s(s(s(z))), s(s(z))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(8735,plain,
% 2.34/2.50 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8734, 8729, 8538])).
% 2.34/2.50 tff(8736,plain,
% 2.34/2.50 (~r(s(s(z)), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8606, 8735, 3008, 61, 494, 535, 7137, 8719])).
% 2.34/2.50 tff(8737,plain,
% 2.34/2.50 (b(s(s(z)), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[122, 8736])).
% 2.34/2.50 tff(8738,plain,
% 2.34/2.50 (~r(s(s(s(s(z)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8576, 8737, 535, 550, 61, 7137])).
% 2.34/2.50 tff(8739,plain,
% 2.34/2.50 (b(s(s(s(s(z)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2860, 8738])).
% 2.34/2.50 tff(8740,plain,
% 2.34/2.50 (~r(s(s(s(elem!1))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3956, 8728, 550, 82, 535, 585, 8719])).
% 2.34/2.50 tff(8741,plain,
% 2.34/2.50 (b(s(s(s(elem!1))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[246, 8740])).
% 2.34/2.50 tff(8742,plain,
% 2.34/2.50 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7632, 97, 61, 8741, 8739])).
% 2.34/2.50 tff(8743,plain,
% 2.34/2.50 (((~![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(z), z)) | (~b(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)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(8744,plain,
% 2.34/2.50 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(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)))), z)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(8745,plain,
% 2.34/2.50 (((~![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(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), 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(z), z)) | (~b(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)))), z))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[8744])).
% 2.34/2.50 tff(8746,plain,
% 2.34/2.50 (((~![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(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), 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(z), z)) | (~b(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)))), z)))),
% 2.34/2.50 inference(transitivity,[status(thm)],[8745, 8743])).
% 2.34/2.50 tff(8747,plain,
% 2.34/2.50 ((~![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(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(8748,plain,
% 2.34/2.50 ((~![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(z), z)) | (~b(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)))), z))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[8747, 8746])).
% 2.34/2.50 tff(8749,plain,
% 2.34/2.50 (~b(s(s(s(s(z)))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8748, 97, 550, 61, 8737, 535, 8739])).
% 2.34/2.50 tff(8750,plain,
% 2.34/2.50 (r(s(s(s(s(z)))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2807, 8749, 2795])).
% 2.34/2.50 tff(8751,plain,
% 2.34/2.50 (~b(s(z), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3979, 8741, 61, 3008])).
% 2.34/2.50 tff(8752,plain,
% 2.34/2.50 (r(s(z), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[181, 8751])).
% 2.34/2.50 tff(8753,plain,
% 2.34/2.50 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7644, 155, 494, 8752, 8750])).
% 2.34/2.50 tff(8754,plain,
% 2.34/2.50 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7637, 53, 8753, 8742])).
% 2.34/2.50 tff(8755,plain,
% 2.34/2.50 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[8754])).
% 2.34/2.50 tff(8756,plain,
% 2.34/2.50 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 2.34/2.50 inference(symmetry,[status(thm)],[8755])).
% 2.34/2.50 tff(8757,plain,
% 2.34/2.50 (s(s(elem!1)) = s(s(s(z)))),
% 2.34/2.50 inference(transitivity,[status(thm)],[167, 8756, 63])).
% 2.34/2.50 tff(8758,plain,
% 2.34/2.50 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[8757])).
% 2.34/2.50 tff(8759,plain,
% 2.34/2.50 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.34/2.50 inference(symmetry,[status(thm)],[8758])).
% 2.34/2.50 tff(8760,plain,
% 2.34/2.50 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[5757, 8752, 8540, 494])).
% 2.34/2.50 tff(8761,plain,
% 2.34/2.50 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3089, 8735, 8760])).
% 2.34/2.50 tff(8762,plain,
% 2.34/2.50 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[8761, 8759])).
% 2.34/2.50 tff(8763,plain,
% 2.34/2.50 (s(s(s(z))) = s(s(elem!1))),
% 2.34/2.50 inference(transitivity,[status(thm)],[2792, 8755, 19])).
% 2.34/2.50 tff(8764,plain,
% 2.34/2.50 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[8763])).
% 2.34/2.50 tff(8765,plain,
% 2.34/2.50 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[8764])).
% 2.34/2.50 tff(8766,plain,
% 2.34/2.50 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[286, 8765])).
% 2.34/2.50 tff(8767,plain,
% 2.34/2.50 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[349, 8766])).
% 2.34/2.50 tff(8768,plain,
% 2.34/2.50 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[523, 8767])).
% 2.34/2.50 tff(8769,plain,
% 2.34/2.50 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7172, 2597, 8691, 1, 1331, 124, 61])).
% 2.34/2.50 tff(8770,plain,
% 2.34/2.50 (r(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[58, 8769])).
% 2.34/2.50 tff(8771,plain,
% 2.34/2.50 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2661, 204, 535, 61])).
% 2.34/2.50 tff(8772,plain,
% 2.34/2.50 (r(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[143, 8771])).
% 2.34/2.50 tff(8773,plain,
% 2.34/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(8774,plain,
% 2.34/2.51 (((~r(s(z), z)) | (~r(s(s(z)), z)) | (~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(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(8775,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[8774])).
% 2.34/2.51 tff(8776,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[8775, 8773])).
% 2.34/2.51 tff(8777,plain,
% 2.34/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(8778,plain,
% 2.34/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[8777, 8776])).
% 2.34/2.51 tff(8779,plain,
% 2.34/2.51 (~r(s(s(z)), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8778, 155, 125, 81, 8709, 8772])).
% 2.34/2.51 tff(8780,plain,
% 2.34/2.51 (b(s(s(z)), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[122, 8779])).
% 2.34/2.51 tff(8781,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6965, 97, 61, 255, 204, 8780])).
% 2.34/2.51 tff(8782,plain,((~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(8783,plain,
% 2.34/2.51 (~b(z, s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8782, 81, 255, 8691, 61, 535])).
% 2.34/2.51 tff(8784,plain,
% 2.34/2.51 (r(z, s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[222, 8783])).
% 2.34/2.51 tff(8785,plain,
% 2.34/2.51 (~r(s(s(s(elem!1))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3987, 8784, 61, 8691, 8770, 535])).
% 2.34/2.51 tff(8786,plain,
% 2.34/2.51 (b(s(s(s(elem!1))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[246, 8785])).
% 2.34/2.51 tff(8787,plain,
% 2.34/2.51 (~b(s(z), s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3979, 8786, 61, 124])).
% 2.34/2.51 tff(8788,plain,
% 2.34/2.51 (r(s(z), s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[181, 8787])).
% 2.34/2.51 tff(8789,plain,
% 2.34/2.51 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[5757, 8788, 2597, 8691])).
% 2.34/2.51 tff(8790,plain,
% 2.34/2.51 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3089, 8789, 1])).
% 2.34/2.51 tff(8791,plain,
% 2.34/2.51 (~b(s(s(s(z))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[4360, 97, 8786, 124, 8790])).
% 2.34/2.51 tff(8792,plain,
% 2.34/2.51 (r(s(s(s(z))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[402, 8791])).
% 2.34/2.51 tff(8793,plain,
% 2.34/2.51 (~b(z, s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6008, 97, 8786, 124, 8790])).
% 2.34/2.51 tff(8794,plain,
% 2.34/2.51 (r(z, s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1318, 8793])).
% 2.34/2.51 tff(8795,plain,
% 2.34/2.51 (~r(s(z), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1308, 8794, 81, 8792])).
% 2.34/2.51 tff(8796,plain,
% 2.34/2.51 (b(s(z), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[253, 8795])).
% 2.34/2.51 tff(8797,plain,
% 2.34/2.51 (((~![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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(8798,plain,
% 2.34/2.51 (((~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(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(8799,plain,
% 2.34/2.51 (((~![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(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[8798])).
% 2.34/2.51 tff(8800,plain,
% 2.34/2.51 (((~![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(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[8799, 8797])).
% 2.34/2.51 tff(8801,plain,
% 2.34/2.51 ((~![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(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(8802,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[8801, 8800])).
% 2.34/2.51 tff(8803,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8802, 97, 535, 1361, 1331, 86])).
% 2.34/2.51 tff(8804,plain,((~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(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(8805,plain,
% 2.34/2.51 (~b(s(s(z)), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8804, 8796, 1331, 535])).
% 2.34/2.51 tff(8806,plain,
% 2.34/2.51 (r(s(s(z)), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[437, 8805])).
% 2.34/2.51 tff(8807,plain,
% 2.34/2.51 (~r(s(s(z)), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[4047, 155, 8794, 8806, 8792])).
% 2.34/2.51 tff(8808,plain,
% 2.34/2.51 (b(s(s(z)), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[625, 8807])).
% 2.34/2.51 tff(8809,plain,
% 2.34/2.51 (~b(s(s(z)), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[105, 8808, 8796, 61])).
% 2.34/2.51 tff(8810,plain,
% 2.34/2.51 (r(s(s(z)), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[122, 8809])).
% 2.34/2.51 tff(8811,plain,
% 2.34/2.51 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[135, 8808, 61, 8786])).
% 2.34/2.51 tff(8812,plain,
% 2.34/2.51 (r(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[143, 8811])).
% 2.34/2.51 tff(8813,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1273, 8812, 8810, 8691, 8788])).
% 2.34/2.51 tff(8814,plain,((~r(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(8815,plain,
% 2.34/2.51 (~r(s(z), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8814, 2597, 1331, 535, 3008, 1, 61, 255])).
% 2.34/2.51 tff(8816,plain,
% 2.34/2.51 (b(s(z), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[568, 8815])).
% 2.34/2.51 tff(8817,plain,
% 2.34/2.51 (~b(s(s(s(s(elem!1)))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3055, 8816, 255, 61])).
% 2.34/2.51 tff(8818,plain,
% 2.34/2.51 (r(s(s(s(s(elem!1)))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[842, 8817])).
% 2.34/2.51 tff(8819,plain,
% 2.34/2.51 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7172, 2597, 3977, 1, 1331, 3008, 61])).
% 2.34/2.51 tff(8820,plain,
% 2.34/2.51 (r(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[58, 8819])).
% 2.34/2.51 tff(8821,plain,
% 2.34/2.51 (~b(s(z), s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[4024, 2597, 255, 61, 535, 8816, 585, 8820])).
% 2.34/2.51 tff(8822,plain,
% 2.34/2.51 (r(s(z), s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[181, 8821])).
% 2.34/2.51 tff(8823,plain,
% 2.34/2.51 (~r(s(s(z)), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8600, 8822, 61, 3977, 8820, 535, 1, 1331, 2597])).
% 2.34/2.51 tff(8824,plain,
% 2.34/2.51 (b(s(s(z)), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[122, 8823])).
% 2.34/2.51 tff(8825,plain,
% 2.34/2.51 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2905, 8824, 535, 61, 8818])).
% 2.34/2.51 tff(8826,plain,
% 2.34/2.51 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[452, 8825])).
% 2.34/2.51 tff(8827,plain,
% 2.34/2.51 (~b(s(s(z)), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3067, 8826, 535, 255])).
% 2.34/2.51 tff(8828,plain,
% 2.34/2.51 (r(s(s(z)), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[437, 8827])).
% 2.34/2.51 tff(8829,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(8830,plain,
% 2.34/2.51 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(8831,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[8830])).
% 2.34/2.51 tff(8832,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[8831, 8829])).
% 2.34/2.51 tff(8833,plain,
% 2.34/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(8834,plain,
% 2.34/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[8833, 8832])).
% 2.34/2.51 tff(8835,plain,
% 2.34/2.51 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8834, 155, 3977, 8820, 8828, 2597])).
% 2.34/2.51 tff(8836,plain,
% 2.34/2.51 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2687, 8835, 4228])).
% 2.34/2.51 tff(8837,plain,
% 2.34/2.51 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3267, 8826, 535, 255])).
% 2.34/2.51 tff(8838,plain,
% 2.34/2.51 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[336, 8837])).
% 2.34/2.51 tff(8839,plain,
% 2.34/2.51 (~b(s(s(z)), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2651, 8824, 535, 61])).
% 2.34/2.51 tff(8840,plain,
% 2.34/2.51 (r(s(s(z)), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[625, 8839])).
% 2.34/2.51 tff(8841,plain,
% 2.34/2.51 (~b(z, s(s(s(s(elem!1)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1494, 8826, 61, 255])).
% 2.34/2.51 tff(8842,plain,
% 2.34/2.51 (r(z, s(s(s(s(elem!1)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1093, 8841])).
% 2.34/2.51 tff(8843,plain,
% 2.34/2.51 (~r(s(s(s(z))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3077, 8842, 8840, 8828, 8838])).
% 2.34/2.51 tff(8844,plain,
% 2.34/2.51 (b(s(s(s(z))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[402, 8843])).
% 2.34/2.51 tff(8845,plain,
% 2.34/2.51 (~b(z, s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3966, 8824, 535, 8816])).
% 2.34/2.51 tff(8846,plain,
% 2.34/2.51 (r(z, s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[222, 8845])).
% 2.34/2.51 tff(8847,plain,
% 2.34/2.51 (~r(s(s(s(elem!1))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3987, 8846, 61, 3977, 8820, 535])).
% 2.34/2.51 tff(8848,plain,
% 2.34/2.51 (b(s(s(s(elem!1))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[246, 8847])).
% 2.34/2.51 tff(8849,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6096, 97, 61, 8848, 8844, 8836])).
% 2.34/2.51 tff(8850,plain,((~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(8851,plain,
% 2.34/2.51 (~r(s(s(s(z))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8850, 255, 535, 61, 1, 1331, 585])).
% 2.34/2.51 tff(8852,plain,
% 2.34/2.51 (b(s(s(s(z))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1358, 8851])).
% 2.34/2.51 tff(8853,plain,
% 2.34/2.51 (((~![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(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(8854,plain,
% 2.34/2.51 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(8855,plain,
% 2.34/2.51 (((~![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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(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(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[8854])).
% 2.34/2.51 tff(8856,plain,
% 2.34/2.51 (((~![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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(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(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.34/2.51 inference(transitivity,[status(thm)],[8855, 8853])).
% 2.34/2.51 tff(8857,plain,
% 2.34/2.51 ((~![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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(8858,plain,
% 2.34/2.51 ((~![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(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[8857, 8856])).
% 2.34/2.51 tff(8859,plain,
% 2.34/2.51 (~b(s(s(s(z))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8858, 97, 61, 255, 8852])).
% 2.34/2.51 tff(8860,plain,
% 2.34/2.51 (r(s(s(s(z))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[402, 8859])).
% 2.34/2.51 tff(8861,plain,
% 2.34/2.51 (~b(s(s(z)), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3585, 8852, 535, 1331])).
% 2.34/2.51 tff(8862,plain,
% 2.34/2.51 (r(s(s(z)), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[437, 8861])).
% 2.34/2.51 tff(8863,plain,
% 2.34/2.51 (((~![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(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(8864,plain,
% 2.34/2.51 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(8865,plain,
% 2.34/2.51 (((~![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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[8864])).
% 2.34/2.51 tff(8866,plain,
% 2.34/2.51 (((~![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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[8865, 8863])).
% 2.34/2.51 tff(8867,plain,
% 2.34/2.51 ((~![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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(8868,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[8867, 8866])).
% 2.34/2.51 tff(8869,plain,
% 2.34/2.51 (~b(z, s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8868, 97, 61, 255, 8852])).
% 2.34/2.51 tff(8870,plain,
% 2.34/2.51 (r(z, s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1318, 8869])).
% 2.34/2.51 tff(8871,plain,
% 2.34/2.51 (~r(s(s(z)), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[4047, 155, 8870, 8862, 8860])).
% 2.34/2.51 tff(8872,plain,
% 2.34/2.51 (b(s(s(z)), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[625, 8871])).
% 2.34/2.51 tff(8873,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8529, 97, 8872, 535, 8852, 1331])).
% 2.34/2.51 tff(8874,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(8875,plain,
% 2.34/2.51 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8874, 8735, 61, 7137, 535, 585])).
% 2.34/2.51 tff(8876,plain,
% 2.34/2.51 (r(s(z), s(s(s(s(elem!1)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[280, 8875])).
% 2.34/2.51 tff(8877,plain,
% 2.34/2.51 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[8757])).
% 2.34/2.51 tff(8878,plain,
% 2.34/2.51 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.34/2.51 inference(symmetry,[status(thm)],[8877])).
% 2.34/2.51 tff(8879,plain,
% 2.34/2.51 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2682, 8735])).
% 2.34/2.51 tff(8880,plain,
% 2.34/2.51 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8834, 155, 8691, 8693, 1961, 8690])).
% 2.34/2.51 tff(8881,plain,
% 2.34/2.51 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2687, 8880, 4228])).
% 2.34/2.51 tff(8882,plain,
% 2.34/2.51 (~b(z, s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[8715, 1961, 61, 124, 1245, 535, 1, 1331])).
% 2.34/2.51 tff(8883,plain,
% 2.34/2.51 (r(z, s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[222, 8882])).
% 2.34/2.51 tff(8884,plain,
% 2.34/2.51 (~r(s(s(s(elem!1))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3987, 8883, 61, 8691, 8693, 535])).
% 2.34/2.51 tff(8885,plain,
% 2.34/2.51 (b(s(s(s(elem!1))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[246, 8884])).
% 2.34/2.51 tff(8886,plain,
% 2.34/2.51 (~b(s(z), s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3979, 8885, 61, 124])).
% 2.34/2.51 tff(8887,plain,
% 2.34/2.51 (r(s(z), s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[181, 8886])).
% 2.34/2.51 tff(8888,plain,
% 2.34/2.51 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[5757, 8887, 8690, 8691])).
% 2.34/2.51 tff(8889,plain,
% 2.34/2.51 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3089, 8888, 1])).
% 2.34/2.51 tff(8890,plain,
% 2.34/2.51 (((~![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(s(s(elem!1))))) | (~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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(8891,plain,
% 2.34/2.51 (((~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(z, s(s(s(elem!1))))) | (~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))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(8892,plain,
% 2.34/2.52 (((~![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(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(z, s(s(s(elem!1))))) | (~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)))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[8891])).
% 2.34/2.52 tff(8893,plain,
% 2.34/2.52 (((~![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(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(z, s(s(s(elem!1))))) | (~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))))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[8892, 8890])).
% 2.34/2.52 tff(8894,plain,
% 2.34/2.52 ((~![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(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)))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(8895,plain,
% 2.34/2.52 ((~![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(s(elem!1))))) | (~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)))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[8894, 8893])).
% 2.34/2.52 tff(8896,plain,
% 2.34/2.52 (~b(s(s(s(z))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[8895, 97, 124, 8889, 8881])).
% 2.34/2.52 tff(8897,plain,
% 2.34/2.52 (r(s(s(s(z))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[402, 8896])).
% 2.34/2.52 tff(8898,plain,
% 2.34/2.52 (((~![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(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(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(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(8899,plain,
% 2.34/2.52 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(8900,plain,
% 2.34/2.52 (((~![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(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[8899])).
% 2.34/2.52 tff(8901,plain,
% 2.34/2.52 (((~![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(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[8900, 8898])).
% 2.34/2.52 tff(8902,plain,
% 2.34/2.52 ((~![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(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(8903,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[8902, 8901])).
% 2.34/2.52 tff(8904,plain,
% 2.34/2.52 (~b(z, s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[8903, 97, 124, 8889, 8881])).
% 2.34/2.52 tff(8905,plain,
% 2.34/2.52 (r(z, s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1318, 8904])).
% 2.34/2.52 tff(8906,plain,
% 2.34/2.52 (~r(s(s(z)), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[8600, 8887, 61, 8691, 8693, 535, 1, 1331, 8690])).
% 2.34/2.52 tff(8907,plain,
% 2.34/2.52 (b(s(s(z)), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[122, 8906])).
% 2.34/2.52 tff(8908,plain,
% 2.34/2.52 (~b(s(s(z)), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2651, 8907, 535, 61])).
% 2.34/2.52 tff(8909,plain,
% 2.34/2.52 (r(s(s(z)), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[625, 8908])).
% 2.34/2.52 tff(8910,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[4047, 155, 8909, 8905, 1961, 8897])).
% 2.34/2.52 tff(8911,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | b(s(z), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(8912,plain,
% 2.34/2.52 (~r(s(s(z)), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[8911, 8875, 61, 7137, 3008, 535, 8735])).
% 2.34/2.52 tff(8913,plain,
% 2.34/2.52 (b(s(s(z)), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[437, 8912])).
% 2.34/2.52 tff(8914,plain,
% 2.34/2.52 (~b(s(z), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[8804, 8913, 7137, 535])).
% 2.34/2.52 tff(8915,plain,
% 2.34/2.52 (r(s(z), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[253, 8914])).
% 2.34/2.52 tff(8916,plain,
% 2.34/2.52 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2638, 8915, 8540, 494])).
% 2.34/2.52 tff(8917,plain,
% 2.34/2.52 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2687, 8916, 8879])).
% 2.34/2.52 tff(8918,plain,
% 2.34/2.52 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[8917, 8878])).
% 2.34/2.52 tff(8919,plain,
% 2.34/2.52 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[8757])).
% 2.34/2.52 tff(8920,plain,
% 2.34/2.52 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 2.34/2.52 inference(symmetry,[status(thm)],[8919])).
% 2.34/2.52 tff(8921,plain,
% 2.34/2.52 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[8763])).
% 2.34/2.52 tff(8922,plain,
% 2.34/2.52 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 2.34/2.52 inference(symmetry,[status(thm)],[8921])).
% 2.34/2.52 tff(8923,plain,
% 2.34/2.52 ((~b(z, s(s(elem!1)))) <=> (~b(z, s(s(s(z)))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[8922])).
% 2.34/2.52 tff(8924,plain,
% 2.34/2.52 (((~![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(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(8925,plain,
% 2.34/2.52 (((~b(s(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(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(8926,plain,
% 2.34/2.52 (((~![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(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[8925])).
% 2.34/2.52 tff(8927,plain,
% 2.34/2.52 (((~![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(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[8926, 8924])).
% 2.34/2.52 tff(8928,plain,
% 2.34/2.52 ((~![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(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(8929,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[8928, 8927])).
% 2.34/2.52 tff(8930,plain,
% 2.34/2.52 (~b(z, s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[8929, 97, 8741, 3008, 8762])).
% 2.34/2.52 tff(8931,plain,
% 2.34/2.52 (~b(z, s(s(s(z))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[8930, 8923])).
% 2.34/2.52 tff(8932,plain,
% 2.34/2.52 (r(z, s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1318, 8931])).
% 2.34/2.52 tff(8933,plain,
% 2.34/2.52 (r(z, s(s(elem!1)))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[8932, 8920])).
% 2.34/2.52 tff(8934,plain,
% 2.34/2.52 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 2.34/2.52 inference(monotonicity,[status(thm)],[8763])).
% 2.34/2.52 tff(8935,plain,
% 2.34/2.52 (r(s(s(elem!1)), z)),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[8669, 8934])).
% 2.34/2.52 tff(8936,plain,
% 2.34/2.52 (~b(s(s(s(s(elem!1)))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7659, 8767, 494, 550, 3008, 8741])).
% 2.34/2.52 tff(8937,plain,
% 2.34/2.52 (r(s(s(s(s(elem!1)))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[842, 8936])).
% 2.34/2.52 tff(8938,plain,
% 2.34/2.52 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7685, 8937, 8935, 8933])).
% 2.34/2.52 tff(8939,plain,
% 2.34/2.52 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1484, 8938, 8766])).
% 2.34/2.52 tff(8940,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1584, 97, 1545, 473, 1529, 2391])).
% 2.34/2.52 tff(8941,plain,((~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(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(8942,plain,
% 2.34/2.52 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[8941, 8939, 8918, 8762])).
% 2.34/2.52 tff(8943,plain,
% 2.34/2.52 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[486, 8942, 8767])).
% 2.34/2.52 tff(8944,plain,
% 2.34/2.52 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[924, 8943, 8752, 8876])).
% 2.34/2.52 tff(8945,plain,
% 2.34/2.52 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[821, 8944, 8768])).
% 2.34/2.52 tff(8946,plain,
% 2.34/2.52 (((~![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(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), z)) | (~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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(8947,plain,
% 2.34/2.52 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(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)))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(8948,plain,
% 2.34/2.52 (((~![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(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(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))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[8947])).
% 2.34/2.52 tff(8949,plain,
% 2.34/2.52 (((~![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(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(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)))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[8948, 8946])).
% 2.34/2.52 tff(8950,plain,
% 2.34/2.52 ((~![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(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(8951,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[8950, 8949])).
% 2.34/2.52 tff(8952,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[8951, 97, 8939, 8741, 3008, 8918, 8945, 8762])).
% 2.34/2.52 tff(8953,plain,(r(z, s(s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | r(s(s(s(z))), s(s(z))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(8954,plain,
% 2.34/2.52 (r(z, s(s(s(elem!1))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[8953, 535, 61, 550, 8538, 82])).
% 2.34/2.52 tff(8955,plain,
% 2.34/2.52 (~b(s(s(z)), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[8535, 535, 61, 550])).
% 2.34/2.52 tff(8956,plain,
% 2.34/2.52 (r(s(s(z)), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[625, 8955])).
% 2.34/2.52 tff(8957,plain,
% 2.34/2.52 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2253, 2, 125, 570, 645])).
% 2.34/2.52 tff(8958,plain,
% 2.34/2.52 (b(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[143, 8957])).
% 2.34/2.52 tff(8959,plain,
% 2.34/2.52 (((~![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(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(8960,plain,
% 2.34/2.52 (((~b(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(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(8961,plain,
% 2.34/2.52 (((~![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(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(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[8960])).
% 2.34/2.52 tff(8962,plain,
% 2.34/2.52 (((~![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(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(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[8961, 8959])).
% 2.34/2.52 tff(8963,plain,
% 2.34/2.52 ((~![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(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))))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(8964,plain,
% 2.34/2.52 ((~![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(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[8963, 8962])).
% 2.34/2.52 tff(8965,plain,
% 2.34/2.52 (~b(s(z), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[8964, 97, 535, 1331, 8958])).
% 2.34/2.52 tff(8966,plain,
% 2.34/2.52 (r(s(z), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[253, 8965])).
% 2.34/2.52 tff(8967,plain,
% 2.34/2.52 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2638, 8966, 2597, 125])).
% 2.34/2.52 tff(8968,plain,
% 2.34/2.52 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2687, 8967, 2466])).
% 2.34/2.52 tff(8969,plain,
% 2.34/2.52 (~r(s(s(z)), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2940, 8966, 2, 2597])).
% 2.34/2.52 tff(8970,plain,
% 2.34/2.52 (b(s(s(z)), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[437, 8969])).
% 2.34/2.52 tff(8971,plain,
% 2.34/2.52 (((~![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(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(8972,plain,
% 2.34/2.52 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(8973,plain,
% 2.34/2.52 (((~![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(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(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(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[8972])).
% 2.34/2.52 tff(8974,plain,
% 2.34/2.52 (((~![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(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(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(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[8973, 8971])).
% 2.34/2.52 tff(8975,plain,
% 2.34/2.52 ((~![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(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(8976,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[8975, 8974])).
% 2.34/2.52 tff(8977,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[8976, 97, 8970, 1331, 8958, 8968])).
% 2.34/2.52 tff(8978,plain,((~r(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(8979,plain,
% 2.34/2.52 (~r(s(s(z)), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[8978, 645, 4228, 8574, 125, 535, 570, 1331])).
% 2.34/2.52 tff(8980,plain,
% 2.34/2.52 (b(s(s(z)), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[122, 8979])).
% 2.34/2.52 tff(8981,plain,
% 2.34/2.53 (~r(s(s(s(s(z)))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[8576, 8980, 535, 550, 61, 1331])).
% 2.34/2.53 tff(8982,plain,
% 2.34/2.53 (b(s(s(s(s(z)))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2860, 8981])).
% 2.34/2.53 tff(8983,plain,
% 2.34/2.53 (~b(s(s(s(s(z)))), s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[8748, 97, 550, 61, 8980, 535, 8982])).
% 2.34/2.53 tff(8984,plain,
% 2.34/2.53 (r(s(s(s(s(z)))), s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2807, 8983, 2795])).
% 2.34/2.53 tff(8985,plain,
% 2.34/2.53 (((~![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(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(8986,plain,
% 2.34/2.53 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), 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(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(8987,plain,
% 2.34/2.53 (((~![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(z)), s(z))) | (~b(s(s(z)), 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(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[8986])).
% 2.34/2.53 tff(8988,plain,
% 2.34/2.53 (((~![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(z)), s(z))) | (~b(s(s(z)), 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(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[8987, 8985])).
% 2.34/2.53 tff(8989,plain,
% 2.34/2.53 ((~![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(z)), s(z))) | (~b(s(s(z)), 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))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(8990,plain,
% 2.34/2.53 ((~![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(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[8989, 8988])).
% 2.34/2.53 tff(8991,plain,
% 2.34/2.53 (~b(s(z), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[8990, 97, 8980, 535, 1331])).
% 2.34/2.53 tff(8992,plain,
% 2.34/2.53 (r(s(z), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[253, 8991])).
% 2.34/2.53 tff(8993,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(8994,plain,
% 2.34/2.53 (((~r(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))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(8995,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[8994])).
% 2.34/2.53 tff(8996,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[8995, 8993])).
% 2.34/2.53 tff(8997,plain,
% 2.34/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(8998,plain,
% 2.34/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[8997, 8996])).
% 2.34/2.53 tff(8999,plain,
% 2.34/2.53 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[8998, 155, 8992, 8574, 8984])).
% 2.34/2.53 tff(9000,plain,
% 2.34/2.53 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[4169, 8999])).
% 2.34/2.53 tff(9001,plain,
% 2.34/2.53 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2638, 8992, 8574, 125])).
% 2.34/2.53 tff(9002,plain,
% 2.34/2.53 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2687, 9001, 4228])).
% 2.34/2.53 tff(9003,plain,
% 2.34/2.53 (((~![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(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(9004,plain,
% 2.34/2.53 (((~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(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(9005,plain,
% 2.34/2.53 (((~![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(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[9004])).
% 2.34/2.53 tff(9006,plain,
% 2.34/2.53 (((~![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(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[9005, 9003])).
% 2.34/2.53 tff(9007,plain,
% 2.34/2.53 ((~![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(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(9008,plain,
% 2.34/2.53 ((~![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(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[9007, 9006])).
% 2.34/2.53 tff(9009,plain,
% 2.34/2.53 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[9008, 97, 1331, 9002, 9000])).
% 2.34/2.53 tff(9010,plain,
% 2.34/2.53 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2839, 97, 550, 61, 8982])).
% 2.34/2.53 tff(9011,plain,
% 2.34/2.53 (r(s(z), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2844, 9010, 2833])).
% 2.34/2.53 tff(9012,plain,
% 2.34/2.53 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7895, 155, 125, 9011, 8984])).
% 2.34/2.53 tff(9013,plain,
% 2.34/2.53 ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7906, 53, 9012])).
% 2.34/2.53 tff(9014,plain,
% 2.34/2.53 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[9013, 9009])).
% 2.34/2.53 tff(9015,plain,
% 2.34/2.53 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[9014])).
% 2.34/2.53 tff(9016,plain,
% 2.34/2.53 (r(z, s(s(s(s(z)))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[570, 9015])).
% 2.34/2.53 tff(9017,plain,
% 2.34/2.53 (~b(s(s(s(z))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2853, 8982, 61, 8574, 550])).
% 2.34/2.53 tff(9018,plain,
% 2.34/2.53 (r(s(s(s(z))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[402, 9017])).
% 2.34/2.53 tff(9019,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 2.34/2.53 tff(9020,plain,
% 2.34/2.53 (((~![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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(9021,plain,
% 2.34/2.53 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(9022,plain,
% 2.34/2.53 (((~![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(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[9021])).
% 2.34/2.53 tff(9023,plain,
% 2.34/2.53 (((~![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(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[9022, 9020])).
% 2.34/2.53 tff(9024,plain,
% 2.34/2.53 ((~![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(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(9025,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[9024, 9023])).
% 2.34/2.53 tff(9026,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[9025, 97, 61, 535, 1331, 1330, 9019, 2796])).
% 2.34/2.53 tff(9027,plain,((~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(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(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(9028,plain,
% 2.34/2.53 (~b(z, s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[9027, 9000, 535, 1331, 61, 8982])).
% 2.34/2.53 tff(9029,plain,
% 2.34/2.53 (r(z, s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1318, 9028])).
% 2.34/2.53 tff(9030,plain,
% 2.34/2.53 (~r(s(s(z)), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[6410, 9029, 9018, 645])).
% 2.34/2.53 tff(9031,plain,
% 2.34/2.53 (b(s(s(z)), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[437, 9030])).
% 2.34/2.53 tff(9032,plain,
% 2.34/2.53 (((~![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(z)), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(9033,plain,
% 2.34/2.53 (((~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(z)), 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))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(9034,plain,
% 2.34/2.53 (((~![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(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(z)), 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)))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[9033])).
% 2.34/2.53 tff(9035,plain,
% 2.34/2.53 (((~![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(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(z)), 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))))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[9034, 9032])).
% 2.34/2.53 tff(9036,plain,
% 2.34/2.53 ((~![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(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)))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(9037,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[9036, 9035])).
% 2.34/2.53 tff(9038,plain,
% 2.34/2.53 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[9037, 97, 9031, 1331, 9000])).
% 2.34/2.53 tff(9039,plain,
% 2.34/2.53 (r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[4192, 9038, 2595])).
% 2.34/2.53 tff(9040,plain,
% 2.34/2.53 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[9014])).
% 2.34/2.53 tff(9041,plain,
% 2.34/2.53 ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[5957, 155, 125, 570, 8574])).
% 2.34/2.53 tff(9042,plain,
% 2.34/2.53 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[9041, 9018])).
% 2.34/2.53 tff(9043,plain,
% 2.34/2.53 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[3089, 9042, 1])).
% 2.34/2.53 tff(9044,plain,
% 2.34/2.53 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[3662, 9043, 1331, 8980])).
% 2.34/2.53 tff(9045,plain,
% 2.34/2.53 (r(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[58, 9044])).
% 2.34/2.53 tff(9046,plain,
% 2.34/2.53 (r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[9045, 9040])).
% 2.34/2.53 tff(9047,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2253, 8681, 8677, 125, 570, 645])).
% 2.34/2.53 tff(9048,plain,((~b(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(9049,plain,
% 2.34/2.53 (~b(z, s(s(z)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[9048, 645, 570, 125, 61, 535, 550])).
% 2.34/2.53 tff(9050,plain,
% 2.34/2.53 (r(z, s(s(z)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[222, 9049])).
% 2.34/2.53 tff(9051,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(9052,plain,
% 2.34/2.53 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(9053,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9052])).
% 2.34/2.54 tff(9054,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[9053, 9051])).
% 2.34/2.54 tff(9055,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(9056,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[9055, 9054])).
% 2.34/2.54 tff(9057,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[9056, 155, 9050, 9046, 9039, 9016])).
% 2.34/2.54 tff(9058,plain,((~r(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(9059,plain,
% 2.34/2.54 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[9058, 8956, 535, 61, 570, 125, 550, 1331])).
% 2.34/2.54 tff(9060,plain,
% 2.34/2.54 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.34/2.54 inference(symmetry,[status(thm)],[9059])).
% 2.34/2.54 tff(9061,plain,
% 2.34/2.54 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9060])).
% 2.34/2.54 tff(9062,plain,
% 2.34/2.54 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9061])).
% 2.34/2.54 tff(9063,plain,
% 2.34/2.54 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9059])).
% 2.34/2.54 tff(9064,plain,
% 2.34/2.54 (s(s(z)) = s(s(elem!1))),
% 2.34/2.54 inference(transitivity,[status(thm)],[73, 9063, 19])).
% 2.34/2.54 tff(9065,plain,
% 2.34/2.54 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9064])).
% 2.34/2.54 tff(9066,plain,
% 2.34/2.54 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.34/2.54 inference(symmetry,[status(thm)],[9065])).
% 2.34/2.54 tff(9067,plain,
% 2.34/2.54 (s(elem!1) = s(z)),
% 2.34/2.54 inference(transitivity,[status(thm)],[30, 9066, 23])).
% 2.34/2.54 tff(9068,plain,
% 2.34/2.54 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(z))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9067])).
% 2.34/2.54 tff(9069,plain,
% 2.34/2.54 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(z) = s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[9068, 265])).
% 2.34/2.54 tff(9070,plain,
% 2.34/2.54 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.34/2.54 inference(symmetry,[status(thm)],[9069])).
% 2.34/2.54 tff(9071,plain,
% 2.34/2.54 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9070])).
% 2.34/2.54 tff(9072,plain,
% 2.34/2.54 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[275, 9071])).
% 2.34/2.54 tff(9073,plain,
% 2.34/2.54 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[6172, 9072])).
% 2.34/2.54 tff(9074,plain,
% 2.34/2.54 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9064])).
% 2.34/2.54 tff(9075,plain,
% 2.34/2.54 (b(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1995, 9059, 1331])).
% 2.34/2.54 tff(9076,plain,
% 2.34/2.54 (~r(s(s(s(s(z)))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[8576, 87, 535, 550, 61, 1331])).
% 2.34/2.54 tff(9077,plain,
% 2.34/2.54 (b(s(s(s(s(z)))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2860, 9076])).
% 2.34/2.54 tff(9078,plain,
% 2.34/2.54 (~b(s(s(s(z))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2853, 9077, 61, 8574, 550])).
% 2.34/2.54 tff(9079,plain,
% 2.34/2.54 (r(s(s(s(z))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[402, 9078])).
% 2.34/2.54 tff(9080,plain,
% 2.34/2.54 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[9041, 9079])).
% 2.34/2.54 tff(9081,plain,
% 2.34/2.54 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9059])).
% 2.34/2.54 tff(9082,plain,
% 2.34/2.54 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9081])).
% 2.34/2.54 tff(9083,plain,
% 2.34/2.54 (b(s(s(s(s(elem!1)))), z)),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[9077, 9082])).
% 2.34/2.54 tff(9084,plain,
% 2.34/2.54 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9059])).
% 2.34/2.54 tff(9085,plain,
% 2.34/2.54 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[9084, 1414])).
% 2.34/2.54 tff(9086,plain,
% 2.34/2.54 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9085])).
% 2.34/2.54 tff(9087,plain,
% 2.34/2.54 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[286, 9086])).
% 2.34/2.54 tff(9088,plain,
% 2.34/2.54 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9081])).
% 2.34/2.54 tff(9089,plain,
% 2.34/2.54 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2839, 97, 550, 61, 9077])).
% 2.34/2.54 tff(9090,plain,
% 2.34/2.54 (r(s(z), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2844, 9089, 2833])).
% 2.34/2.54 tff(9091,plain,
% 2.34/2.54 (r(s(z), s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[9090, 9088])).
% 2.34/2.54 tff(9092,plain,
% 2.34/2.54 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9081])).
% 2.34/2.54 tff(9093,plain,
% 2.34/2.54 (~b(s(s(s(s(z)))), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[8748, 97, 550, 61, 87, 535, 9077])).
% 2.34/2.54 tff(9094,plain,
% 2.34/2.54 (r(s(s(s(s(z)))), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2807, 9093, 2795])).
% 2.34/2.54 tff(9095,plain,
% 2.34/2.54 (r(s(s(s(s(elem!1)))), s(z))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[9094, 9092])).
% 2.34/2.54 tff(9096,plain,
% 2.34/2.54 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[503, 9095, 125, 9091])).
% 2.34/2.54 tff(9097,plain,
% 2.34/2.54 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[486, 9096, 9087])).
% 2.34/2.54 tff(9098,plain,
% 2.34/2.54 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[8474, 9097, 1331, 9083, 9080, 9075])).
% 2.34/2.54 tff(9099,plain,
% 2.34/2.54 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[336, 9098])).
% 2.34/2.54 tff(9100,plain,
% 2.34/2.54 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[9099, 9074])).
% 2.34/2.54 tff(9101,plain,
% 2.34/2.54 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9064])).
% 2.34/2.54 tff(9102,plain,
% 2.34/2.54 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.34/2.54 inference(transitivity,[status(thm)],[9101, 1428])).
% 2.34/2.54 tff(9103,plain,
% 2.34/2.54 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9102])).
% 2.34/2.54 tff(9104,plain,
% 2.34/2.54 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[331, 9103])).
% 2.34/2.54 tff(9105,plain,
% 2.34/2.54 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.34/2.54 inference(symmetry,[status(thm)],[9063])).
% 2.34/2.54 tff(9106,plain,
% 2.34/2.54 (s(s(elem!1)) = s(s(z))),
% 2.34/2.54 inference(transitivity,[status(thm)],[167, 9105, 72])).
% 2.34/2.54 tff(9107,plain,
% 2.34/2.54 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9106])).
% 2.34/2.54 tff(9108,plain,
% 2.34/2.54 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.34/2.54 inference(symmetry,[status(thm)],[9107])).
% 2.34/2.54 tff(9109,plain,
% 2.34/2.54 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[9108, 1531])).
% 2.34/2.54 tff(9110,plain,
% 2.34/2.54 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9109])).
% 2.34/2.54 tff(9111,plain,
% 2.34/2.54 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[43, 9110])).
% 2.34/2.54 tff(9112,plain,
% 2.34/2.54 (s(z) = s(elem!1)),
% 2.34/2.54 inference(transitivity,[status(thm)],[24, 9065, 29])).
% 2.34/2.54 tff(9113,plain,
% 2.34/2.54 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9112])).
% 2.34/2.54 tff(9114,plain,
% 2.34/2.54 (z = elem!1),
% 2.34/2.54 inference(transitivity,[status(thm)],[1443, 9113, 85])).
% 2.34/2.54 tff(9115,plain,
% 2.34/2.54 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9114])).
% 2.34/2.54 tff(9116,plain,
% 2.34/2.54 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9064])).
% 2.34/2.54 tff(9117,plain,
% 2.34/2.54 (r(s(s(elem!1)), z)),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[8956, 9116])).
% 2.34/2.54 tff(9118,plain,
% 2.34/2.54 (r(s(s(elem!1)), elem!1)),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[9117, 9115])).
% 2.34/2.54 tff(9119,plain,
% 2.34/2.54 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9114])).
% 2.34/2.54 tff(9120,plain,
% 2.34/2.54 (r(elem!1, s(s(s(elem!1))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[570, 9119])).
% 2.34/2.54 tff(9121,plain,
% 2.34/2.54 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9114])).
% 2.34/2.54 tff(9122,plain,
% 2.34/2.54 (r(s(s(s(z))), z) <=> r(s(s(s(elem!1))), z)),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9059])).
% 2.34/2.54 tff(9123,plain,
% 2.34/2.54 (r(s(s(s(elem!1))), z)),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[9079, 9122])).
% 2.34/2.54 tff(9124,plain,
% 2.34/2.54 (r(s(s(s(elem!1))), elem!1)),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[9123, 9121])).
% 2.34/2.54 tff(9125,plain,
% 2.34/2.54 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1571, 155, 9124, 9120, 9118])).
% 2.34/2.54 tff(9126,plain,
% 2.34/2.54 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[8079, 9125, 9111])).
% 2.34/2.54 tff(9127,plain,
% 2.34/2.54 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9106])).
% 2.34/2.54 tff(9128,plain,
% 2.34/2.54 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.34/2.54 inference(symmetry,[status(thm)],[9127])).
% 2.34/2.54 tff(9129,plain,
% 2.34/2.54 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[9075, 9128])).
% 2.34/2.54 tff(9130,plain,
% 2.34/2.54 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[8941, 9097, 9129, 9126])).
% 2.34/2.54 tff(9131,plain,
% 2.34/2.54 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1484, 9130, 9104])).
% 2.34/2.54 tff(9132,plain,
% 2.34/2.54 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9114])).
% 2.34/2.54 tff(9133,plain,
% 2.34/2.54 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9064])).
% 2.34/2.54 tff(9134,plain,
% 2.34/2.54 (~b(z, s(s(z)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[9048, 8956, 570, 125, 61, 535, 550])).
% 2.34/2.54 tff(9135,plain,
% 2.34/2.54 (r(z, s(s(z)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[222, 9134])).
% 2.34/2.54 tff(9136,plain,
% 2.34/2.54 (r(z, s(s(elem!1)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[9135, 9133])).
% 2.34/2.54 tff(9137,plain,
% 2.34/2.54 (r(elem!1, s(s(elem!1)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[9136, 9132])).
% 2.34/2.54 tff(9138,plain,
% 2.34/2.54 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[6197, 9087, 9059])).
% 2.34/2.54 tff(9139,plain,
% 2.34/2.54 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7544, 9138])).
% 2.34/2.54 tff(9140,plain,
% 2.34/2.54 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9114])).
% 2.34/2.54 tff(9141,plain,
% 2.34/2.54 ((s(s(s(s(s(elem!1))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[9140, 6292])).
% 2.34/2.54 tff(9142,plain,
% 2.34/2.54 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.34/2.54 inference(transitivity,[status(thm)],[9141, 6293])).
% 2.34/2.54 tff(9143,plain,
% 2.34/2.54 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9142])).
% 2.34/2.54 tff(9144,plain,
% 2.34/2.54 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[6299, 9143])).
% 2.34/2.54 tff(9145,plain,
% 2.34/2.54 (elem!1 = z),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1888, 9114])).
% 2.34/2.54 tff(9146,plain,
% 2.34/2.54 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[9085, 2507])).
% 2.34/2.54 tff(9147,plain,
% 2.34/2.54 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9146])).
% 2.34/2.54 tff(9148,plain,
% 2.34/2.54 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[286, 9147])).
% 2.34/2.54 tff(9149,plain,
% 2.34/2.54 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9059])).
% 2.34/2.54 tff(9150,plain,
% 2.34/2.54 (~b(s(z), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[8990, 97, 87, 535, 1331])).
% 2.34/2.54 tff(9151,plain,
% 2.34/2.54 (r(s(z), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[253, 9150])).
% 2.34/2.54 tff(9152,plain,
% 2.34/2.54 (r(s(z), s(s(s(elem!1))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[9151, 9149])).
% 2.34/2.54 tff(9153,plain,
% 2.34/2.54 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1136, 9095, 125, 9152])).
% 2.34/2.54 tff(9154,plain,
% 2.34/2.54 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[821, 9153, 9148])).
% 2.34/2.54 tff(9155,plain,
% 2.34/2.54 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[8474, 1749, 876, 60, 473, 1331])).
% 2.34/2.54 tff(9156,plain,
% 2.34/2.54 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[336, 9155])).
% 2.34/2.54 tff(9157,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(9158,plain,
% 2.34/2.54 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(9159,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9158])).
% 2.34/2.54 tff(9160,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[9159, 9157])).
% 2.34/2.54 tff(9161,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(9162,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[9161, 9160])).
% 2.34/2.54 tff(9163,plain,
% 2.34/2.54 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[9162, 155, 463, 9156, 288, 645])).
% 2.34/2.54 tff(9164,plain,
% 2.34/2.54 (b(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[143, 9163])).
% 2.34/2.54 tff(9165,plain,
% 2.34/2.54 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2270, 97, 60, 1331, 9164])).
% 2.34/2.54 tff(9166,plain,
% 2.34/2.54 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[3089, 9165, 1749])).
% 2.34/2.54 tff(9167,plain,
% 2.34/2.54 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9166])).
% 2.34/2.54 tff(9168,plain,
% 2.34/2.54 (s(s(z)) = s(s(elem!1))),
% 2.34/2.54 inference(transitivity,[status(thm)],[73, 9167, 19])).
% 2.34/2.54 tff(9169,plain,
% 2.34/2.54 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9168])).
% 2.34/2.54 tff(9170,plain,
% 2.34/2.54 (s(z) = s(elem!1)),
% 2.34/2.54 inference(transitivity,[status(thm)],[24, 9169, 29])).
% 2.34/2.54 tff(9171,plain,
% 2.34/2.54 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9170])).
% 2.34/2.54 tff(9172,plain,
% 2.34/2.54 (z = elem!1),
% 2.34/2.54 inference(transitivity,[status(thm)],[1443, 9171, 85])).
% 2.34/2.54 tff(9173,plain,
% 2.34/2.54 (r(z, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9172])).
% 2.34/2.54 tff(9174,plain,
% 2.34/2.54 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[463, 9173])).
% 2.34/2.54 tff(9175,plain,
% 2.34/2.54 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9172, 9168])).
% 2.34/2.54 tff(9176,plain,
% 2.34/2.54 (r(elem!1, s(s(elem!1)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[226, 9175])).
% 2.34/2.54 tff(9177,plain,
% 2.34/2.54 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9168])).
% 2.34/2.54 tff(9178,plain,
% 2.34/2.54 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[9156, 9177])).
% 2.34/2.54 tff(9179,plain,
% 2.34/2.54 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2741, 9164, 473, 805])).
% 2.34/2.54 tff(9180,plain,
% 2.34/2.54 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[452, 9179])).
% 2.34/2.54 tff(9181,plain,
% 2.34/2.54 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1822, 9166, 9180])).
% 2.34/2.54 tff(9182,plain,
% 2.34/2.54 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), 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)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(9183,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9182])).
% 2.34/2.54 tff(9184,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[9183, 3845])).
% 2.34/2.54 tff(9185,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(9186,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[9185, 9184])).
% 2.34/2.54 tff(9187,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[9186, 155, 9181, 9178, 9176, 9174])).
% 2.34/2.54 tff(9188,plain,(r(s(s(s(z))), s(s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(9189,plain,
% 2.34/2.54 (~r(z, s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[9188, 9097, 1331, 9135, 9075, 9123, 9080, 9154, 8956, 9083])).
% 2.34/2.54 tff(9190,plain,
% 2.34/2.54 (b(z, s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1093, 9189])).
% 2.34/2.54 tff(9191,plain,
% 2.34/2.54 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2407, 9190, 9145])).
% 2.34/2.54 tff(9192,plain,
% 2.34/2.54 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9114])).
% 2.34/2.54 tff(9193,plain,
% 2.34/2.54 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[9083, 9192])).
% 2.34/2.54 tff(9194,plain,
% 2.34/2.54 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7551, 155, 1813, 1522, 6276])).
% 2.34/2.54 tff(9195,plain,
% 2.34/2.54 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[6254, 9194, 6243])).
% 2.34/2.54 tff(9196,assumption,(~(s(s(s(s(s(elem!1))))) = elem!1)), introduced(assumption)).
% 2.34/2.54 tff(9197,plain,
% 2.34/2.54 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[6313, 6309, 9196])).
% 2.34/2.54 tff(9198,plain,
% 2.34/2.54 (((~![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(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))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(9199,plain,
% 2.34/2.54 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(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))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(9200,plain,
% 2.34/2.54 (((~![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(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9199])).
% 2.34/2.54 tff(9201,plain,
% 2.34/2.54 (((~![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(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.54 inference(transitivity,[status(thm)],[9200, 9198])).
% 2.34/2.54 tff(9202,plain,
% 2.34/2.54 ((~![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(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(9203,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[9202, 9201])).
% 2.34/2.54 tff(9204,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[9203, 97, 1458, 2392, 9197, 9195])).
% 2.34/2.54 tff(9205,plain,((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (s(s(s(s(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)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(9206,plain,
% 2.34/2.54 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[9205, 9193, 9191, 9144, 9139, 9118, 9137, 9131, 9100])).
% 2.34/2.54 tff(9207,plain,
% 2.34/2.54 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[6269, 9206, 9073])).
% 2.34/2.54 tff(9208,plain,
% 2.34/2.54 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7499, 97, 9097, 9129, 9154, 9126, 9207])).
% 2.34/2.54 tff(9209,plain,
% 2.34/2.54 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[9208, 9062])).
% 2.34/2.54 tff(9210,plain,
% 2.34/2.54 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9060])).
% 2.34/2.54 tff(9211,plain,
% 2.34/2.54 ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9210])).
% 2.34/2.54 tff(9212,plain,
% 2.34/2.54 (r(s(s(s(s(s(elem!1))))), s(elem!1)) <=> r(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9067])).
% 2.34/2.54 tff(9213,plain,
% 2.34/2.54 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.34/2.54 inference(symmetry,[status(thm)],[9212])).
% 2.34/2.54 tff(9214,plain,
% 2.34/2.54 (~(s(s(s(s(s(elem!1))))) = s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[6222, 9059])).
% 2.34/2.54 tff(9215,plain,
% 2.34/2.54 (b(s(s(s(s(s(elem!1))))), s(elem!1)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9067])).
% 2.34/2.54 tff(9216,plain,
% 2.34/2.54 ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) <=> (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9215])).
% 2.34/2.54 tff(9217,plain,
% 2.34/2.54 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[9112, 9064])).
% 2.34/2.54 tff(9218,plain,
% 2.34/2.54 (b(s(elem!1), s(s(elem!1)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[535, 9217])).
% 2.34/2.55 tff(9219,plain,
% 2.34/2.55 (((~![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(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(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(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(9220,plain,
% 2.34/2.55 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(9221,plain,
% 2.34/2.55 (((~![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(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(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(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[9220])).
% 2.34/2.55 tff(9222,plain,
% 2.34/2.55 (((~![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(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(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(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[9221, 9219])).
% 2.34/2.55 tff(9223,plain,
% 2.34/2.55 ((~![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(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(9224,plain,
% 2.34/2.55 ((~![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(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[9223, 9222])).
% 2.34/2.55 tff(9225,plain,
% 2.34/2.55 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9224, 97, 9126, 9207, 9218])).
% 2.34/2.55 tff(9226,plain,
% 2.34/2.55 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[9225, 9216])).
% 2.34/2.55 tff(9227,plain,
% 2.34/2.55 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[6239, 9226, 9214])).
% 2.34/2.55 tff(9228,plain,
% 2.34/2.55 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[9227, 9213])).
% 2.34/2.55 tff(9229,plain,
% 2.34/2.55 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[9067])).
% 2.34/2.55 tff(9230,plain,
% 2.34/2.55 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.55 inference(symmetry,[status(thm)],[9229])).
% 2.34/2.55 tff(9231,plain,
% 2.34/2.55 (r(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[125, 9230])).
% 2.34/2.55 tff(9232,plain,
% 2.34/2.55 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[9067])).
% 2.34/2.55 tff(9233,plain,
% 2.34/2.55 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.34/2.55 inference(symmetry,[status(thm)],[9232])).
% 2.34/2.55 tff(9234,plain,
% 2.34/2.55 (r(s(elem!1), s(s(s(elem!1))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[9152, 9233])).
% 2.34/2.55 tff(9235,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(9236,plain,
% 2.34/2.55 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(9237,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[9236])).
% 2.34/2.55 tff(9238,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[9237, 9235])).
% 2.34/2.55 tff(9239,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(9240,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[9239, 9238])).
% 2.34/2.55 tff(9241,plain,
% 2.34/2.55 ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9240, 155, 9234, 9231])).
% 2.34/2.55 tff(9242,plain,
% 2.34/2.55 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9241, 9228])).
% 2.34/2.55 tff(9243,plain,
% 2.34/2.55 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[9242, 9211])).
% 2.34/2.55 tff(9244,plain,
% 2.34/2.55 (s(s(s(s(s(elem!1))))) = s(s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[6289, 9243, 9209])).
% 2.34/2.55 tff(9245,plain,
% 2.34/2.55 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 2.34/2.55 inference(transitivity,[status(thm)],[9244, 9059])).
% 2.34/2.55 tff(9246,plain,
% 2.34/2.55 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(elem!1))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[9245])).
% 2.34/2.55 tff(9247,plain,
% 2.34/2.55 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.34/2.55 inference(transitivity,[status(thm)],[6168, 9246, 19])).
% 2.34/2.55 tff(9248,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9104, 9247])).
% 2.34/2.55 tff(9249,plain,((~b(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(9250,plain,
% 2.34/2.55 (~b(s(s(z)), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9249, 8954, 7137, 494, 535, 550, 61])).
% 2.34/2.55 tff(9251,plain,
% 2.34/2.55 (r(s(s(z)), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[122, 9250])).
% 2.34/2.55 tff(9252,plain,
% 2.34/2.55 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[8978, 9251, 8956, 8540, 494, 535, 8954, 7137])).
% 2.34/2.55 tff(9253,plain,
% 2.34/2.55 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[9252])).
% 2.34/2.55 tff(9254,plain,
% 2.34/2.55 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.34/2.55 inference(symmetry,[status(thm)],[9253])).
% 2.34/2.55 tff(9255,plain,
% 2.34/2.55 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[9254])).
% 2.34/2.55 tff(9256,plain,
% 2.34/2.55 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.55 inference(symmetry,[status(thm)],[9255])).
% 2.34/2.55 tff(9257,plain,
% 2.34/2.55 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(z)))), z)),
% 2.34/2.55 inference(monotonicity,[status(thm)],[9253])).
% 2.34/2.55 tff(9258,plain,
% 2.34/2.55 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.34/2.55 inference(symmetry,[status(thm)],[9257])).
% 2.34/2.55 tff(9259,plain,
% 2.34/2.55 (r(z, s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[6374, 9252, 8954])).
% 2.34/2.55 tff(9260,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(9261,plain,
% 2.34/2.55 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(9262,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[9261])).
% 2.34/2.55 tff(9263,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[9262, 9260])).
% 2.34/2.55 tff(9264,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(9265,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[9264, 9263])).
% 2.34/2.55 tff(9266,plain,
% 2.34/2.55 (~r(s(s(z)), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9265, 155, 8956, 9251, 9259, 8540])).
% 2.34/2.55 tff(9267,plain,
% 2.34/2.55 (b(s(s(z)), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[437, 9266])).
% 2.34/2.55 tff(9268,plain,
% 2.34/2.55 (~b(z, s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9048, 8956, 8954, 494, 61, 535, 550])).
% 2.34/2.55 tff(9269,plain,
% 2.34/2.55 (r(z, s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[222, 9268])).
% 2.34/2.55 tff(9270,plain,
% 2.34/2.55 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7117, 4153, 2597, 535, 1300, 1361])).
% 2.34/2.55 tff(9271,plain,
% 2.34/2.55 (r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2886, 9270, 80])).
% 2.34/2.55 tff(9272,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2881, 155, 226, 645, 9271, 4153])).
% 2.34/2.55 tff(9273,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(9274,plain,
% 2.34/2.55 (~r(s(s(s(s(z)))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9273, 9269, 8956, 8540, 535, 9259, 9267])).
% 2.34/2.55 tff(9275,plain,
% 2.34/2.55 (b(s(s(s(s(z)))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2860, 9274])).
% 2.34/2.55 tff(9276,plain,
% 2.34/2.55 (b(s(s(s(s(elem!1)))), z)),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[9275, 9258])).
% 2.34/2.55 tff(9277,plain,
% 2.34/2.55 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3055, 9276, 550, 61])).
% 2.34/2.55 tff(9278,plain,
% 2.34/2.55 (r(s(z), s(s(s(s(elem!1)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[280, 9277])).
% 2.34/2.55 tff(9279,plain,
% 2.34/2.55 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2715, 9276, 550, 61])).
% 2.34/2.55 tff(9280,plain,
% 2.34/2.55 (r(s(s(s(s(elem!1)))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[511, 9279])).
% 2.34/2.55 tff(9281,plain,
% 2.34/2.55 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[503, 9280, 494, 9278])).
% 2.34/2.55 tff(9282,plain,
% 2.34/2.55 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.34/2.55 inference(symmetry,[status(thm)],[9252])).
% 2.34/2.55 tff(9283,plain,
% 2.34/2.55 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[9282])).
% 2.34/2.55 tff(9284,plain,
% 2.34/2.55 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[9283, 1414])).
% 2.34/2.55 tff(9285,plain,
% 2.34/2.55 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[9284])).
% 2.34/2.55 tff(9286,plain,
% 2.34/2.55 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[286, 9285])).
% 2.34/2.55 tff(9287,plain,
% 2.34/2.55 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2253, 9251, 494, 8954, 8956])).
% 2.34/2.55 tff(9288,plain,
% 2.34/2.55 (b(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[143, 9287])).
% 2.34/2.55 tff(9289,plain,
% 2.34/2.55 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[9252])).
% 2.34/2.55 tff(9290,plain,
% 2.34/2.55 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.34/2.55 inference(symmetry,[status(thm)],[9289])).
% 2.34/2.55 tff(9291,plain,
% 2.34/2.55 (~b(s(z), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[8804, 9267, 7137, 535])).
% 2.34/2.55 tff(9292,plain,
% 2.34/2.55 (r(s(z), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[253, 9291])).
% 2.34/2.55 tff(9293,plain,
% 2.34/2.55 (r(s(z), s(s(s(elem!1))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[9292, 9290])).
% 2.34/2.55 tff(9294,plain,
% 2.34/2.55 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1136, 9280, 494, 9293])).
% 2.34/2.55 tff(9295,plain,
% 2.34/2.55 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[4129, 9294, 9288, 9286, 9281])).
% 2.34/2.55 tff(9296,plain,
% 2.34/2.55 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[336, 9295])).
% 2.34/2.55 tff(9297,plain,
% 2.34/2.55 (r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[9296, 9256])).
% 2.34/2.55 tff(9298,plain,
% 2.34/2.55 (~b(s(s(s(s(z)))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2802, 97, 550, 61, 9275])).
% 2.34/2.55 tff(9299,plain,
% 2.34/2.55 (r(s(s(s(s(z)))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2807, 9298, 2795])).
% 2.34/2.55 tff(9300,plain,
% 2.34/2.55 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2839, 97, 550, 61, 9275])).
% 2.34/2.55 tff(9301,plain,
% 2.34/2.55 (r(s(z), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2844, 9300, 2833])).
% 2.34/2.55 tff(9302,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[4203, 155, 9251, 9301, 9299, 9297])).
% 2.34/2.55 tff(9303,plain,((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | r(s(s(s(z))), s(s(z))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(9304,plain,
% 2.34/2.55 (r(s(s(s(z))), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9303, 8505, 61, 550, 82])).
% 2.34/2.55 tff(9305,plain,
% 2.34/2.55 (~b(s(s(s(z))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[8667, 585, 550, 8505, 61, 82])).
% 2.34/2.55 tff(9306,plain,
% 2.34/2.55 (r(s(s(s(z))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[402, 9305])).
% 2.34/2.55 tff(9307,plain,
% 2.34/2.55 (~r(z, s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[6467, 9306, 9304, 8537])).
% 2.34/2.55 tff(9308,plain,
% 2.34/2.55 (~b(z, s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[8717, 9306, 7137, 8505, 61, 550, 494, 585])).
% 2.34/2.55 tff(9309,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[222, 9308, 9307])).
% 2.34/2.55 tff(9310,plain,(r(z, s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(9311,plain,
% 2.34/2.55 (r(z, s(s(s(elem!1))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9310, 550, 61, 82])).
% 2.34/2.55 tff(9312,plain,
% 2.34/2.55 (~b(s(s(z)), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9249, 9311, 7137, 494, 8505, 550, 61])).
% 2.34/2.55 tff(9313,plain,
% 2.34/2.55 (r(s(s(z)), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[122, 9312])).
% 2.34/2.55 tff(9314,plain,
% 2.34/2.55 (~r(s(s(z)), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[6389, 9313, 9304, 8505, 9311, 494, 61, 8537, 8533])).
% 2.34/2.55 tff(9315,plain,
% 2.34/2.55 (b(s(s(z)), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[437, 9314])).
% 2.34/2.55 tff(9316,plain,
% 2.34/2.55 (~b(z, s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9048, 9311, 8505, 494, 61, 8537, 550])).
% 2.34/2.55 tff(9317,plain,
% 2.34/2.55 (r(z, s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[222, 9316])).
% 2.34/2.55 tff(9318,plain,
% 2.34/2.55 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[8978, 9313, 8505, 8537, 494, 8533, 9311, 7137])).
% 2.34/2.55 tff(9319,plain,
% 2.34/2.55 (r(z, s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[6374, 9318, 9311])).
% 2.34/2.55 tff(9320,plain,
% 2.34/2.55 (~r(s(s(s(s(z)))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9273, 9319, 8505, 8533, 8537, 9317, 9315])).
% 2.34/2.55 tff(9321,plain,
% 2.34/2.55 (~r(s(s(s(z))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[6467, 9317, 9304, 8537])).
% 2.34/2.55 tff(9322,plain,
% 2.34/2.55 (b(s(s(s(z))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[402, 9321])).
% 2.34/2.55 tff(9323,plain,
% 2.34/2.55 (~b(s(s(s(s(z)))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2853, 9322, 61, 8533, 550])).
% 2.34/2.55 tff(9324,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2860, 9323, 9320])).
% 2.34/2.55 tff(9325,plain,((~b(s(z), z)) | (~b(z, s(z))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(9326,plain,
% 2.34/2.55 (~b(s(z), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9325, 82, 61])).
% 2.34/2.55 tff(9327,plain,
% 2.34/2.55 (r(s(z), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[568, 9326])).
% 2.34/2.55 tff(9328,plain,
% 2.34/2.55 (~r(s(z), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2587, 9327, 61])).
% 2.34/2.55 tff(9329,plain,
% 2.34/2.55 (b(s(z), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[548, 9328])).
% 2.34/2.55 tff(9330,plain,
% 2.34/2.55 (~r(s(z), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2587, 81, 61])).
% 2.34/2.55 tff(9331,plain,
% 2.34/2.55 (b(s(z), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[548, 9330])).
% 2.34/2.55 tff(9332,plain,
% 2.34/2.55 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2661, 204, 61, 9331])).
% 2.34/2.55 tff(9333,plain,
% 2.34/2.55 (r(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[143, 9332])).
% 2.34/2.55 tff(9334,plain,
% 2.34/2.55 (~b(s(s(z)), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[8695, 204, 9331, 61])).
% 2.34/2.55 tff(9335,plain,
% 2.34/2.55 (r(s(s(z)), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[122, 9334])).
% 2.34/2.55 tff(9336,plain,
% 2.34/2.55 (~b(z, s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2962, 83, 61, 9331])).
% 2.34/2.55 tff(9337,plain,
% 2.34/2.55 (r(z, s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[222, 9336])).
% 2.34/2.55 tff(9338,plain,
% 2.34/2.55 (~r(s(s(s(z))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[5827, 1960, 125, 81, 9337, 1])).
% 2.34/2.55 tff(9339,plain,
% 2.34/2.55 (b(s(s(s(z))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1358, 9338])).
% 2.34/2.55 tff(9340,plain,
% 2.34/2.55 (~b(z, s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[8519, 97, 61, 9331, 9339])).
% 2.34/2.55 tff(9341,plain,
% 2.34/2.55 (r(z, s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1318, 9340])).
% 2.34/2.55 tff(9342,plain,
% 2.34/2.55 (~b(s(s(s(z))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[8511, 97, 61, 9331, 9339])).
% 2.34/2.55 tff(9343,plain,
% 2.34/2.55 (r(s(s(s(z))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[402, 9342])).
% 2.34/2.55 tff(9344,plain,
% 2.34/2.55 (~r(s(z), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1308, 9343, 81, 9341])).
% 2.34/2.55 tff(9345,plain,
% 2.34/2.55 (b(s(z), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[253, 9344])).
% 2.34/2.55 tff(9346,plain,
% 2.34/2.55 (~r(s(s(z)), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1969, 9341, 1960, 9337])).
% 2.34/2.55 tff(9347,plain,
% 2.34/2.55 (b(s(s(z)), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[437, 9346])).
% 2.34/2.55 tff(9348,plain,
% 2.34/2.55 (((~![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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), 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(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(9349,plain,
% 2.34/2.55 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(9350,plain,
% 2.34/2.55 (((~![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))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(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(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[9349])).
% 2.34/2.55 tff(9351,plain,
% 2.34/2.55 (((~![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))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(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(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[9350, 9348])).
% 2.34/2.55 tff(9352,plain,
% 2.34/2.55 ((~![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))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(9353,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[9352, 9351])).
% 2.34/2.55 tff(9354,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9353, 97, 61, 83, 9331, 9347, 9339, 9345])).
% 2.34/2.55 tff(9355,plain,((~r(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(9356,plain,
% 2.34/2.55 (~r(s(s(s(z))), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9355, 1, 83, 81, 125, 61])).
% 2.34/2.55 tff(9357,plain,
% 2.34/2.55 (b(s(s(s(z))), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[421, 9356])).
% 2.34/2.55 tff(9358,plain,
% 2.34/2.55 (((~![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(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(9359,plain,
% 2.34/2.55 (((~b(s(s(z)), z)) | (~b(s(s(z)), 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(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(9360,plain,
% 2.34/2.55 (((~![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)), z)) | (~b(s(s(z)), 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(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[9359])).
% 2.34/2.55 tff(9361,plain,
% 2.34/2.55 (((~![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)), z)) | (~b(s(s(z)), 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(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[9360, 9358])).
% 2.34/2.55 tff(9362,plain,
% 2.34/2.55 ((~![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)), z)) | (~b(s(s(z)), 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))))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(9363,plain,
% 2.34/2.55 ((~![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(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[9362, 9361])).
% 2.34/2.55 tff(9364,plain,
% 2.34/2.55 (~b(s(z), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9363, 97, 83, 9331, 9357])).
% 2.34/2.55 tff(9365,plain,
% 2.34/2.55 (r(s(z), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[253, 9364])).
% 2.34/2.55 tff(9366,plain,
% 2.34/2.55 (~b(s(s(s(z))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[8531, 9357, 61, 9331])).
% 2.34/2.56 tff(9367,plain,
% 2.34/2.56 (r(s(s(s(z))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1358, 9366])).
% 2.34/2.56 tff(9368,plain,
% 2.34/2.56 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2638, 9365, 9367, 125])).
% 2.34/2.56 tff(9369,plain,
% 2.34/2.56 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2687, 9368, 4228])).
% 2.34/2.56 tff(9370,plain,
% 2.34/2.56 (~b(s(s(z)), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2651, 83, 9331, 61])).
% 2.34/2.56 tff(9371,plain,
% 2.34/2.56 (r(s(s(z)), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[122, 9370])).
% 2.34/2.56 tff(9372,plain,
% 2.34/2.56 (~r(s(s(z)), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2940, 9365, 9371, 9367])).
% 2.34/2.56 tff(9373,plain,
% 2.34/2.56 (b(s(s(z)), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[437, 9372])).
% 2.34/2.56 tff(9374,plain,
% 2.34/2.56 (((~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(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~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(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(9375,plain,
% 2.34/2.56 (((~![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(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(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[9374])).
% 2.34/2.56 tff(9376,plain,
% 2.34/2.56 (((~![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(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(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[9375, 7597])).
% 2.34/2.56 tff(9377,plain,
% 2.34/2.56 ((~![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(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(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(9378,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[9377, 9376])).
% 2.34/2.56 tff(9379,plain,
% 2.34/2.56 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9378, 97, 9373, 9357, 9369])).
% 2.34/2.56 tff(9380,plain,
% 2.34/2.56 (r(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[58, 9379])).
% 2.34/2.56 tff(9381,plain,
% 2.34/2.56 (~r(s(s(s(elem!1))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3987, 9380, 9331, 125, 61, 9337])).
% 2.34/2.56 tff(9382,plain,
% 2.34/2.56 (b(s(s(s(elem!1))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[246, 9381])).
% 2.34/2.56 tff(9383,plain,
% 2.34/2.56 (~b(z, s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7847, 9382, 9357, 9369])).
% 2.34/2.56 tff(9384,plain,
% 2.34/2.56 (r(z, s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1318, 9383])).
% 2.34/2.56 tff(9385,plain,
% 2.34/2.56 (~r(s(s(s(z))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1308, 9384, 81, 9365])).
% 2.34/2.56 tff(9386,plain,
% 2.34/2.56 (b(s(s(s(z))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[402, 9385])).
% 2.34/2.56 tff(9387,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[409, 97, 61, 83, 9357, 9386])).
% 2.34/2.56 tff(9388,plain,((s(s(s(z))) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(9389,plain,
% 2.34/2.56 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9388, 83, 61, 81, 125])).
% 2.34/2.56 tff(9390,plain,
% 2.34/2.56 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2677, 2590, 9389])).
% 2.34/2.56 tff(9391,plain,
% 2.34/2.56 (r(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[58, 9390])).
% 2.34/2.56 tff(9392,plain,
% 2.34/2.56 (~r(s(s(s(elem!1))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3987, 9391, 9331, 125, 61, 9337])).
% 2.34/2.56 tff(9393,plain,
% 2.34/2.56 (b(s(s(s(elem!1))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[246, 9392])).
% 2.34/2.56 tff(9394,plain,
% 2.34/2.56 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[135, 9393, 61, 83])).
% 2.34/2.56 tff(9395,plain,
% 2.34/2.56 (r(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[143, 9394])).
% 2.34/2.56 tff(9396,plain,
% 2.34/2.56 (~r(s(z), s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1273, 9395, 125, 9371])).
% 2.34/2.56 tff(9397,plain,
% 2.34/2.56 (b(s(z), s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[181, 9396])).
% 2.34/2.56 tff(9398,plain,
% 2.34/2.56 (~b(z, s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3979, 9397, 61, 9393])).
% 2.34/2.56 tff(9399,plain,
% 2.34/2.56 (r(z, s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[590, 9398])).
% 2.34/2.56 tff(9400,plain,
% 2.34/2.56 (~r(z, s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[5949, 9399, 2591, 9395, 9337])).
% 2.34/2.56 tff(9401,plain,
% 2.34/2.56 (b(z, s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1318, 9400])).
% 2.34/2.56 tff(9402,plain,
% 2.34/2.56 (~r(s(s(s(z))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2035, 9401, 61, 81, 9397, 2591, 83])).
% 2.34/2.56 tff(9403,plain,
% 2.34/2.56 (b(s(s(s(z))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[402, 9402])).
% 2.34/2.56 tff(9404,plain,
% 2.34/2.56 (((~![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)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(9405,plain,
% 2.34/2.56 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(9406,plain,
% 2.34/2.56 (((~![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(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(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(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[9405])).
% 2.34/2.56 tff(9407,plain,
% 2.34/2.56 (((~![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(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(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(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.34/2.56 inference(transitivity,[status(thm)],[9406, 9404])).
% 2.34/2.56 tff(9408,plain,
% 2.34/2.56 ((~![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(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(9409,plain,
% 2.34/2.56 ((~![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)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[9408, 9407])).
% 2.34/2.56 tff(9410,plain,
% 2.34/2.56 (~b(s(s(z)), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9409, 97, 83, 9401, 9403])).
% 2.34/2.56 tff(9411,plain,
% 2.34/2.56 (r(s(s(z)), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[437, 9410])).
% 2.34/2.56 tff(9412,plain,
% 2.34/2.56 (~b(s(z), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2615, 9403, 61, 9401])).
% 2.34/2.56 tff(9413,plain,
% 2.34/2.56 (r(s(z), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[253, 9412])).
% 2.34/2.56 tff(9414,plain,
% 2.34/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(9415,plain,
% 2.34/2.56 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~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(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(9416,plain,
% 2.34/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[9415])).
% 2.34/2.56 tff(9417,plain,
% 2.34/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[9416, 9414])).
% 2.34/2.56 tff(9418,plain,
% 2.34/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(9419,plain,
% 2.34/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[9418, 9417])).
% 2.34/2.56 tff(9420,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9419, 155, 125, 9371, 9413, 9395, 9411])).
% 2.34/2.56 tff(9421,plain,(b(s(s(s(z))), s(s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(9422,plain,
% 2.34/2.56 (b(s(s(s(z))), s(s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9421, 83, 125, 61, 81])).
% 2.34/2.56 tff(9423,plain,
% 2.34/2.56 (b(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1995, 9422, 9389])).
% 2.34/2.56 tff(9424,plain,
% 2.34/2.56 (((~![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), s(s(s(elem!1))))) | (~b(s(z), s(s(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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(9425,plain,
% 2.34/2.56 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(9426,plain,
% 2.34/2.56 (((~![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)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[9425])).
% 2.34/2.56 tff(9427,plain,
% 2.34/2.56 (((~![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)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[9426, 9424])).
% 2.34/2.56 tff(9428,plain,
% 2.34/2.56 ((~![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)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(9429,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[9428, 9427])).
% 2.34/2.56 tff(9430,plain,
% 2.34/2.56 (~b(s(z), s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9429, 97, 9423, 83, 9331])).
% 2.34/2.56 tff(9431,plain,
% 2.34/2.56 (~b(s(s(s(elem!1))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1390, 9423, 83, 61])).
% 2.34/2.56 tff(9432,plain,
% 2.34/2.56 (r(s(s(s(elem!1))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[246, 9431])).
% 2.34/2.56 tff(9433,plain,
% 2.34/2.56 (~b(s(s(s(z))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[8531, 9422, 61, 9331])).
% 2.34/2.56 tff(9434,plain,
% 2.34/2.56 (r(s(s(s(z))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1358, 9433])).
% 2.34/2.56 tff(9435,plain,
% 2.34/2.56 (~b(z, s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7205, 9423, 83, 125, 9371, 61, 9422, 9434])).
% 2.34/2.56 tff(9436,plain,
% 2.34/2.56 (r(z, s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[590, 9435])).
% 2.34/2.56 tff(9437,plain,
% 2.34/2.56 (~r(s(z), s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1423, 155, 9436, 81, 9432])).
% 2.34/2.56 tff(9438,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[181, 9437, 9430])).
% 2.34/2.56 tff(9439,plain,((~b(s(s(z)), z)) | (~r(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(9440,plain,
% 2.34/2.56 (~b(s(s(z)), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9439, 81, 61, 125])).
% 2.34/2.56 tff(9441,plain,
% 2.34/2.56 (r(s(s(z)), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[625, 9440])).
% 2.34/2.56 tff(9442,plain,
% 2.34/2.56 ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[8778, 155, 125, 81, 9441])).
% 2.34/2.56 tff(9443,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9442, 9335, 9333])).
% 2.34/2.56 tff(9444,plain,((~b(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(9445,plain,
% 2.34/2.56 (~b(z, s(s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9444, 125, 81, 61])).
% 2.34/2.56 tff(9446,plain,
% 2.34/2.56 (r(z, s(s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[222, 9445])).
% 2.34/2.56 tff(9447,plain,
% 2.34/2.56 (~r(s(s(s(z))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[6467, 1960, 9441, 9446])).
% 2.34/2.56 tff(9448,plain,
% 2.34/2.56 (b(s(s(s(z))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[402, 9447])).
% 2.34/2.56 tff(9449,plain,
% 2.34/2.56 (~r(s(s(s(z))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[5827, 1960, 125, 81, 9446, 1])).
% 2.34/2.56 tff(9450,plain,
% 2.34/2.56 (b(s(s(s(z))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1358, 9449])).
% 2.34/2.56 tff(9451,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[8511, 97, 61, 9331, 9450, 9448])).
% 2.34/2.56 tff(9452,plain,((~r(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(9453,plain,
% 2.34/2.56 (~r(s(s(s(z))), s(s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9452, 1, 125, 81, 61])).
% 2.34/2.56 tff(9454,plain,
% 2.34/2.56 (b(s(s(s(z))), s(s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[421, 9453])).
% 2.34/2.56 tff(9455,plain,
% 2.34/2.56 (~b(s(s(s(z))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[8531, 9454, 61, 9331])).
% 2.34/2.56 tff(9456,plain,
% 2.34/2.56 (r(s(s(s(z))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1358, 9455])).
% 2.34/2.56 tff(9457,plain,
% 2.34/2.56 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[8874, 585, 61, 9454, 9331, 1])).
% 2.34/2.56 tff(9458,plain,
% 2.34/2.56 (~r(s(s(z)), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[8911, 9457, 61, 9454, 9331, 3008, 1])).
% 2.34/2.56 tff(9459,plain,
% 2.34/2.56 (b(s(s(z)), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[437, 9458])).
% 2.34/2.56 tff(9460,plain,
% 2.34/2.56 (~b(s(z), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[8804, 9459, 9454, 9331])).
% 2.34/2.56 tff(9461,plain,
% 2.34/2.56 (r(s(z), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[253, 9460])).
% 2.34/2.56 tff(9462,plain,
% 2.34/2.56 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7172, 3008, 1, 9454, 125, 9456, 61])).
% 2.34/2.56 tff(9463,plain,
% 2.34/2.56 (r(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[58, 9462])).
% 2.34/2.56 tff(9464,plain,
% 2.34/2.56 (~r(s(s(s(elem!1))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3987, 9463, 9331, 125, 61, 9446])).
% 2.34/2.56 tff(9465,plain,
% 2.34/2.56 (b(s(s(s(elem!1))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[246, 9464])).
% 2.34/2.56 tff(9466,plain,
% 2.34/2.56 (~b(s(z), s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7877, 3008, 9441, 61, 9446, 9454, 1, 125, 9456])).
% 2.34/2.56 tff(9467,plain,
% 2.34/2.56 (r(s(z), s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[181, 9466])).
% 2.34/2.56 tff(9468,plain,
% 2.34/2.56 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[5757, 9467, 9456, 125])).
% 2.34/2.56 tff(9469,plain,
% 2.34/2.56 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3089, 9468, 1])).
% 2.34/2.56 tff(9470,plain,
% 2.34/2.56 (~b(s(s(s(z))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[6379, 9469, 9465, 61])).
% 2.34/2.56 tff(9471,plain,
% 2.34/2.56 (r(s(s(s(z))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[402, 9470])).
% 2.34/2.56 tff(9472,plain,
% 2.34/2.56 (~r(z, s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1308, 9471, 81, 9461])).
% 2.34/2.56 tff(9473,plain,
% 2.34/2.56 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2638, 9461, 9456, 125])).
% 2.34/2.56 tff(9474,plain,
% 2.34/2.56 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2687, 9473, 4228])).
% 2.34/2.56 tff(9475,plain,
% 2.34/2.56 (~b(z, s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7847, 9474, 9454, 9465])).
% 2.34/2.56 tff(9476,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1318, 9475, 9472])).
% 2.34/2.56 tff(9477,plain,(r(z, s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(9478,plain,
% 2.34/2.56 (r(z, s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9477, 1, 125, 61, 81])).
% 2.34/2.56 tff(9479,plain,
% 2.34/2.56 (~r(s(s(z)), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[8978, 9478, 9331, 9441, 125, 4228, 9456, 9454])).
% 2.34/2.56 tff(9480,plain,
% 2.34/2.56 (b(s(s(z)), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[122, 9479])).
% 2.34/2.56 tff(9481,plain,
% 2.34/2.56 (~b(s(z), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[8990, 97, 9480, 9331, 9454])).
% 2.34/2.56 tff(9482,plain,
% 2.34/2.56 (r(s(z), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[253, 9481])).
% 2.34/2.56 tff(9483,plain,
% 2.34/2.56 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2638, 9482, 9456, 125])).
% 2.34/2.56 tff(9484,plain,
% 2.34/2.56 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2687, 9483, 4228])).
% 2.34/2.56 tff(9485,plain,
% 2.34/2.56 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3662, 60, 1331, 87])).
% 2.34/2.56 tff(9486,plain,
% 2.34/2.56 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3089, 9485, 1])).
% 2.34/2.56 tff(9487,plain,
% 2.34/2.56 (~r(s(s(s(z))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[5957, 155, 125, 570, 2597, 9486])).
% 2.34/2.56 tff(9488,plain,
% 2.34/2.56 (b(s(s(s(z))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[402, 9487])).
% 2.34/2.56 tff(9489,plain,
% 2.34/2.56 (((~![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(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(9490,plain,
% 2.34/2.56 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(9491,plain,
% 2.34/2.56 (((~![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(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[9490])).
% 2.34/2.56 tff(9492,plain,
% 2.34/2.56 (((~![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(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[9491, 9489])).
% 2.34/2.57 tff(9493,plain,
% 2.34/2.57 ((~![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(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(9494,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9493, 9492])).
% 2.34/2.57 tff(9495,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9494, 97, 61, 60, 87, 1331, 9488, 5941])).
% 2.34/2.57 tff(9496,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(9497,plain,
% 2.34/2.57 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9496, 9480, 61, 9454, 9484, 125, 9478, 9456, 1])).
% 2.34/2.57 tff(9498,plain,
% 2.34/2.57 (r(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[58, 9497])).
% 2.34/2.57 tff(9499,plain,
% 2.34/2.57 (~r(s(s(s(elem!1))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[3987, 9498, 9331, 125, 61, 9446])).
% 2.34/2.57 tff(9500,plain,
% 2.34/2.57 (b(s(s(s(elem!1))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[246, 9499])).
% 2.34/2.57 tff(9501,plain,
% 2.34/2.57 (~b(z, s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7847, 9500, 9454, 9484])).
% 2.34/2.57 tff(9502,plain,
% 2.34/2.57 (r(z, s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1318, 9501])).
% 2.34/2.57 tff(9503,plain,
% 2.34/2.57 (~r(s(s(s(z))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1308, 9502, 81, 9482])).
% 2.34/2.57 tff(9504,plain,
% 2.34/2.57 (b(s(s(s(z))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[402, 9503])).
% 2.34/2.57 tff(9505,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6096, 97, 61, 9500, 9504, 9484])).
% 2.34/2.57 tff(9506,plain,((s(s(s(z))) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(9507,plain,
% 2.34/2.57 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9506, 81, 61, 125])).
% 2.34/2.57 tff(9508,plain,
% 2.34/2.57 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9507])).
% 2.34/2.57 tff(9509,plain,
% 2.34/2.57 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9508])).
% 2.34/2.57 tff(9510,plain,
% 2.34/2.57 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9507])).
% 2.34/2.57 tff(9511,plain,
% 2.34/2.57 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 2.34/2.57 inference(symmetry,[status(thm)],[9510])).
% 2.34/2.57 tff(9512,plain,
% 2.34/2.57 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[2677, 2590, 9507])).
% 2.34/2.57 tff(9513,plain,
% 2.34/2.57 (r(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[58, 9512])).
% 2.34/2.57 tff(9514,plain,
% 2.34/2.57 (~r(s(s(s(elem!1))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[3987, 9513, 9331, 125, 61, 9446])).
% 2.34/2.57 tff(9515,plain,
% 2.34/2.57 (b(s(s(s(elem!1))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[246, 9514])).
% 2.34/2.57 tff(9516,plain,
% 2.34/2.57 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.34/2.57 inference(symmetry,[status(thm)],[9507])).
% 2.34/2.57 tff(9517,plain,
% 2.34/2.57 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9516])).
% 2.34/2.57 tff(9518,plain,
% 2.34/2.57 (b(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.34/2.57 inference(symmetry,[status(thm)],[9517])).
% 2.34/2.57 tff(9519,plain,
% 2.34/2.57 (~(s(s(s(s(s(elem!1))))) = s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7491, 9507])).
% 2.34/2.57 tff(9520,plain,
% 2.34/2.57 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9516])).
% 2.34/2.57 tff(9521,plain,
% 2.34/2.57 ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9520])).
% 2.34/2.57 tff(9522,plain,
% 2.34/2.57 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9507])).
% 2.34/2.57 tff(9523,plain,
% 2.34/2.57 (s(s(z)) = s(s(elem!1))),
% 2.34/2.57 inference(transitivity,[status(thm)],[73, 9522, 19])).
% 2.34/2.57 tff(9524,plain,
% 2.34/2.57 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9523])).
% 2.34/2.57 tff(9525,plain,
% 2.34/2.57 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.34/2.57 inference(symmetry,[status(thm)],[9524])).
% 2.34/2.57 tff(9526,plain,
% 2.34/2.57 (s(elem!1) = s(z)),
% 2.34/2.57 inference(transitivity,[status(thm)],[30, 9525, 23])).
% 2.34/2.57 tff(9527,plain,
% 2.34/2.57 (r(s(s(s(s(s(elem!1))))), s(elem!1)) <=> r(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9526])).
% 2.34/2.57 tff(9528,plain,
% 2.34/2.57 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.34/2.57 inference(symmetry,[status(thm)],[9527])).
% 2.34/2.57 tff(9529,plain,
% 2.34/2.57 (~(s(s(s(s(s(elem!1))))) = s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6222, 9507])).
% 2.34/2.57 tff(9530,plain,
% 2.34/2.57 (b(s(s(s(s(s(elem!1))))), s(elem!1)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9526])).
% 2.34/2.57 tff(9531,plain,
% 2.34/2.57 ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) <=> (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9530])).
% 2.34/2.57 tff(9532,plain,
% 2.34/2.57 (s(z) = s(elem!1)),
% 2.34/2.57 inference(transitivity,[status(thm)],[24, 9524, 29])).
% 2.34/2.57 tff(9533,plain,
% 2.34/2.57 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9532, 9523])).
% 2.34/2.57 tff(9534,plain,
% 2.34/2.57 (b(s(elem!1), s(s(elem!1)))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9331, 9533])).
% 2.34/2.57 tff(9535,plain,
% 2.34/2.57 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(z))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9526])).
% 2.34/2.57 tff(9536,plain,
% 2.34/2.57 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(z) = s(s(s(s(elem!1)))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[9535, 265])).
% 2.34/2.57 tff(9537,plain,
% 2.34/2.57 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.34/2.57 inference(symmetry,[status(thm)],[9536])).
% 2.34/2.57 tff(9538,plain,
% 2.34/2.57 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9537])).
% 2.34/2.57 tff(9539,plain,
% 2.34/2.57 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[275, 9538])).
% 2.34/2.57 tff(9540,plain,
% 2.34/2.57 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6172, 9539])).
% 2.34/2.57 tff(9541,plain,
% 2.34/2.57 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9532])).
% 2.34/2.57 tff(9542,plain,
% 2.34/2.57 (z = elem!1),
% 2.34/2.57 inference(transitivity,[status(thm)],[1443, 9541, 85])).
% 2.34/2.57 tff(9543,plain,
% 2.34/2.57 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9542])).
% 2.34/2.57 tff(9544,plain,
% 2.34/2.57 ((s(s(s(s(s(elem!1))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[9543, 6292])).
% 2.34/2.57 tff(9545,plain,
% 2.34/2.57 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.34/2.57 inference(transitivity,[status(thm)],[9544, 6293])).
% 2.34/2.57 tff(9546,plain,
% 2.34/2.57 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9545])).
% 2.34/2.57 tff(9547,plain,
% 2.34/2.57 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[6299, 9546])).
% 2.34/2.57 tff(9548,plain,
% 2.34/2.57 (~b(s(z), s(s(s(elem!1))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[3979, 124, 61, 126])).
% 2.34/2.57 tff(9549,plain,
% 2.34/2.57 (r(s(z), s(s(s(elem!1))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[181, 9548])).
% 2.34/2.57 tff(9550,plain,
% 2.34/2.57 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9542])).
% 2.34/2.57 tff(9551,plain,
% 2.34/2.57 (b(elem!1, s(s(s(elem!1))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[124, 9550])).
% 2.34/2.57 tff(9552,plain,
% 2.34/2.57 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9542])).
% 2.34/2.57 tff(9553,plain,
% 2.34/2.57 (b(s(s(s(elem!1))), elem!1)),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[126, 9552])).
% 2.34/2.57 tff(9554,plain,
% 2.34/2.57 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9526])).
% 2.34/2.57 tff(9555,plain,
% 2.34/2.57 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.57 inference(symmetry,[status(thm)],[9554])).
% 2.34/2.57 tff(9556,plain,
% 2.34/2.57 (r(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[125, 9555])).
% 2.34/2.57 tff(9557,plain,
% 2.34/2.57 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9542, 9532])).
% 2.34/2.57 tff(9558,plain,
% 2.34/2.57 (b(elem!1, s(elem!1))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[61, 9557])).
% 2.34/2.57 tff(9559,assumption,(b(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 2.34/2.57 tff(9560,plain,
% 2.34/2.57 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6322, 97, 6316, 6315, 9559])).
% 2.34/2.57 tff(9561,plain,
% 2.34/2.57 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9560, 7493])).
% 2.34/2.57 tff(9562,plain,
% 2.34/2.57 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6289, 9561, 7492])).
% 2.34/2.57 tff(9563,plain,
% 2.34/2.57 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9562, 7485])).
% 2.34/2.57 tff(9564,plain,
% 2.34/2.57 (r(s(elem!1), s(s(s(elem!1))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[225, 8169])).
% 2.34/2.57 tff(9565,assumption,(r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 2.34/2.57 tff(9566,plain,
% 2.34/2.57 (((~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(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(9567,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9566])).
% 2.34/2.57 tff(9568,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[9567, 9235])).
% 2.34/2.57 tff(9569,plain,
% 2.34/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(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))))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(9570,plain,
% 2.34/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9569, 9568])).
% 2.34/2.57 tff(9571,plain,
% 2.34/2.57 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9570, 155, 9565, 9564, 9563])).
% 2.34/2.57 tff(9572,plain,
% 2.34/2.57 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9571, 8139])).
% 2.34/2.57 tff(9573,plain,
% 2.34/2.57 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6239, 9572, 6223])).
% 2.34/2.57 tff(9574,plain,
% 2.34/2.57 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9573, 8138])).
% 2.34/2.57 tff(9575,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 2.34/2.57 tff(9576,plain,
% 2.34/2.57 (((~![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(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $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(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(9577,plain,
% 2.34/2.57 (((~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(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(9578,plain,
% 2.34/2.57 (((~![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), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(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(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9577])).
% 2.34/2.57 tff(9579,plain,
% 2.34/2.57 (((~![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), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(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(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.57 inference(transitivity,[status(thm)],[9578, 9576])).
% 2.34/2.57 tff(9580,plain,
% 2.34/2.57 ((~![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), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(9581,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9580, 9579])).
% 2.34/2.57 tff(9582,plain,
% 2.34/2.57 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9581, 97, 9575, 9559, 6226])).
% 2.34/2.57 tff(9583,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9582, 9574])).
% 2.34/2.57 tff(9584,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(9585,plain,
% 2.34/2.57 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9584, 9558, 9507, 9534, 9556, 9553, 9551, 9549])).
% 2.34/2.57 tff(9586,plain,
% 2.34/2.57 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6313, 9585, 9547])).
% 2.34/2.57 tff(9587,plain,
% 2.34/2.57 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9542])).
% 2.34/2.57 tff(9588,plain,
% 2.34/2.57 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9523])).
% 2.34/2.57 tff(9589,plain,
% 2.34/2.57 (r(z, s(s(elem!1)))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9446, 9588])).
% 2.34/2.57 tff(9590,plain,
% 2.34/2.57 (r(elem!1, s(s(elem!1)))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9589, 9587])).
% 2.34/2.57 tff(9591,plain,
% 2.34/2.57 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9542])).
% 2.34/2.57 tff(9592,plain,
% 2.34/2.57 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9523])).
% 2.34/2.57 tff(9593,plain,
% 2.34/2.57 (r(s(s(elem!1)), z)),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9441, 9592])).
% 2.34/2.57 tff(9594,plain,
% 2.34/2.57 (r(s(s(elem!1)), elem!1)),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9593, 9591])).
% 2.34/2.57 tff(9595,plain,
% 2.34/2.57 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(9596,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9595])).
% 2.34/2.57 tff(9597,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.57 inference(transitivity,[status(thm)],[9596, 6303])).
% 2.34/2.57 tff(9598,plain,
% 2.34/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(9599,plain,
% 2.34/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9598, 9597])).
% 2.34/2.57 tff(9600,plain,
% 2.34/2.57 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9599, 155, 9594, 9590, 9586])).
% 2.34/2.57 tff(9601,plain,
% 2.34/2.57 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6269, 9600, 9540])).
% 2.34/2.57 tff(9602,plain,
% 2.34/2.57 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.34/2.57 inference(symmetry,[status(thm)],[9522])).
% 2.34/2.57 tff(9603,plain,
% 2.34/2.57 (s(s(elem!1)) = s(s(z))),
% 2.34/2.57 inference(transitivity,[status(thm)],[167, 9602, 72])).
% 2.34/2.57 tff(9604,plain,
% 2.34/2.57 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9603])).
% 2.34/2.57 tff(9605,plain,
% 2.34/2.57 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.34/2.57 inference(symmetry,[status(thm)],[9604])).
% 2.34/2.57 tff(9606,plain,
% 2.34/2.57 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9542])).
% 2.34/2.57 tff(9607,plain,
% 2.34/2.57 (r(s(z), z) <=> r(s(elem!1), z)),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9532])).
% 2.34/2.57 tff(9608,plain,
% 2.34/2.57 (r(s(elem!1), z)),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[81, 9607])).
% 2.34/2.57 tff(9609,plain,
% 2.34/2.57 (r(s(elem!1), elem!1)),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9608, 9606])).
% 2.34/2.57 tff(9610,plain,
% 2.34/2.57 (r(s(elem!1), s(s(s(s(s(elem!1)))))) <=> r(s(z), s(s(s(s(s(elem!1))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[1411])).
% 2.34/2.57 tff(9611,plain,
% 2.34/2.57 (r(s(z), s(s(s(s(s(elem!1)))))) <=> r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.34/2.57 inference(symmetry,[status(thm)],[9610])).
% 2.34/2.57 tff(9612,plain,
% 2.34/2.57 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(z) = s(s(s(s(s(elem!1))))))),
% 2.34/2.57 inference(commutativity,[status(thm)],[])).
% 2.34/2.57 tff(9613,plain,
% 2.34/2.57 ((s(z) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(z))),
% 2.34/2.57 inference(symmetry,[status(thm)],[9612])).
% 2.34/2.57 tff(9614,assumption,(s(z) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.34/2.57 tff(9615,plain,
% 2.34/2.57 (s(s(s(s(s(elem!1))))) = s(z)),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9614, 9613])).
% 2.34/2.57 tff(9616,assumption,(~(s(s(s(s(s(elem!1))))) = s(z))), introduced(assumption)).
% 2.34/2.57 tff(9617,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9616, 9615])).
% 2.34/2.57 tff(9618,plain,((~(s(z) = s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(elem!1))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(9619,plain,
% 2.34/2.57 (~(s(z) = s(s(s(s(s(elem!1))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9618, 6223])).
% 2.34/2.57 tff(9620,plain,
% 2.34/2.57 (b(s(elem!1), s(s(s(s(s(elem!1)))))) <=> b(s(z), s(s(s(s(s(elem!1))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[1411])).
% 2.34/2.57 tff(9621,plain,
% 2.34/2.57 ((~b(s(elem!1), s(s(s(s(s(elem!1))))))) <=> (~b(s(z), s(s(s(s(s(elem!1)))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9620])).
% 2.34/2.57 tff(9622,plain,
% 2.34/2.57 (((~![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(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1), s(s(s(s(s(elem!1))))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(9623,plain,
% 2.34/2.57 (((~b(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(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(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(elem!1), s(s(s(s(s(elem!1))))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(9624,plain,
% 2.34/2.57 (((~![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(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(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(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[9623])).
% 2.34/2.57 tff(9625,plain,
% 2.34/2.57 (((~![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(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(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(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[9624, 9622])).
% 2.34/2.57 tff(9626,plain,
% 2.34/2.57 ((~![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(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(9627,plain,
% 2.34/2.57 ((~![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(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9626, 9625])).
% 2.34/2.57 tff(9628,plain,
% 2.34/2.57 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9627, 97, 6227, 6226, 8216])).
% 2.34/2.57 tff(9629,plain,
% 2.34/2.57 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9628, 9621])).
% 2.34/2.57 tff(9630,plain,
% 2.34/2.57 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1)))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(9631,plain,
% 2.34/2.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1)))))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(9632,plain,
% 2.34/2.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1))))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9631, 9630])).
% 2.34/2.57 tff(9633,plain,
% 2.34/2.57 ((s(z) = s(s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9632, 53])).
% 2.34/2.57 tff(9634,plain,
% 2.34/2.57 (r(s(z), s(s(s(s(s(elem!1))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9633, 9629, 9619])).
% 2.34/2.57 tff(9635,plain,
% 2.34/2.57 (r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[9634, 9611])).
% 2.34/2.57 tff(9636,plain,
% 2.34/2.57 (((~![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(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(9637,plain,
% 2.34/2.57 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(9638,plain,
% 2.34/2.57 (((~![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(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(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(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[9637])).
% 2.34/2.58 tff(9639,plain,
% 2.34/2.58 (((~![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(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(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(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[9638, 9636])).
% 2.34/2.58 tff(9640,plain,
% 2.34/2.58 ((~![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(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(9641,plain,
% 2.34/2.58 ((~![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(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9640, 9639])).
% 2.34/2.58 tff(9642,plain,
% 2.34/2.58 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9641, 97, 6227, 6226, 8216])).
% 2.34/2.58 tff(9643,plain,
% 2.34/2.58 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9642, 6225])).
% 2.34/2.58 tff(9644,plain,
% 2.34/2.58 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[6239, 9643, 6223])).
% 2.34/2.58 tff(9645,plain,
% 2.34/2.58 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9644, 6213])).
% 2.34/2.58 tff(9646,plain,
% 2.34/2.58 ((~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)))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9240, 155, 9565])).
% 2.34/2.58 tff(9647,plain,
% 2.34/2.58 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9646, 9645, 9564])).
% 2.34/2.58 tff(9648,plain,
% 2.34/2.58 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9647, 6275])).
% 2.34/2.58 tff(9649,plain,
% 2.34/2.58 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[6289, 9648, 7492])).
% 2.34/2.58 tff(9650,plain,
% 2.34/2.58 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9649, 6272])).
% 2.34/2.58 tff(9651,plain,
% 2.34/2.58 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(9652,plain,
% 2.34/2.58 (((~![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(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[9651])).
% 2.34/2.58 tff(9653,plain,
% 2.34/2.58 (((~![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(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[9652, 6317])).
% 2.34/2.58 tff(9654,plain,
% 2.34/2.58 ((~![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(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(9655,plain,
% 2.34/2.58 ((~![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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9654, 9653])).
% 2.34/2.58 tff(9656,plain,
% 2.34/2.58 ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9655, 97, 6316, 6315])).
% 2.34/2.58 tff(9657,plain,
% 2.34/2.58 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9656, 9650])).
% 2.34/2.58 tff(9658,plain,
% 2.34/2.58 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[6313, 9657, 6300])).
% 2.34/2.58 tff(9659,plain,
% 2.34/2.58 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[6295])).
% 2.34/2.58 tff(9660,plain,
% 2.34/2.58 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[6299, 9659])).
% 2.34/2.58 tff(9661,plain,
% 2.34/2.58 (((~![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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(9662,plain,
% 2.34/2.58 (((~b(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(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(9663,plain,
% 2.34/2.58 (((~![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(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(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[9662])).
% 2.34/2.58 tff(9664,plain,
% 2.34/2.58 (((~![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(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(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[9663, 9661])).
% 2.34/2.58 tff(9665,plain,
% 2.34/2.58 ((~![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(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(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(9666,plain,
% 2.34/2.58 ((~![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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9665, 9664])).
% 2.34/2.58 tff(9667,plain,
% 2.34/2.58 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9666, 97, 6316, 6315])).
% 2.34/2.58 tff(9668,plain,
% 2.34/2.58 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9667, 9650])).
% 2.34/2.58 tff(9669,plain,
% 2.34/2.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1)))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(9670,plain,
% 2.34/2.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1)))))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(9671,plain,
% 2.34/2.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9670, 9669])).
% 2.34/2.58 tff(9672,plain,
% 2.34/2.58 ((elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9671, 53])).
% 2.34/2.58 tff(9673,plain,
% 2.34/2.58 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9672, 9668, 9660])).
% 2.34/2.58 tff(9674,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(9675,plain,
% 2.34/2.58 (((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(9676,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[9675])).
% 2.34/2.58 tff(9677,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[9676, 9674])).
% 2.34/2.58 tff(9678,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(9679,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9678, 9677])).
% 2.34/2.58 tff(9680,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9679, 155, 1932, 9673, 9658, 9635])).
% 2.34/2.58 tff(9681,plain,((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(9682,plain,
% 2.34/2.58 (~b(s(s(elem!1)), s(elem!1))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9681, 9601, 9553, 9551, 9507, 9556, 9549, 9534, 9609])).
% 2.34/2.58 tff(9683,plain,
% 2.34/2.58 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[1399, 1401])).
% 2.34/2.58 tff(9684,plain,
% 2.34/2.58 (b(s(s(elem!1)), s(elem!1))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[87, 9683])).
% 2.34/2.58 tff(9685,assumption,(~b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 2.34/2.58 tff(9686,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9685, 9684])).
% 2.34/2.58 tff(9687,plain,((~b(s(s(z)), s(z))) | b(s(s(elem!1)), s(elem!1)) | (~(s(s(s(z))) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(9688,plain,
% 2.34/2.58 (~b(s(s(z)), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9687, 9682, 9507])).
% 2.34/2.58 tff(9689,plain,
% 2.34/2.58 (r(s(s(z)), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[122, 9688])).
% 2.34/2.58 tff(9690,plain,
% 2.34/2.58 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9442, 9689])).
% 2.34/2.58 tff(9691,plain,
% 2.34/2.58 (b(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[143, 9690])).
% 2.34/2.58 tff(9692,plain,
% 2.34/2.58 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9691, 9605])).
% 2.34/2.58 tff(9693,plain,
% 2.34/2.58 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9224, 97, 9692, 9601, 9534])).
% 2.34/2.58 tff(9694,plain,
% 2.34/2.58 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9693, 9531])).
% 2.34/2.58 tff(9695,plain,
% 2.34/2.58 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[6239, 9694, 9529])).
% 2.34/2.58 tff(9696,plain,
% 2.34/2.58 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9695, 9528])).
% 2.34/2.58 tff(9697,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(9698,plain,
% 2.34/2.58 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(9699,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[9698])).
% 2.34/2.58 tff(9700,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[9699, 9697])).
% 2.34/2.58 tff(9701,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(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))))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(9702,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9701, 9700])).
% 2.34/2.58 tff(9703,plain,
% 2.34/2.58 ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9702, 155, 9609, 9586, 9556])).
% 2.34/2.58 tff(9704,plain,
% 2.34/2.58 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9703, 9696])).
% 2.34/2.58 tff(9705,plain,
% 2.34/2.58 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9704, 9521])).
% 2.34/2.58 tff(9706,plain,
% 2.34/2.58 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[6289, 9705, 9519])).
% 2.34/2.58 tff(9707,plain,
% 2.34/2.58 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9706, 9518])).
% 2.34/2.58 tff(9708,plain,
% 2.34/2.58 (((~![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(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(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(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))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(9709,plain,
% 2.34/2.58 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(9710,plain,
% 2.34/2.58 (((~![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(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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)))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[9709])).
% 2.34/2.58 tff(9711,plain,
% 2.34/2.58 (((~![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(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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))))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[9710, 9708])).
% 2.34/2.58 tff(9712,plain,
% 2.34/2.58 ((~![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(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(9713,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9712, 9711])).
% 2.34/2.58 tff(9714,plain,
% 2.34/2.58 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9713, 97, 9553, 9692, 9601])).
% 2.34/2.58 tff(9715,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9714, 9707])).
% 2.34/2.58 tff(9716,plain,((~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(9717,plain,
% 2.34/2.58 (~b(z, s(s(s(elem!1))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9716, 9515, 81, 125, 61])).
% 2.34/2.58 tff(9718,plain,
% 2.34/2.58 (r(z, s(s(s(elem!1))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[590, 9717])).
% 2.34/2.58 tff(9719,plain,
% 2.34/2.58 (r(z, s(s(s(z))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9718, 9511])).
% 2.34/2.58 tff(9720,plain,
% 2.34/2.58 (~r(s(s(s(z))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[6467, 2591, 9441, 9446])).
% 2.34/2.58 tff(9721,plain,
% 2.34/2.58 (b(s(s(s(z))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[402, 9720])).
% 2.34/2.58 tff(9722,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[8511, 97, 61, 535, 1360, 1216])).
% 2.34/2.58 tff(9723,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(9724,plain,
% 2.34/2.58 (~b(s(s(s(z))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9723, 9721, 9331, 61])).
% 2.34/2.58 tff(9725,plain,
% 2.34/2.58 (r(s(s(s(z))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[1358, 9724])).
% 2.34/2.58 tff(9726,plain,
% 2.34/2.58 (~r(s(s(z)), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[1969, 9719, 2591, 9446])).
% 2.34/2.58 tff(9727,plain,
% 2.34/2.58 (b(s(s(z)), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[437, 9726])).
% 2.34/2.58 tff(9728,plain,
% 2.34/2.58 (~r(s(s(s(s(z)))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9273, 9727, 9331, 9441, 9725, 9446, 9719])).
% 2.34/2.58 tff(9729,plain,
% 2.34/2.58 (b(s(s(s(s(z)))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[2860, 9728])).
% 2.34/2.58 tff(9730,plain,
% 2.34/2.58 (b(s(s(s(s(elem!1)))), z)),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9729, 9509])).
% 2.34/2.58 tff(9731,plain,
% 2.34/2.58 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[9507])).
% 2.34/2.58 tff(9732,plain,
% 2.34/2.58 (~b(s(z), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[4270, 9727, 9721, 9331])).
% 2.34/2.58 tff(9733,plain,
% 2.34/2.58 (r(s(z), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[253, 9732])).
% 2.34/2.58 tff(9734,plain,
% 2.34/2.58 (r(s(z), s(s(s(elem!1))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9733, 9731])).
% 2.34/2.58 tff(9735,plain,
% 2.34/2.58 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[9507])).
% 2.34/2.58 tff(9736,plain,
% 2.34/2.58 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[9735, 1414])).
% 2.34/2.58 tff(9737,plain,
% 2.34/2.58 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[9736])).
% 2.34/2.58 tff(9738,plain,
% 2.34/2.58 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[286, 9737])).
% 2.34/2.58 tff(9739,plain,
% 2.34/2.58 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.34/2.58 inference(monotonicity,[status(thm)],[9542])).
% 2.34/2.58 tff(9740,plain,
% 2.34/2.58 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.34/2.58 inference(transitivity,[status(thm)],[9509, 9739])).
% 2.34/2.58 tff(9741,plain,
% 2.34/2.58 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9729, 9740])).
% 2.34/2.58 tff(9742,plain,
% 2.34/2.58 (b(s(s(s(elem!1))), elem!1)),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[9515, 9552])).
% 2.34/2.58 tff(9743,plain,
% 2.34/2.58 (((~![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(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(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(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(9744,plain,
% 2.34/2.59 (((~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(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(9745,plain,
% 2.34/2.59 (((~![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(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(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[9744])).
% 2.34/2.59 tff(9746,plain,
% 2.34/2.59 (((~![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(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(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.34/2.59 inference(transitivity,[status(thm)],[9745, 9743])).
% 2.34/2.59 tff(9747,plain,
% 2.34/2.59 ((~![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(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)))))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(9748,plain,
% 2.34/2.59 ((~![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(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[9747, 9746])).
% 2.34/2.59 tff(9749,plain,
% 2.34/2.59 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[9748, 97, 9742, 9741, 9558])).
% 2.34/2.59 tff(9750,plain,
% 2.34/2.59 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[486, 9749, 9738])).
% 2.34/2.59 tff(9751,plain,
% 2.34/2.59 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[578, 9750, 81, 9718, 9734])).
% 2.34/2.59 tff(9752,plain,
% 2.34/2.59 (b(s(z), s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[280, 9751])).
% 2.34/2.59 tff(9753,plain,
% 2.34/2.59 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3812, 9752, 9331, 9730])).
% 2.34/2.59 tff(9754,plain,
% 2.34/2.59 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[336, 9753])).
% 2.34/2.59 tff(9755,plain,
% 2.34/2.59 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[9736, 2507])).
% 2.34/2.59 tff(9756,plain,
% 2.34/2.59 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[9755])).
% 2.34/2.59 tff(9757,plain,
% 2.34/2.59 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[286, 9756])).
% 2.34/2.59 tff(9758,plain,
% 2.34/2.59 (((~![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(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(9759,plain,
% 2.34/2.59 (((~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(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(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(9760,plain,
% 2.34/2.59 (((~![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(elem!1, 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))), 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(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[9759])).
% 2.34/2.59 tff(9761,plain,
% 2.34/2.59 (((~![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(elem!1, 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))), 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(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[9760, 9758])).
% 2.34/2.59 tff(9762,plain,
% 2.34/2.59 ((~![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(elem!1, 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))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(9763,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[9762, 9761])).
% 2.34/2.59 tff(9764,plain,
% 2.34/2.59 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[9763, 97, 9742, 9741, 9558])).
% 2.34/2.59 tff(9765,plain,
% 2.34/2.59 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[821, 9764, 9757])).
% 2.34/2.59 tff(9766,plain,
% 2.34/2.59 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1136, 9765, 125, 9734])).
% 2.34/2.59 tff(9767,plain,
% 2.34/2.59 (b(s(s(s(s(elem!1)))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[511, 9766])).
% 2.34/2.59 tff(9768,plain,
% 2.34/2.59 (~b(z, s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[8295, 9767, 61, 9752])).
% 2.34/2.59 tff(9769,plain,
% 2.34/2.59 (r(z, s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1093, 9768])).
% 2.34/2.59 tff(9770,plain,
% 2.34/2.59 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3067, 9752, 9331, 9727])).
% 2.34/2.59 tff(9771,plain,
% 2.34/2.59 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[452, 9770])).
% 2.34/2.59 tff(9772,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3852, 9771, 9769, 9507, 9446, 9754])).
% 2.34/2.59 tff(9773,plain,(b(s(s(s(z))), s(s(z))) | (~b(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(9774,plain,
% 2.34/2.59 (b(s(s(s(z))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[9773, 9327, 61, 494])).
% 2.34/2.59 tff(9775,plain,
% 2.34/2.59 (~b(s(s(s(z))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[8531, 9774, 61, 9329])).
% 2.34/2.59 tff(9776,plain,
% 2.34/2.59 (r(s(s(s(z))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1358, 9775])).
% 2.34/2.59 tff(9777,plain,
% 2.34/2.59 (~b(s(s(z)), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[9439, 9327, 61, 494])).
% 2.34/2.59 tff(9778,plain,
% 2.34/2.59 (r(s(s(z)), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[625, 9777])).
% 2.34/2.59 tff(9779,plain,
% 2.34/2.59 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[9506, 9327, 61, 494])).
% 2.34/2.59 tff(9780,plain,
% 2.34/2.59 (b(s(z), s(s(s(z))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[193, 6624])).
% 2.34/2.59 tff(9781,plain,
% 2.34/2.59 (~b(s(s(z)), s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[8804, 9780, 1331, 535])).
% 2.34/2.59 tff(9782,plain,
% 2.34/2.59 (r(s(s(z)), s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[437, 9781])).
% 2.34/2.59 tff(9783,plain,
% 2.34/2.59 (~r(s(s(z)), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[5689, 9782, 81, 645, 2597])).
% 2.34/2.59 tff(9784,plain,
% 2.34/2.59 (b(s(s(z)), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[122, 9783])).
% 2.34/2.59 tff(9785,plain,
% 2.34/2.59 (b(s(s(elem!1)), s(elem!1))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[9687, 9784, 1393])).
% 2.34/2.59 tff(9786,plain,
% 2.34/2.59 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[1401, 1399])).
% 2.34/2.59 tff(9787,plain,
% 2.34/2.59 (b(s(elem!1), s(s(elem!1)))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[535, 9786])).
% 2.34/2.59 tff(9788,plain,
% 2.34/2.59 (b(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1995, 1331, 1393])).
% 2.34/2.59 tff(9789,plain,
% 2.34/2.59 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[9788, 1501])).
% 2.34/2.59 tff(9790,plain,
% 2.34/2.59 (((~![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(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1), s(s(elem!1)))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(9791,plain,
% 2.34/2.59 (((~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(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(9792,plain,
% 2.34/2.59 (((~![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(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(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[9791])).
% 2.34/2.59 tff(9793,plain,
% 2.34/2.59 (((~![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(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(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[9792, 9790])).
% 2.34/2.59 tff(9794,plain,
% 2.34/2.59 ((~![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(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))))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(9795,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[9794, 9793])).
% 2.34/2.59 tff(9796,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[9795, 97, 9789, 4448, 9787, 9785])).
% 2.34/2.59 tff(9797,plain,((~b(s(z), s(s(s(elem!1))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(9798,plain,
% 2.34/2.59 (~b(s(z), s(s(s(elem!1))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[9797, 9779, 9327, 9778, 9776, 9774, 9329])).
% 2.34/2.59 tff(9799,plain,
% 2.34/2.59 (r(s(z), s(s(s(elem!1))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[181, 9798])).
% 2.34/2.59 tff(9800,plain,
% 2.34/2.59 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[9779])).
% 2.34/2.59 tff(9801,plain,
% 2.34/2.59 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[9800, 1414])).
% 2.34/2.59 tff(9802,plain,
% 2.34/2.59 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[9801, 2507])).
% 2.34/2.59 tff(9803,plain,
% 2.34/2.59 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[9802])).
% 2.34/2.59 tff(9804,plain,
% 2.34/2.59 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[286, 9803])).
% 2.34/2.59 tff(9805,plain,
% 2.34/2.59 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[9779, 6631])).
% 2.34/2.59 tff(9806,plain,
% 2.34/2.59 (~b(s(s(s(elem!1))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[9716, 124, 9327, 494, 61])).
% 2.34/2.59 tff(9807,plain,
% 2.34/2.59 (r(s(s(s(elem!1))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[246, 9806])).
% 2.34/2.59 tff(9808,plain,
% 2.34/2.59 (~b(z, s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[9444, 494, 9327, 61])).
% 2.34/2.59 tff(9809,plain,
% 2.34/2.59 (r(z, s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[222, 9808])).
% 2.34/2.59 tff(9810,plain,
% 2.34/2.59 (~r(s(s(z)), s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[5689, 2, 9327, 9778, 9776])).
% 2.34/2.59 tff(9811,plain,
% 2.34/2.59 (b(s(s(z)), s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[437, 9810])).
% 2.34/2.59 tff(9812,plain,
% 2.34/2.59 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1102, 488, 82, 9327, 288])).
% 2.34/2.59 tff(9813,plain,
% 2.34/2.59 (b(s(z), s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[280, 9812])).
% 2.34/2.59 tff(9814,plain,
% 2.34/2.59 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3067, 9813, 9329, 9811])).
% 2.34/2.59 tff(9815,plain,
% 2.34/2.59 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[452, 9814])).
% 2.34/2.59 tff(9816,plain,
% 2.34/2.59 (~r(z, s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1436, 488, 494, 9327, 288])).
% 2.34/2.59 tff(9817,plain,
% 2.34/2.59 (b(z, s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1093, 9816])).
% 2.34/2.59 tff(9818,plain,
% 2.34/2.59 (~b(s(s(s(s(elem!1)))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[8316, 9817, 61, 9813])).
% 2.34/2.59 tff(9819,plain,
% 2.34/2.59 (r(s(s(s(s(elem!1)))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[842, 9818])).
% 2.34/2.59 tff(9820,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3278, 9819, 9815, 9809, 2, 495])).
% 2.34/2.59 tff(9821,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), z)) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(9822,plain,
% 2.34/2.59 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[9821, 495, 2, 61, 9807, 82])).
% 2.34/2.59 tff(9823,plain,
% 2.34/2.59 (~b(s(s(s(elem!1))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[2091, 255, 124, 61])).
% 2.34/2.59 tff(9824,plain,
% 2.34/2.59 (r(s(s(s(elem!1))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[493, 9823])).
% 2.34/2.59 tff(9825,plain,
% 2.34/2.59 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1273, 9824, 2, 3009])).
% 2.34/2.59 tff(9826,plain,
% 2.34/2.59 (b(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[141, 53, 42, 9825])).
% 2.34/2.59 tff(9827,plain,
% 2.34/2.59 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1136, 9824, 3009, 495])).
% 2.34/2.59 tff(9828,plain,
% 2.34/2.59 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3154, 255, 176])).
% 2.34/2.59 tff(9829,plain,
% 2.34/2.59 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[523, 9828])).
% 2.34/2.59 tff(9830,plain,
% 2.34/2.59 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[821, 9829, 9827])).
% 2.34/2.59 tff(9831,plain,
% 2.34/2.59 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[486, 9828, 1150])).
% 2.34/2.59 tff(9832,plain,
% 2.34/2.59 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[2741, 9831, 9830, 9826])).
% 2.34/2.59 tff(9833,plain,
% 2.34/2.59 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[452, 9832])).
% 2.34/2.59 tff(9834,plain,
% 2.34/2.59 (~b(s(z), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[2661, 204, 61, 127])).
% 2.34/2.59 tff(9835,plain,
% 2.34/2.59 (r(s(z), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[548, 9834])).
% 2.34/2.59 tff(9836,plain,
% 2.34/2.59 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1267, 155, 125, 2, 9835])).
% 2.34/2.59 tff(9837,plain,
% 2.34/2.59 (b(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[58, 9836])).
% 2.34/2.59 tff(9838,plain,
% 2.34/2.59 (((~![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(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(9839,plain,
% 2.34/2.59 (((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(9840,plain,
% 2.34/2.59 (((~![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(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[9839])).
% 2.34/2.59 tff(9841,plain,
% 2.34/2.59 (((~![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(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[9840, 9838])).
% 2.34/2.59 tff(9842,plain,
% 2.34/2.59 ((~![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(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(9843,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[9842, 9841])).
% 2.34/2.59 tff(9844,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[9843, 97, 124, 339, 204, 9837])).
% 2.34/2.59 tff(9845,plain,((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(9846,plain,
% 2.34/2.59 (~b(z, s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[9845, 339, 124, 9824, 2, 61, 127])).
% 2.34/2.59 tff(9847,plain,
% 2.34/2.59 (r(z, s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[222, 9846])).
% 2.34/2.59 tff(9848,plain,
% 2.34/2.59 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[4129, 339, 127, 815, 1150])).
% 2.34/2.59 tff(9849,plain,
% 2.34/2.59 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[354, 9848])).
% 2.34/2.59 tff(9850,plain,
% 2.34/2.59 (b(z, s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[369, 9849, 124])).
% 2.34/2.59 tff(9851,plain,
% 2.34/2.59 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1494, 9850, 61, 255])).
% 2.34/2.59 tff(9852,plain,
% 2.34/2.59 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[452, 9851])).
% 2.34/2.59 tff(9853,plain,
% 2.34/2.59 (~b(s(s(s(s(elem!1)))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[8316, 9850, 61, 255])).
% 2.34/2.59 tff(9854,plain,
% 2.34/2.59 (r(s(s(s(s(elem!1)))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[842, 9853])).
% 2.34/2.59 tff(9855,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3278, 9854, 9852, 495, 9847, 2])).
% 2.34/2.59 tff(9856,plain,((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(9857,plain,
% 2.34/2.59 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[9856, 255, 2, 61, 495, 124, 9826, 9827, 1150])).
% 2.34/2.59 tff(9858,plain,
% 2.34/2.59 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[336, 9857])).
% 2.34/2.59 tff(9859,plain,
% 2.34/2.59 (((~![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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(9860,plain,
% 2.34/2.59 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(9861,plain,
% 2.34/2.59 (((~![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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[9860])).
% 2.34/2.59 tff(9862,plain,
% 2.34/2.59 (((~![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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[9861, 9859])).
% 2.34/2.59 tff(9863,plain,
% 2.34/2.59 ((~![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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 2.34/2.60 inference(quant_inst,[status(thm)],[])).
% 2.34/2.60 tff(9864,plain,
% 2.34/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.34/2.60 inference(modus_ponens,[status(thm)],[9863, 9862])).
% 2.34/2.60 tff(9865,plain,
% 2.34/2.60 ($false),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[9864, 97, 124, 372, 473, 805])).
% 2.34/2.60 tff(9866,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.60 tff(9867,plain,
% 2.34/2.60 (~b(z, s(s(s(s(elem!1)))))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[9866, 9830, 9831, 124])).
% 2.34/2.60 tff(9868,plain,
% 2.34/2.60 (r(z, s(s(s(s(elem!1)))))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[1093, 9867])).
% 2.34/2.60 tff(9869,plain,
% 2.34/2.60 (~r(s(z), z)),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[2153, 645, 309, 463, 2])).
% 2.34/2.60 tff(9870,plain,
% 2.34/2.60 (b(s(z), z)),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[568, 9869])).
% 2.34/2.60 tff(9871,plain,
% 2.34/2.60 (~b(s(s(s(s(elem!1)))), z)),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[3055, 9870, 61, 255])).
% 2.34/2.60 tff(9872,plain,
% 2.34/2.60 (r(s(s(s(s(elem!1)))), z)),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[842, 9871])).
% 2.34/2.60 tff(9873,plain,
% 2.34/2.60 ($false),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[3128, 155, 463, 309, 9872, 645])).
% 2.34/2.60 tff(9874,plain,((~r(s(s(z)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.60 tff(9875,plain,
% 2.34/2.60 (~r(s(s(z)), z)),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[9874, 9868, 9858, 61, 255, 2])).
% 2.34/2.60 tff(9876,plain,
% 2.34/2.60 (b(s(s(z)), z)),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[625, 9875])).
% 2.34/2.60 tff(9877,plain,
% 2.34/2.60 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[306, 204, 124, 83])).
% 2.34/2.60 tff(9878,plain,
% 2.34/2.60 (r(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[58, 9877])).
% 2.34/2.60 tff(9879,plain,
% 2.34/2.60 ($false),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[1267, 155, 125, 2, 9835, 9878])).
% 2.34/2.60 tff(9880,plain,((~b(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.60 tff(9881,plain,
% 2.34/2.60 (~b(z, s(s(z)))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[9880, 9824, 2, 124, 9876, 61, 9826])).
% 2.34/2.60 tff(9882,plain,
% 2.34/2.60 (r(z, s(s(z)))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[222, 9881])).
% 2.34/2.60 tff(9883,plain,
% 2.34/2.60 ($false),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[3820, 155, 9868, 9858, 9882, 9833])).
% 2.34/2.60 tff(9884,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))) | b(s(z), s(s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.60 tff(9885,plain,
% 2.34/2.60 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[9884, 9822, 61, 124, 495, 9798, 2])).
% 2.34/2.60 tff(9886,plain,
% 2.34/2.60 (r(s(z), s(s(s(s(elem!1)))))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[280, 9885])).
% 2.34/2.60 tff(9887,plain,
% 2.34/2.60 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[1136, 495, 494, 9799])).
% 2.34/2.60 tff(9888,plain,
% 2.34/2.60 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[821, 9887, 9804])).
% 2.34/2.60 tff(9889,plain,
% 2.34/2.60 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.34/2.60 inference(monotonicity,[status(thm)],[9801])).
% 2.34/2.60 tff(9890,plain,
% 2.34/2.60 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.34/2.60 inference(modus_ponens,[status(thm)],[286, 9889])).
% 2.34/2.60 tff(9891,plain,
% 2.34/2.60 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[486, 9822, 9890])).
% 2.34/2.60 tff(9892,plain,
% 2.34/2.60 (~b(z, s(s(s(s(elem!1)))))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[9866, 9891, 124, 9888])).
% 2.34/2.60 tff(9893,plain,
% 2.34/2.60 (r(z, s(s(s(s(elem!1)))))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[1093, 9892])).
% 2.34/2.60 tff(9894,plain,
% 2.34/2.60 ($false),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[4930, 9893, 9886, 9327, 9807, 9799])).
% 2.34/2.60 tff(9895,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.60 tff(9896,plain,
% 2.34/2.60 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[9895, 2, 61, 124, 82])).
% 2.34/2.60 tff(9897,plain,
% 2.34/2.60 (b(s(s(s(s(elem!1)))), s(z))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[511, 9896])).
% 2.34/2.60 tff(9898,plain,
% 2.34/2.60 (b(s(s(s(elem!1))), s(s(z)))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[1995, 9774, 9779])).
% 2.34/2.60 tff(9899,plain,
% 2.34/2.60 (~b(z, s(s(s(s(elem!1)))))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[543, 9897, 9329, 61])).
% 2.34/2.60 tff(9900,plain,
% 2.34/2.60 (r(z, s(s(s(s(elem!1)))))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[1093, 9899])).
% 2.34/2.60 tff(9901,plain,
% 2.34/2.60 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[1436, 9900, 494, 9327, 9807])).
% 2.34/2.60 tff(9902,plain,
% 2.34/2.60 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[486, 9901, 9890])).
% 2.34/2.60 tff(9903,plain,
% 2.34/2.60 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[2153, 9900, 9327, 9778, 2])).
% 2.34/2.60 tff(9904,plain,
% 2.34/2.60 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[336, 9903])).
% 2.34/2.60 tff(9905,plain,
% 2.34/2.60 ($false),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[753, 9904, 9902, 9898, 9897])).
% 2.34/2.60 tff(9906,plain,((~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.60 tff(9907,plain,
% 2.34/2.60 (~r(s(s(z)), s(z))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[9906, 124, 61, 82])).
% 2.34/2.60 tff(9908,plain,
% 2.34/2.60 (b(s(s(z)), s(z))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[122, 9907])).
% 2.44/2.60 tff(9909,plain,
% 2.44/2.60 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[5757, 9799, 9776, 494])).
% 2.44/2.60 tff(9910,plain,
% 2.44/2.60 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 2.44/2.60 inference(monotonicity,[status(thm)],[1393])).
% 2.44/2.60 tff(9911,plain,
% 2.44/2.60 (b(s(s(s(elem!1))), z)),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[1216, 9910])).
% 2.44/2.60 tff(9912,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[239, 9911])).
% 2.44/2.60 tff(9913,plain,((~b(s(s(s(z))), z)) | b(s(s(s(elem!1))), z) | (~(s(s(s(z))) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(9914,plain,
% 2.44/2.60 (~b(s(s(s(z))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9913, 9806, 9779])).
% 2.44/2.60 tff(9915,plain,
% 2.44/2.60 (r(s(s(s(z))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[402, 9914])).
% 2.44/2.60 tff(9916,plain,
% 2.44/2.60 (b(s(s(s(z))), s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9773, 81, 61, 125])).
% 2.44/2.60 tff(9917,plain,
% 2.44/2.60 (b(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1995, 9916, 9507])).
% 2.44/2.60 tff(9918,plain,
% 2.44/2.60 (~b(z, s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[543, 513, 9331, 61])).
% 2.44/2.60 tff(9919,plain,
% 2.44/2.60 (r(z, s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1093, 9918])).
% 2.44/2.60 tff(9920,plain,
% 2.44/2.60 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[3077, 9919, 9441, 386, 1961])).
% 2.44/2.60 tff(9921,plain,
% 2.44/2.60 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[336, 9920])).
% 2.44/2.60 tff(9922,plain,
% 2.44/2.60 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1436, 9919, 125, 81, 288])).
% 2.44/2.60 tff(9923,plain,
% 2.44/2.60 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[486, 9922, 9738])).
% 2.44/2.60 tff(9924,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[753, 9923, 9921, 9917, 513])).
% 2.44/2.60 tff(9925,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(9926,plain,
% 2.44/2.60 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9925, 1961, 9327, 9807, 9915, 494, 61])).
% 2.44/2.60 tff(9927,plain,
% 2.44/2.60 (r(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[511, 9926])).
% 2.44/2.60 tff(9928,plain,
% 2.44/2.60 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9866, 372, 124, 9888])).
% 2.44/2.60 tff(9929,plain,
% 2.44/2.60 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[503, 3480, 125, 495])).
% 2.44/2.60 tff(9930,plain,
% 2.44/2.60 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[486, 9929, 2718])).
% 2.44/2.60 tff(9931,plain,
% 2.44/2.60 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.44/2.60 inference(symmetry,[status(thm)],[9930])).
% 2.44/2.60 tff(9932,plain,
% 2.44/2.60 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[9931])).
% 2.44/2.60 tff(9933,plain,
% 2.44/2.60 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[9932, 2679])).
% 2.44/2.60 tff(9934,plain,
% 2.44/2.60 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(elem!1)))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[9933])).
% 2.44/2.60 tff(9935,plain,
% 2.44/2.60 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[286, 9934])).
% 2.44/2.60 tff(9936,plain,
% 2.44/2.60 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[3089, 1749, 9935])).
% 2.44/2.60 tff(9937,plain,
% 2.44/2.60 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[340])).
% 2.44/2.60 tff(9938,plain,
% 2.44/2.60 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.44/2.60 inference(symmetry,[status(thm)],[9937])).
% 2.44/2.60 tff(9939,plain,
% 2.44/2.60 ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[9938])).
% 2.44/2.60 tff(9940,plain,
% 2.44/2.60 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[1762, 9939])).
% 2.44/2.60 tff(9941,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1702, 9940])).
% 2.44/2.60 tff(9942,plain,(b(s(s(s(z))), s(s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(9943,plain,
% 2.44/2.60 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9942, 9936, 9930])).
% 2.44/2.60 tff(9944,plain,
% 2.44/2.60 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[9930])).
% 2.44/2.60 tff(9945,plain,
% 2.44/2.60 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.44/2.60 inference(symmetry,[status(thm)],[9944])).
% 2.44/2.60 tff(9946,plain,
% 2.44/2.60 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[349, 9930])).
% 2.44/2.60 tff(9947,plain,
% 2.44/2.60 (s(s(s(s(elem!1)))) = elem!1),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1734, 9946])).
% 2.44/2.60 tff(9948,plain,
% 2.44/2.60 (~(s(s(s(z))) = elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1742, 9930])).
% 2.44/2.60 tff(9949,plain,
% 2.44/2.60 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2225, 9948, 1216, 372, 441, 9947])).
% 2.44/2.60 tff(9950,plain,
% 2.44/2.60 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[9949, 9945])).
% 2.44/2.60 tff(9951,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1749, 9950])).
% 2.44/2.60 tff(9952,plain,((~b(z, s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(9953,plain,
% 2.44/2.60 (~b(s(s(s(z))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9952, 1749, 372, 441, 2718, 125, 495, 61])).
% 2.44/2.60 tff(9954,plain,
% 2.44/2.60 (r(s(s(s(z))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[402, 9953])).
% 2.44/2.60 tff(9955,plain,
% 2.44/2.60 (~r(s(s(s(z))), s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2625, 155, 226, 645, 9954])).
% 2.44/2.60 tff(9956,plain,
% 2.44/2.60 (b(s(s(s(z))), s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[421, 9955])).
% 2.44/2.60 tff(9957,plain,
% 2.44/2.60 (((~![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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(9958,plain,
% 2.44/2.60 (((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(9959,plain,
% 2.44/2.60 (((~![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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z)))))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[9958])).
% 2.44/2.60 tff(9960,plain,
% 2.44/2.60 (((~![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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[9959, 9957])).
% 2.44/2.60 tff(9961,plain,
% 2.44/2.60 ((~![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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(9962,plain,
% 2.44/2.60 ((~![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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z)))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[9961, 9960])).
% 2.44/2.60 tff(9963,plain,
% 2.44/2.60 (~b(z, s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9962, 97, 372, 441, 9943])).
% 2.44/2.60 tff(9964,plain,
% 2.44/2.60 (r(z, s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1318, 9963])).
% 2.44/2.60 tff(9965,plain,
% 2.44/2.60 (~r(s(s(z)), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2554, 155, 645, 9964, 9954])).
% 2.44/2.60 tff(9966,plain,
% 2.44/2.60 (b(s(s(z)), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[437, 9965])).
% 2.44/2.60 tff(9967,plain,
% 2.44/2.60 (((~![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(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(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(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(9968,plain,
% 2.44/2.60 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(9969,plain,
% 2.44/2.60 (((~![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(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[9968])).
% 2.44/2.60 tff(9970,plain,
% 2.44/2.60 (((~![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(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[9969, 9967])).
% 2.44/2.60 tff(9971,plain,
% 2.44/2.60 ((~![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(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(9972,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[9971, 9970])).
% 2.44/2.60 tff(9973,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9972, 97, 441, 9966, 9956, 9943])).
% 2.44/2.60 tff(9974,plain,(r(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(9975,plain,
% 2.44/2.60 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9974, 9928, 61, 9809, 9909, 495, 494, 9778, 372])).
% 2.44/2.60 tff(9976,plain,
% 2.44/2.60 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[452, 9975])).
% 2.44/2.60 tff(9977,plain,
% 2.44/2.60 (~r(s(s(s(s(elem!1)))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2905, 9976, 9329, 61, 9908])).
% 2.44/2.60 tff(9978,plain,
% 2.44/2.60 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[486, 9928, 9890])).
% 2.44/2.60 tff(9979,plain,
% 2.44/2.60 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1102, 9978, 82, 9327, 9807])).
% 2.44/2.60 tff(9980,plain,
% 2.44/2.60 (b(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[280, 9979])).
% 2.44/2.60 tff(9981,plain,
% 2.44/2.60 (~b(s(s(s(s(elem!1)))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[8316, 9980, 61, 372])).
% 2.44/2.60 tff(9982,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[842, 9981, 9977])).
% 2.44/2.60 tff(9983,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | b(s(s(s(elem!1))), s(z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(9984,plain,
% 2.44/2.60 (~b(z, s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9983, 9927, 82, 61, 124])).
% 2.44/2.60 tff(9985,plain,
% 2.44/2.60 (r(z, s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1093, 9984])).
% 2.44/2.60 tff(9986,plain,
% 2.44/2.60 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1436, 9985, 494, 9327, 9807])).
% 2.44/2.60 tff(9987,plain,
% 2.44/2.60 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[486, 9986, 9890])).
% 2.44/2.60 tff(9988,plain,
% 2.44/2.60 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[3077, 9985, 9778, 9915, 1961])).
% 2.44/2.60 tff(9989,plain,
% 2.44/2.60 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[336, 9988])).
% 2.44/2.60 tff(9990,plain,
% 2.44/2.60 (~b(s(s(s(s(elem!1)))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[8474, 9989, 9774, 9987, 9909, 9898])).
% 2.44/2.60 tff(9991,plain,
% 2.44/2.60 (r(s(s(s(s(elem!1)))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[842, 9990])).
% 2.44/2.60 tff(9992,plain,
% 2.44/2.60 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1111, 9985, 61, 9327, 124, 9807, 9890])).
% 2.44/2.60 tff(9993,plain,
% 2.44/2.60 (b(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[280, 9992])).
% 2.44/2.60 tff(9994,plain,
% 2.44/2.60 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[3267, 9989, 9329, 9993])).
% 2.44/2.60 tff(9995,plain,
% 2.44/2.60 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[452, 9994])).
% 2.44/2.60 tff(9996,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2905, 9995, 9991, 9329, 61, 9908])).
% 2.44/2.60 tff(9997,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(9998,plain,
% 2.44/2.60 (~r(s(s(z)), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9997, 124, 61, 82])).
% 2.44/2.60 tff(9999,plain,
% 2.44/2.60 (b(s(s(z)), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[437, 9998])).
% 2.44/2.60 tff(10000,plain,
% 2.44/2.60 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1111, 463, 61, 81, 124, 288, 1418])).
% 2.44/2.60 tff(10001,plain,
% 2.44/2.60 (b(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[280, 10000])).
% 2.44/2.60 tff(10002,plain,
% 2.44/2.60 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[3067, 10001, 9331, 1361])).
% 2.44/2.60 tff(10003,plain,
% 2.44/2.60 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[452, 10002])).
% 2.44/2.60 tff(10004,plain,
% 2.44/2.60 (~r(s(s(s(s(elem!1)))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2905, 10003, 9331, 61, 87])).
% 2.44/2.60 tff(10005,plain,
% 2.44/2.60 (b(s(s(s(s(elem!1)))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[842, 10004])).
% 2.44/2.60 tff(10006,plain,
% 2.44/2.60 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[3852, 10003, 1393, 226, 463])).
% 2.44/2.60 tff(10007,plain,
% 2.44/2.60 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[336, 10006])).
% 2.44/2.60 tff(10008,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[3812, 10007, 10005, 9331, 10001])).
% 2.44/2.60 tff(10009,plain,((~r(z, s(s(s(s(elem!1)))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(10010,plain,
% 2.44/2.60 (~r(z, s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[10009, 9908, 9809, 61, 9779, 9999, 9327, 124, 9807])).
% 2.44/2.60 tff(10011,plain,
% 2.44/2.60 (b(z, s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1093, 10010])).
% 2.44/2.60 tff(10012,plain,
% 2.44/2.60 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[543, 10011, 9329, 61])).
% 2.44/2.60 tff(10013,plain,
% 2.44/2.60 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9983, 10011, 82, 61, 124])).
% 2.44/2.60 tff(10014,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[511, 10013, 10012])).
% 2.44/2.60 tff(10015,plain,((~b(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(10016,plain,
% 2.44/2.60 (~b(z, s(s(s(elem!1))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[10015, 82, 61])).
% 2.44/2.60 tff(10017,plain,
% 2.44/2.60 (r(z, s(s(s(elem!1))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[590, 10016])).
% 2.44/2.60 tff(10018,plain,
% 2.44/2.60 (r(z, s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[6374, 10017, 9805])).
% 2.44/2.60 tff(10019,plain,
% 2.44/2.60 (~b(s(s(s(z))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[8531, 9916, 61, 9331])).
% 2.44/2.60 tff(10020,plain,
% 2.44/2.60 (r(s(s(s(z))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1358, 10019])).
% 2.44/2.60 tff(10021,plain,
% 2.44/2.60 (~b(s(z), s(s(s(elem!1))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9797, 9507, 81, 9441, 10020, 9916, 9331])).
% 2.44/2.60 tff(10022,plain,
% 2.44/2.60 (r(s(z), s(s(s(elem!1))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[181, 10021])).
% 2.44/2.60 tff(10023,plain,
% 2.44/2.60 (~r(s(s(z)), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[5689, 2, 81, 9441, 10020])).
% 2.44/2.60 tff(10024,plain,
% 2.44/2.60 (b(s(s(z)), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[437, 10023])).
% 2.44/2.60 tff(10025,plain,
% 2.44/2.60 (~r(s(s(s(s(z)))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9273, 10024, 9331, 9441, 10020, 9446, 1300])).
% 2.44/2.60 tff(10026,plain,
% 2.44/2.60 (b(s(s(s(s(z)))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2860, 10025])).
% 2.44/2.60 tff(10027,plain,
% 2.44/2.60 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[10026, 9740])).
% 2.44/2.60 tff(10028,plain,
% 2.44/2.60 (elem!1 = z),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1888, 9542])).
% 2.44/2.60 tff(10029,plain,
% 2.44/2.60 (~b(s(z), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[6628, 10021, 9507])).
% 2.44/2.60 tff(10030,plain,
% 2.44/2.60 (r(s(z), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[253, 10029])).
% 2.44/2.60 tff(10031,plain,
% 2.44/2.60 (~r(s(s(s(z))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1308, 1300, 81, 10030])).
% 2.44/2.60 tff(10032,plain,
% 2.44/2.60 (b(s(s(s(z))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[402, 10031])).
% 2.44/2.60 tff(10033,plain,
% 2.44/2.60 (b(s(s(s(elem!1))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9913, 10032, 9507])).
% 2.44/2.60 tff(10034,plain,
% 2.44/2.60 (b(s(s(s(elem!1))), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[8380, 10033, 10028])).
% 2.44/2.60 tff(10035,plain,
% 2.44/2.60 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9763, 97, 10034, 10027, 9558])).
% 2.44/2.60 tff(10036,plain,
% 2.44/2.60 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[821, 10035, 9757])).
% 2.44/2.60 tff(10037,plain,
% 2.44/2.60 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1136, 10036, 125, 10022])).
% 2.44/2.60 tff(10038,plain,
% 2.44/2.60 (b(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[511, 10037])).
% 2.44/2.60 tff(10039,plain,
% 2.44/2.60 (~b(z, s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[543, 10038, 9331, 61])).
% 2.44/2.60 tff(10040,plain,
% 2.44/2.60 (r(z, s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1093, 10039])).
% 2.44/2.60 tff(10041,plain,
% 2.44/2.60 (b(s(s(s(s(elem!1)))), z)),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[10026, 9509])).
% 2.44/2.60 tff(10042,plain,
% 2.44/2.60 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9748, 97, 10034, 10027, 9558])).
% 2.44/2.60 tff(10043,plain,
% 2.44/2.60 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[486, 10042, 9738])).
% 2.44/2.60 tff(10044,plain,
% 2.44/2.60 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[924, 10043, 10036, 10022])).
% 2.44/2.60 tff(10045,plain,
% 2.44/2.60 (b(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[280, 10044])).
% 2.44/2.60 tff(10046,plain,
% 2.44/2.60 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[3812, 10045, 9331, 10041])).
% 2.44/2.60 tff(10047,plain,
% 2.44/2.60 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[336, 10046])).
% 2.44/2.60 tff(10048,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2153, 10047, 10040, 81, 9441, 2])).
% 2.44/2.60 tff(10049,plain,((~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(10050,plain,
% 2.44/2.60 (~r(s(s(z)), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[10049, 9327, 61, 494, 10018])).
% 2.44/2.60 tff(10051,plain,
% 2.44/2.60 (b(s(s(z)), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[122, 10050])).
% 2.44/2.60 tff(10052,plain,
% 2.44/2.60 (~b(s(z), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[6628, 9798, 9779])).
% 2.44/2.60 tff(10053,plain,
% 2.44/2.60 (r(s(z), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[253, 10052])).
% 2.44/2.60 tff(10054,plain,
% 2.44/2.60 (~r(s(s(s(z))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1308, 10018, 9327, 10053])).
% 2.44/2.60 tff(10055,plain,
% 2.44/2.60 (b(s(s(s(z))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[402, 10054])).
% 2.44/2.60 tff(10056,plain,
% 2.44/2.60 (b(s(s(s(elem!1))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9913, 10055, 9779])).
% 2.44/2.60 tff(10057,plain,
% 2.44/2.60 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[543, 372, 535, 61])).
% 2.44/2.60 tff(10058,plain,
% 2.44/2.60 (r(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[511, 10057])).
% 2.44/2.60 tff(10059,plain,
% 2.44/2.60 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1136, 10058, 125, 225])).
% 2.44/2.60 tff(10060,plain,
% 2.44/2.60 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[821, 10059, 802])).
% 2.44/2.60 tff(10061,plain,
% 2.44/2.60 (((~![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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(10062,plain,
% 2.44/2.60 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(10063,plain,
% 2.44/2.60 (((~![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(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[10062])).
% 2.44/2.60 tff(10064,plain,
% 2.44/2.60 (((~![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(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.44/2.61 inference(transitivity,[status(thm)],[10063, 10061])).
% 2.44/2.61 tff(10065,plain,
% 2.44/2.61 ((~![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(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(10066,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[10065, 10064])).
% 2.44/2.61 tff(10067,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[10066, 97, 126, 372, 805, 876])).
% 2.44/2.61 tff(10068,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(10069,plain,
% 2.44/2.61 (~b(s(s(s(s(elem!1)))), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[10068, 10060, 126, 372])).
% 2.44/2.61 tff(10070,plain,
% 2.44/2.61 (r(s(s(s(s(elem!1)))), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[842, 10069])).
% 2.44/2.61 tff(10071,plain,
% 2.44/2.61 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2905, 10070, 535, 61, 87])).
% 2.44/2.61 tff(10072,plain,
% 2.44/2.61 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[452, 10071])).
% 2.44/2.61 tff(10073,plain,
% 2.44/2.61 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[9974, 10072, 61, 226, 1749, 10058, 125, 645, 372])).
% 2.44/2.61 tff(10074,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[3303, 10073, 10072, 126, 372])).
% 2.44/2.61 tff(10075,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~r(z, s(s(z)))) | r(s(s(s(z))), s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(10076,plain,
% 2.44/2.61 (~b(z, s(s(s(s(elem!1)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[10075, 10056, 61, 9809, 9909, 494, 9778, 9329, 10051, 9804, 9799])).
% 2.44/2.61 tff(10077,plain,
% 2.44/2.61 (r(z, s(s(s(s(elem!1)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1093, 10076])).
% 2.44/2.61 tff(10078,plain,
% 2.44/2.61 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[9779])).
% 2.44/2.61 tff(10079,plain,
% 2.44/2.61 (s(s(z)) = s(s(elem!1))),
% 2.44/2.61 inference(transitivity,[status(thm)],[73, 10078, 19])).
% 2.44/2.61 tff(10080,plain,
% 2.44/2.61 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[10079])).
% 2.44/2.61 tff(10081,plain,
% 2.44/2.61 (s(z) = s(elem!1)),
% 2.44/2.61 inference(transitivity,[status(thm)],[24, 10080, 29])).
% 2.44/2.61 tff(10082,plain,
% 2.44/2.61 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[10081])).
% 2.44/2.61 tff(10083,plain,
% 2.44/2.61 (z = elem!1),
% 2.44/2.61 inference(transitivity,[status(thm)],[1443, 10082, 85])).
% 2.44/2.61 tff(10084,plain,
% 2.44/2.61 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[10083, 10081])).
% 2.44/2.61 tff(10085,plain,
% 2.44/2.61 (b(elem!1, s(elem!1))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[61, 10084])).
% 2.44/2.61 tff(10086,plain,
% 2.44/2.61 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[578, 488, 81, 570, 225])).
% 2.44/2.61 tff(10087,plain,
% 2.44/2.61 (b(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[280, 10086])).
% 2.44/2.61 tff(10088,plain,
% 2.44/2.61 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[8403, 488, 570, 463, 226])).
% 2.44/2.61 tff(10089,plain,
% 2.44/2.61 (r(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[1961, 8044])).
% 2.44/2.61 tff(10090,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[137, 10089])).
% 2.44/2.61 tff(10091,plain,((~r(s(s(z)), s(s(s(z))))) | r(s(s(z)), s(s(s(elem!1)))) | (~(s(s(s(z))) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(10092,plain,
% 2.44/2.61 (~r(s(s(z)), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[10091, 10088, 1393])).
% 2.44/2.61 tff(10093,plain,
% 2.44/2.61 (b(s(s(z)), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[437, 10092])).
% 2.44/2.61 tff(10094,plain,
% 2.44/2.61 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[3067, 10093, 9331, 10087])).
% 2.44/2.61 tff(10095,plain,
% 2.44/2.61 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[452, 10094])).
% 2.44/2.61 tff(10096,plain,
% 2.44/2.61 (~r(s(s(s(s(elem!1)))), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2905, 10095, 9331, 61, 87])).
% 2.44/2.61 tff(10097,plain,
% 2.44/2.61 (b(s(s(s(s(elem!1)))), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[842, 10096])).
% 2.44/2.61 tff(10098,plain,
% 2.44/2.61 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[3852, 10095, 1393, 226, 463])).
% 2.44/2.61 tff(10099,plain,
% 2.44/2.61 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[336, 10098])).
% 2.44/2.61 tff(10100,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[3812, 10099, 10097, 9331, 10087])).
% 2.44/2.61 tff(10101,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(10102,plain,
% 2.44/2.61 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[10101, 9779, 9809, 10077, 61, 10051, 10017, 9327, 9799])).
% 2.44/2.61 tff(10103,plain,
% 2.44/2.61 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[486, 10102, 9890])).
% 2.44/2.61 tff(10104,plain,
% 2.44/2.61 (elem!1 = z),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1888, 10083])).
% 2.44/2.61 tff(10105,plain,
% 2.44/2.61 (b(s(s(s(elem!1))), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[8380, 10056, 10104])).
% 2.44/2.61 tff(10106,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[9748, 97, 6316, 473, 1458, 9575])).
% 2.44/2.61 tff(10107,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(10108,plain,
% 2.44/2.61 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[10107, 10105, 10103, 10085])).
% 2.44/2.61 tff(10109,plain,
% 2.44/2.61 (~b(s(s(s(s(elem!1)))), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[4474, 10108, 10083])).
% 2.44/2.61 tff(10110,plain,
% 2.44/2.61 (r(s(s(s(s(elem!1)))), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[842, 10109])).
% 2.44/2.61 tff(10111,plain,
% 2.44/2.61 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[4887, 10110, 9327, 10077])).
% 2.44/2.61 tff(10112,plain,
% 2.44/2.61 (b(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[280, 10111])).
% 2.44/2.61 tff(10113,plain,
% 2.44/2.61 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2905, 10110, 9329, 61, 10051])).
% 2.44/2.61 tff(10114,plain,
% 2.44/2.61 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[452, 10113])).
% 2.44/2.61 tff(10115,plain,
% 2.44/2.61 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[3326, 10110, 9778, 9779, 10077])).
% 2.44/2.61 tff(10116,plain,
% 2.44/2.61 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[336, 10115])).
% 2.44/2.61 tff(10117,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[3267, 10116, 10114, 9329, 10112])).
% 2.44/2.61 tff(10118,plain,(b(s(s(s(elem!1))), s(z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(10119,plain,
% 2.44/2.61 (b(s(s(s(elem!1))), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[10118, 61])).
% 2.44/2.61 tff(10120,plain,
% 2.44/2.61 (((~![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(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(10121,plain,
% 2.44/2.61 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(10122,plain,
% 2.44/2.61 (((~![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(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[10121])).
% 2.44/2.61 tff(10123,plain,
% 2.44/2.61 (((~![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(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[10122, 10120])).
% 2.44/2.61 tff(10124,plain,
% 2.44/2.61 ((~![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(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(10125,plain,
% 2.44/2.61 ((~![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(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[10124, 10123])).
% 2.44/2.61 tff(10126,plain,
% 2.44/2.61 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[10125, 97, 1139, 550, 1360])).
% 2.44/2.61 tff(10127,plain,
% 2.44/2.61 (((~![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(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(10128,plain,
% 2.44/2.61 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(10129,plain,
% 2.44/2.61 (((~![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(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[10128])).
% 2.44/2.61 tff(10130,plain,
% 2.44/2.61 (((~![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(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[10129, 10127])).
% 2.44/2.61 tff(10131,plain,
% 2.44/2.61 ((~![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(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(10132,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[10131, 10130])).
% 2.44/2.61 tff(10133,plain,
% 2.44/2.61 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[10132, 97, 1139, 550, 1360])).
% 2.44/2.61 tff(10134,plain,
% 2.44/2.61 (~b(z, s(s(s(elem!1))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1164, 61, 1139, 550])).
% 2.44/2.61 tff(10135,plain,
% 2.44/2.61 (r(z, s(s(s(elem!1))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[590, 10134])).
% 2.44/2.61 tff(10136,plain,
% 2.44/2.61 (~r(z, s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[5852, 10135, 10133, 1, 10126])).
% 2.44/2.61 tff(10137,plain,
% 2.44/2.61 (b(z, s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1318, 10136])).
% 2.44/2.61 tff(10138,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[3391, 97, 550, 61, 1360, 10137])).
% 2.44/2.61 tff(10139,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(10140,plain,
% 2.44/2.61 (~b(s(s(s(z))), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[10139, 1, 61, 10119, 2589])).
% 2.44/2.61 tff(10141,plain,
% 2.44/2.61 (r(s(s(s(z))), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1358, 10140])).
% 2.44/2.61 tff(10142,plain,
% 2.44/2.61 (~b(s(z), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1666, 1216, 61, 3, 83])).
% 2.44/2.61 tff(10143,plain,
% 2.44/2.61 (~r(s(z), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1297, 1216, 61, 3, 83])).
% 2.44/2.61 tff(10144,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[253, 10143, 10142])).
% 2.44/2.61 tff(10145,plain,((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(10146,plain,
% 2.44/2.61 (~b(s(s(s(z))), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[10145, 83, 3, 61])).
% 2.44/2.61 tff(10147,plain,
% 2.44/2.61 (r(s(s(s(z))), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[402, 10146])).
% 2.44/2.61 tff(10148,plain,
% 2.44/2.61 (~b(s(s(z)), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2992, 97, 2589, 61, 83])).
% 2.44/2.61 tff(10149,plain,
% 2.44/2.61 (r(s(s(z)), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[122, 10148])).
% 2.44/2.61 tff(10150,plain,
% 2.44/2.61 (~r(s(s(s(z))), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[3004, 83, 2589, 10141, 61])).
% 2.44/2.61 tff(10151,plain,
% 2.44/2.61 (b(s(s(s(z))), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[421, 10150])).
% 2.44/2.61 tff(10152,plain,
% 2.44/2.61 (~r(s(s(z)), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2940, 7837, 2, 2597])).
% 2.44/2.61 tff(10153,plain,
% 2.44/2.61 (b(s(s(z)), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[437, 10152])).
% 2.44/2.61 tff(10154,plain,
% 2.44/2.61 (((~![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)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(10155,plain,
% 2.44/2.61 (((~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(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(10156,plain,
% 2.44/2.61 (((~![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(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(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[10155])).
% 2.44/2.61 tff(10157,plain,
% 2.44/2.61 (((~![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(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(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[10156, 10154])).
% 2.44/2.61 tff(10158,plain,
% 2.44/2.61 ((~![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(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)))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(10159,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[10158, 10157])).
% 2.44/2.61 tff(10160,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[10159, 97, 83, 10153, 1331, 1330])).
% 2.44/2.61 tff(10161,plain,((~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(10162,plain,
% 2.44/2.61 (~b(z, s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[10161, 83, 10151, 10149, 10141, 2589])).
% 2.44/2.61 tff(10163,plain,
% 2.44/2.61 (r(z, s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1318, 10162])).
% 2.44/2.61 tff(10164,plain,
% 2.44/2.61 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[135, 126, 61, 83])).
% 2.44/2.61 tff(10165,plain,
% 2.44/2.61 (r(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[143, 10164])).
% 2.44/2.61 tff(10166,plain,
% 2.44/2.61 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1390, 126, 83, 61])).
% 2.44/2.61 tff(10167,plain,
% 2.44/2.61 (r(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[58, 10166])).
% 2.44/2.61 tff(10168,plain,
% 2.44/2.61 (~r(s(z), s(s(s(elem!1))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[5875, 10167, 3, 10165])).
% 2.44/2.61 tff(10169,plain,
% 2.44/2.61 (b(s(z), s(s(s(elem!1))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[181, 10168])).
% 2.44/2.61 tff(10170,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2323, 97, 10119, 10169, 61, 126])).
% 2.44/2.61 tff(10171,plain,((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(10172,plain,
% 2.44/2.61 (~b(s(s(s(elem!1))), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[10171, 83, 3, 61])).
% 2.44/2.61 tff(10173,plain,
% 2.44/2.61 (r(s(s(s(elem!1))), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[246, 10172])).
% 2.44/2.61 tff(10174,plain,
% 2.44/2.61 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2488, 155, 10173, 10163, 10147])).
% 2.44/2.61 tff(10175,plain,
% 2.44/2.61 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2687, 10174, 4228])).
% 2.44/2.61 tff(10176,plain,
% 2.44/2.61 (~b(z, s(s(s(elem!1))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1164, 2589, 61, 10119])).
% 2.44/2.61 tff(10177,plain,
% 2.44/2.61 (r(z, s(s(s(elem!1))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[590, 10176])).
% 2.44/2.61 tff(10178,plain,
% 2.44/2.61 (((~![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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(10179,plain,
% 2.44/2.61 (((~b(s(s(z)), z)) | (~b(s(s(z)), 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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(10180,plain,
% 2.44/2.61 (((~![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)), z)) | (~b(s(s(z)), 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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[10179])).
% 2.44/2.61 tff(10181,plain,
% 2.44/2.61 (((~![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)), z)) | (~b(s(s(z)), 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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 2.44/2.61 inference(transitivity,[status(thm)],[10180, 10178])).
% 2.44/2.61 tff(10182,plain,
% 2.44/2.61 ((~![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)), z)) | (~b(s(s(z)), 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)))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(10183,plain,
% 2.44/2.61 ((~![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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[10182, 10181])).
% 2.44/2.61 tff(10184,plain,
% 2.44/2.61 (~b(s(s(s(z))), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[10183, 97, 204, 83, 10151])).
% 2.44/2.61 tff(10185,plain,
% 2.44/2.61 (r(s(s(s(z))), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[402, 10184])).
% 2.44/2.61 tff(10186,plain,
% 2.44/2.61 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[7433, 10185, 83, 10151, 204])).
% 2.44/2.61 tff(10187,plain,
% 2.44/2.61 (r(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2886, 10186, 80])).
% 2.44/2.61 tff(10188,plain,
% 2.44/2.61 (~b(s(s(z)), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[7811, 204, 61, 2589])).
% 2.44/2.61 tff(10189,plain,
% 2.44/2.61 (r(s(s(z)), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[122, 10188])).
% 2.44/2.61 tff(10190,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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)))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(10191,plain,
% 2.44/2.62 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(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)))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(10192,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[10191])).
% 2.44/2.62 tff(10193,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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)))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[10192, 10190])).
% 2.44/2.62 tff(10194,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(10195,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[10194, 10193])).
% 2.44/2.62 tff(10196,plain,
% 2.44/2.62 (~r(s(s(s(s(z)))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10195, 155, 10189, 3, 10187])).
% 2.44/2.62 tff(10197,plain,
% 2.44/2.62 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2807, 10196, 2795])).
% 2.44/2.62 tff(10198,plain,
% 2.44/2.62 (((~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)))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(10199,plain,
% 2.44/2.62 (((~![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(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))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[10198])).
% 2.44/2.62 tff(10200,plain,
% 2.44/2.62 (((~![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(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)))),
% 2.44/2.62 inference(transitivity,[status(thm)],[10199, 2797])).
% 2.44/2.62 tff(10201,plain,
% 2.44/2.62 ((~![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(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)))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(10202,plain,
% 2.44/2.62 ((~![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(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[10201, 10200])).
% 2.44/2.62 tff(10203,plain,
% 2.44/2.62 (~b(s(s(s(s(z)))), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10202, 97, 2589, 61, 10197])).
% 2.44/2.62 tff(10204,plain,
% 2.44/2.62 (r(s(s(s(s(z)))), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2860, 10203])).
% 2.44/2.62 tff(10205,plain,
% 2.44/2.62 (((~![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))), s(z))) | (~b(s(s(s(elem!1))), 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(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(10206,plain,
% 2.44/2.62 (((~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(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(10207,plain,
% 2.44/2.62 (((~![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(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(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[10206])).
% 2.44/2.62 tff(10208,plain,
% 2.44/2.62 (((~![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(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(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[10207, 10205])).
% 2.44/2.62 tff(10209,plain,
% 2.44/2.62 ((~![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(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))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(10210,plain,
% 2.44/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[10209, 10208])).
% 2.44/2.62 tff(10211,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10210, 97, 1139, 550, 126, 204])).
% 2.44/2.62 tff(10212,plain,((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(10213,plain,
% 2.44/2.62 (~b(s(s(s(elem!1))), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10212, 204, 10119, 2589])).
% 2.44/2.62 tff(10214,plain,
% 2.44/2.62 (r(s(s(s(elem!1))), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[246, 10213])).
% 2.44/2.62 tff(10215,plain,
% 2.44/2.62 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1674, 155, 10177, 10214, 10185])).
% 2.44/2.62 tff(10216,plain,
% 2.44/2.62 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[3089, 10215, 1])).
% 2.44/2.62 tff(10217,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 2.44/2.62 tff(10218,plain,
% 2.44/2.62 (~b(s(s(s(s(z)))), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10202, 97, 550, 61, 10217])).
% 2.44/2.62 tff(10219,plain,
% 2.44/2.62 (r(s(s(s(s(z)))), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2860, 10218])).
% 2.44/2.62 tff(10220,plain,
% 2.44/2.62 (~b(z, s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1164, 550, 61, 10119])).
% 2.44/2.62 tff(10221,plain,
% 2.44/2.62 (r(z, s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[590, 10220])).
% 2.44/2.62 tff(10222,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(10223,plain,
% 2.44/2.62 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(10224,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[10223])).
% 2.44/2.62 tff(10225,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[10224, 10222])).
% 2.44/2.62 tff(10226,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(10227,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[10226, 10225])).
% 2.44/2.62 tff(10228,plain,
% 2.44/2.62 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10227, 155, 10221, 288, 10219])).
% 2.44/2.62 tff(10229,plain,
% 2.44/2.62 (((~![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))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(10230,plain,
% 2.44/2.62 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(10231,plain,
% 2.44/2.62 (((~![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(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[10230])).
% 2.44/2.62 tff(10232,plain,
% 2.44/2.62 (((~![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(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[10231, 10229])).
% 2.44/2.62 tff(10233,plain,
% 2.44/2.62 ((~![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(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(10234,plain,
% 2.44/2.62 ((~![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))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[10233, 10232])).
% 2.44/2.62 tff(10235,plain,
% 2.44/2.62 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10234, 97, 10119, 550, 10217])).
% 2.44/2.62 tff(10236,plain,
% 2.44/2.62 ((s(s(s(s(z)))) = s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[7637, 53, 10235])).
% 2.44/2.62 tff(10237,plain,
% 2.44/2.62 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10236, 10228])).
% 2.44/2.62 tff(10238,plain,
% 2.44/2.62 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[10237])).
% 2.44/2.62 tff(10239,plain,
% 2.44/2.62 (s(s(s(z))) = s(s(elem!1))),
% 2.44/2.62 inference(transitivity,[status(thm)],[2792, 10238, 19])).
% 2.44/2.62 tff(10240,plain,
% 2.44/2.62 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[10239])).
% 2.44/2.62 tff(10241,plain,
% 2.44/2.62 (s(s(z)) = s(elem!1)),
% 2.44/2.62 inference(transitivity,[status(thm)],[73, 10240, 29])).
% 2.44/2.62 tff(10242,plain,
% 2.44/2.62 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[10239, 10241])).
% 2.44/2.62 tff(10243,plain,
% 2.44/2.62 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[1331, 10242])).
% 2.44/2.62 tff(10244,plain,
% 2.44/2.62 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 2.44/2.62 inference(symmetry,[status(thm)],[10240])).
% 2.44/2.62 tff(10245,plain,
% 2.44/2.62 (s(elem!1) = s(s(z))),
% 2.44/2.62 inference(transitivity,[status(thm)],[30, 10244, 72])).
% 2.44/2.62 tff(10246,plain,
% 2.44/2.62 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[10245])).
% 2.44/2.62 tff(10247,plain,
% 2.44/2.62 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.44/2.62 inference(symmetry,[status(thm)],[10246])).
% 2.44/2.62 tff(10248,plain,
% 2.44/2.62 (b(s(elem!1), s(s(s(elem!1))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[127, 10247])).
% 2.44/2.62 tff(10249,plain,
% 2.44/2.62 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 2.44/2.62 inference(symmetry,[status(thm)],[10238])).
% 2.44/2.62 tff(10250,plain,
% 2.44/2.62 (s(s(elem!1)) = s(s(s(z)))),
% 2.44/2.62 inference(transitivity,[status(thm)],[167, 10249, 63])).
% 2.44/2.62 tff(10251,plain,
% 2.44/2.62 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[10250])).
% 2.44/2.62 tff(10252,plain,
% 2.44/2.62 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.44/2.62 inference(symmetry,[status(thm)],[10251])).
% 2.44/2.62 tff(10253,plain,
% 2.44/2.62 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[1702, 10252])).
% 2.44/2.62 tff(10254,plain,
% 2.44/2.62 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[10241])).
% 2.44/2.62 tff(10255,plain,
% 2.44/2.62 (s(z) = elem!1),
% 2.44/2.62 inference(transitivity,[status(thm)],[24, 10254, 85])).
% 2.44/2.62 tff(10256,plain,
% 2.44/2.62 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 2.44/2.62 inference(monotonicity,[status(thm)],[10255])).
% 2.44/2.62 tff(10257,plain,
% 2.44/2.62 (b(s(s(s(elem!1))), elem!1)),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[10119, 10256])).
% 2.44/2.62 tff(10258,plain,
% 2.44/2.62 (((~![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))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(10259,plain,
% 2.44/2.62 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), 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(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(10260,plain,
% 2.44/2.62 (((~![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))), elem!1)) | (~b(s(s(s(elem!1))), 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(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[10259])).
% 2.44/2.62 tff(10261,plain,
% 2.44/2.62 (((~![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))), elem!1)) | (~b(s(s(s(elem!1))), 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(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[10260, 10258])).
% 2.44/2.62 tff(10262,plain,
% 2.44/2.62 ((~![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))), elem!1)) | (~b(s(s(s(elem!1))), 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))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(10263,plain,
% 2.44/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[10262, 10261])).
% 2.44/2.62 tff(10264,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10263, 97, 10257, 10253, 10248, 10243])).
% 2.44/2.62 tff(10265,plain,((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(10266,plain,
% 2.44/2.62 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10265, 10216, 10151, 10214, 2589, 61, 10197])).
% 2.44/2.62 tff(10267,plain,
% 2.44/2.62 (r(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[143, 10266])).
% 2.44/2.62 tff(10268,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(10269,plain,
% 2.44/2.62 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(10270,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[10269])).
% 2.44/2.62 tff(10271,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[10270, 10268])).
% 2.44/2.62 tff(10272,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(10273,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[10272, 10271])).
% 2.44/2.62 tff(10274,plain,
% 2.44/2.62 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10273, 155, 10214, 10267, 10187, 10204])).
% 2.44/2.62 tff(10275,plain,
% 2.44/2.62 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10234, 97, 10119, 2589, 10197])).
% 2.44/2.62 tff(10276,plain,
% 2.44/2.62 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[7637, 53, 10275, 10274])).
% 2.44/2.63 tff(10277,plain,
% 2.44/2.63 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10276])).
% 2.44/2.63 tff(10278,plain,
% 2.44/2.63 (s(s(s(z))) = s(s(elem!1))),
% 2.44/2.63 inference(transitivity,[status(thm)],[2792, 10277, 19])).
% 2.44/2.63 tff(10279,plain,
% 2.44/2.63 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10278])).
% 2.44/2.63 tff(10280,plain,
% 2.44/2.63 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10279])).
% 2.44/2.63 tff(10281,plain,
% 2.44/2.63 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[286, 10280])).
% 2.44/2.63 tff(10282,plain,
% 2.44/2.63 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[349, 10281])).
% 2.44/2.63 tff(10283,plain,
% 2.44/2.63 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[523, 10282])).
% 2.44/2.63 tff(10284,plain,
% 2.44/2.63 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10276])).
% 2.44/2.63 tff(10285,plain,
% 2.44/2.63 (r(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[10187, 10284])).
% 2.44/2.63 tff(10286,plain,
% 2.44/2.63 (~r(s(z), s(s(s(elem!1))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[5875, 10285, 3, 10267])).
% 2.44/2.63 tff(10287,plain,
% 2.44/2.63 (b(s(z), s(s(s(elem!1))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[181, 10286])).
% 2.44/2.63 tff(10288,plain,
% 2.44/2.63 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1808, 10287, 61, 10119, 10214, 10177, 10283])).
% 2.44/2.63 tff(10289,plain,
% 2.44/2.63 (~b(z, s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1339, 204, 83, 10151])).
% 2.44/2.63 tff(10290,plain,
% 2.44/2.63 (r(z, s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1318, 10289])).
% 2.44/2.63 tff(10291,plain,
% 2.44/2.63 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2488, 155, 10214, 10290, 10185])).
% 2.44/2.63 tff(10292,plain,
% 2.44/2.63 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2687, 10291, 4228])).
% 2.44/2.63 tff(10293,plain,
% 2.44/2.63 (~r(s(s(s(z))), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[3004, 83, 2589, 2597, 61])).
% 2.44/2.63 tff(10294,plain,
% 2.44/2.63 (b(s(s(s(z))), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[421, 10293])).
% 2.44/2.63 tff(10295,plain,
% 2.44/2.63 (~b(s(s(s(z))), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[10183, 97, 204, 83, 10294])).
% 2.44/2.63 tff(10296,plain,
% 2.44/2.63 (r(s(s(s(z))), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[402, 10295])).
% 2.44/2.63 tff(10297,plain,
% 2.44/2.63 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[7433, 10296, 83, 10294, 204])).
% 2.44/2.63 tff(10298,plain,
% 2.44/2.63 (r(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2886, 10297, 80])).
% 2.44/2.63 tff(10299,plain,
% 2.44/2.63 (~r(s(s(s(s(z)))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[10195, 155, 10189, 3, 10298])).
% 2.44/2.63 tff(10300,plain,
% 2.44/2.63 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2807, 10299, 2795])).
% 2.44/2.63 tff(10301,plain,
% 2.44/2.63 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[558, 4937, 2589, 61])).
% 2.44/2.63 tff(10302,plain,
% 2.44/2.63 (r(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[511, 10301])).
% 2.44/2.63 tff(10303,plain,
% 2.44/2.63 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4141, 4138, 10177])).
% 2.44/2.63 tff(10304,plain,
% 2.44/2.63 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[558, 372, 2589, 61])).
% 2.44/2.63 tff(10305,plain,
% 2.44/2.63 (r(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[511, 10304])).
% 2.44/2.63 tff(10306,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(10307,plain,
% 2.44/2.63 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(10308,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10307])).
% 2.44/2.63 tff(10309,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[10308, 10306])).
% 2.44/2.63 tff(10310,plain,
% 2.44/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(10311,plain,
% 2.44/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[10310, 10309])).
% 2.44/2.63 tff(10312,plain,
% 2.44/2.63 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[10311, 155, 10189, 3, 10305])).
% 2.44/2.63 tff(10313,plain,
% 2.44/2.63 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[452, 10312])).
% 2.44/2.63 tff(10314,plain,
% 2.44/2.63 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1494, 10313, 61, 372])).
% 2.44/2.63 tff(10315,plain,
% 2.44/2.63 (r(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[280, 10314])).
% 2.44/2.63 tff(10316,plain,
% 2.44/2.63 (~b(s(s(s(z))), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[10183, 97, 204, 83, 1331])).
% 2.44/2.63 tff(10317,plain,
% 2.44/2.63 (r(s(s(s(z))), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[402, 10316])).
% 2.44/2.63 tff(10318,plain,
% 2.44/2.63 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[7433, 10317, 83, 1331, 204])).
% 2.44/2.63 tff(10319,plain,
% 2.44/2.63 (r(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2886, 10318, 80])).
% 2.44/2.63 tff(10320,plain,
% 2.44/2.63 (~b(s(z), s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1710, 193, 10119, 1702])).
% 2.44/2.63 tff(10321,plain,
% 2.44/2.63 (r(s(z), s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[253, 10320])).
% 2.44/2.63 tff(10322,plain,
% 2.44/2.63 (~r(s(s(z)), s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2940, 10321, 2, 2597])).
% 2.44/2.63 tff(10323,plain,
% 2.44/2.63 (b(s(s(z)), s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[437, 10322])).
% 2.44/2.63 tff(10324,plain,
% 2.44/2.63 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[8976, 97, 10323, 1331, 5941])).
% 2.44/2.63 tff(10325,plain,
% 2.44/2.63 (r(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[143, 10324])).
% 2.44/2.63 tff(10326,plain,
% 2.44/2.63 (((~![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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(10327,plain,
% 2.44/2.63 (((~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(elem!1))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(10328,plain,
% 2.44/2.63 (((~![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(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10327])).
% 2.44/2.63 tff(10329,plain,
% 2.44/2.63 (((~![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(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[10328, 10326])).
% 2.44/2.63 tff(10330,plain,
% 2.44/2.63 ((~![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(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(10331,plain,
% 2.44/2.63 ((~![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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[10330, 10329])).
% 2.44/2.63 tff(10332,plain,
% 2.44/2.63 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[10331, 97, 204, 83, 10323, 1331, 5941])).
% 2.44/2.63 tff(10333,plain,
% 2.44/2.63 (r(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[58, 10332])).
% 2.44/2.63 tff(10334,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(10335,plain,
% 2.44/2.63 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(10336,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10335])).
% 2.44/2.63 tff(10337,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[10336, 10334])).
% 2.44/2.63 tff(10338,plain,
% 2.44/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(10339,plain,
% 2.44/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[10338, 10337])).
% 2.44/2.63 tff(10340,plain,
% 2.44/2.63 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[10339, 155, 10333, 10325, 10319])).
% 2.44/2.63 tff(10341,plain,
% 2.44/2.63 (((~![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))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(10342,plain,
% 2.44/2.63 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(10343,plain,
% 2.44/2.63 (((~![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(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10342])).
% 2.44/2.63 tff(10344,plain,
% 2.44/2.63 (((~![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(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[10343, 10341])).
% 2.44/2.63 tff(10345,plain,
% 2.44/2.63 ((~![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(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(10346,plain,
% 2.44/2.63 ((~![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))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[10345, 10344])).
% 2.44/2.63 tff(10347,plain,
% 2.44/2.63 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[10346, 97, 10119, 193, 10217])).
% 2.44/2.63 tff(10348,plain,
% 2.44/2.63 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[7637, 53, 10347, 10340])).
% 2.44/2.63 tff(10349,plain,
% 2.44/2.63 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10348])).
% 2.44/2.63 tff(10350,plain,
% 2.44/2.63 (s(s(s(z))) = s(s(elem!1))),
% 2.44/2.63 inference(transitivity,[status(thm)],[2792, 10349, 19])).
% 2.44/2.63 tff(10351,plain,
% 2.44/2.63 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10350])).
% 2.44/2.63 tff(10352,plain,
% 2.44/2.63 (s(s(z)) = s(elem!1)),
% 2.44/2.63 inference(transitivity,[status(thm)],[73, 10351, 29])).
% 2.44/2.63 tff(10353,plain,
% 2.44/2.63 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10352])).
% 2.44/2.63 tff(10354,plain,
% 2.44/2.63 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10350])).
% 2.44/2.63 tff(10355,plain,
% 2.44/2.63 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10354])).
% 2.44/2.63 tff(10356,plain,
% 2.44/2.63 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[286, 10355])).
% 2.44/2.63 tff(10357,plain,
% 2.44/2.63 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10352])).
% 2.44/2.63 tff(10358,plain,
% 2.44/2.63 (s(z) = elem!1),
% 2.44/2.63 inference(transitivity,[status(thm)],[24, 10357, 85])).
% 2.44/2.63 tff(10359,plain,
% 2.44/2.63 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10358, 10350])).
% 2.44/2.63 tff(10360,plain,
% 2.44/2.63 (r(elem!1, s(s(elem!1)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[10321, 10359])).
% 2.44/2.63 tff(10361,plain,
% 2.44/2.63 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10350, 10358])).
% 2.44/2.63 tff(10362,plain,
% 2.44/2.63 (r(s(s(elem!1)), elem!1)),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[2597, 10361])).
% 2.44/2.63 tff(10363,plain,
% 2.44/2.63 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10358])).
% 2.44/2.63 tff(10364,plain,
% 2.44/2.63 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[495, 10363])).
% 2.44/2.63 tff(10365,plain,
% 2.44/2.63 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[6107, 155, 10364, 10362, 10360])).
% 2.44/2.63 tff(10366,plain,
% 2.44/2.63 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1484, 10365, 10356])).
% 2.44/2.63 tff(10367,plain,
% 2.44/2.63 (((~![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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, 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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(10368,plain,
% 2.44/2.63 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(10369,plain,
% 2.44/2.63 (((~![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(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10368])).
% 2.44/2.63 tff(10370,plain,
% 2.44/2.63 (((~![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(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[10369, 10367])).
% 2.44/2.63 tff(10371,plain,
% 2.44/2.63 ((~![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(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(10372,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[10371, 10370])).
% 2.44/2.63 tff(10373,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[10372, 97, 1545, 372, 339, 83])).
% 2.44/2.63 tff(10374,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(10375,plain,
% 2.44/2.63 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[10374, 10366, 372, 83])).
% 2.44/2.63 tff(10376,plain,
% 2.44/2.63 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[336, 10375])).
% 2.44/2.63 tff(10377,plain,
% 2.44/2.63 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[10376, 10353])).
% 2.44/2.63 tff(10378,plain,
% 2.44/2.63 ((s(z) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10358])).
% 2.44/2.63 tff(10379,plain,
% 2.44/2.63 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.44/2.63 inference(transitivity,[status(thm)],[10378, 1900])).
% 2.44/2.63 tff(10380,plain,
% 2.44/2.63 ((s(z) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[10379, 1901])).
% 2.44/2.63 tff(10381,plain,
% 2.44/2.63 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10380])).
% 2.44/2.63 tff(10382,plain,
% 2.44/2.63 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[275, 10381])).
% 2.44/2.63 tff(10383,plain,
% 2.44/2.63 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 2.44/2.63 inference(commutativity,[status(thm)],[])).
% 2.44/2.63 tff(10384,plain,
% 2.44/2.63 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 2.44/2.63 inference(symmetry,[status(thm)],[10383])).
% 2.44/2.63 tff(10385,plain,
% 2.44/2.63 (elem!1 = s(z)),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[7772, 10384])).
% 2.44/2.63 tff(10386,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 2.44/2.63 tff(10387,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[10386, 10385])).
% 2.44/2.63 tff(10388,plain,((~(s(z) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(10389,plain,
% 2.44/2.63 (elem!1 = s(z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[10388, 10358])).
% 2.44/2.63 tff(10390,plain,
% 2.44/2.63 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[5279, 10376, 10333, 488])).
% 2.44/2.63 tff(10391,plain,
% 2.44/2.63 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[452, 10390])).
% 2.44/2.63 tff(10392,plain,
% 2.44/2.63 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1494, 10391, 61, 372])).
% 2.44/2.63 tff(10393,assumption,(elem!1 = s(z)), introduced(assumption)).
% 2.44/2.63 tff(10394,plain,
% 2.44/2.63 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10393])).
% 2.44/2.63 tff(10395,plain,
% 2.44/2.63 (b(s(z), s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 2.44/2.63 inference(symmetry,[status(thm)],[10394])).
% 2.44/2.63 tff(10396,plain,
% 2.44/2.63 ((~b(s(z), s(s(s(s(elem!1)))))) <=> (~b(elem!1, s(s(s(s(elem!1))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10395])).
% 2.44/2.63 tff(10397,plain,
% 2.44/2.63 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[1245, 10396])).
% 2.44/2.63 tff(10398,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2392, 10397])).
% 2.44/2.63 tff(10399,plain,((~(elem!1 = s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(10400,plain,
% 2.44/2.63 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[10399, 10392, 10389])).
% 2.44/2.63 tff(10401,plain,
% 2.44/2.63 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1930, 10400, 10382])).
% 2.44/2.63 tff(10402,plain,
% 2.44/2.63 (r(s(s(z)), s(z)) <=> r(s(elem!1), elem!1)),
% 2.44/2.63 inference(monotonicity,[status(thm)],[10352, 10358])).
% 2.44/2.63 tff(10403,plain,
% 2.44/2.63 (r(s(elem!1), elem!1)),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[2, 10402])).
% 2.44/2.63 tff(10404,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1947, 155, 10364, 10403, 10401, 10377])).
% 2.44/2.63 tff(10405,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(10406,plain,
% 2.44/2.63 (~b(s(z), s(s(s(elem!1))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[10405, 4934, 372, 61, 83, 2597, 10305, 10189, 10300, 204, 10294, 5941, 1702])).
% 2.44/2.63 tff(10407,plain,
% 2.44/2.63 (r(s(z), s(s(s(elem!1))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[181, 10406])).
% 2.44/2.63 tff(10408,plain,
% 2.44/2.63 (~b(z, s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1339, 204, 83, 10294])).
% 2.44/2.63 tff(10409,plain,
% 2.44/2.63 (r(z, s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1318, 10408])).
% 2.44/2.63 tff(10410,plain,
% 2.44/2.63 (~b(s(s(s(s(elem!1)))), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1832, 10313, 61, 83])).
% 2.44/2.63 tff(10411,plain,
% 2.44/2.63 (r(s(s(s(s(elem!1)))), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[842, 10410])).
% 2.44/2.63 tff(10412,plain,
% 2.44/2.63 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4101, 10411, 1702, 3701, 10177, 10409, 10296, 10214])).
% 2.44/2.63 tff(10413,plain,
% 2.44/2.63 (r(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[58, 10412])).
% 2.44/2.63 tff(10414,plain,
% 2.44/2.63 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[669, 372, 339, 83])).
% 2.44/2.63 tff(10415,plain,
% 2.44/2.63 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1154, 10414, 1139])).
% 2.44/2.63 tff(10416,plain,
% 2.44/2.63 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[486, 10415, 2718])).
% 2.44/2.63 tff(10417,plain,
% 2.44/2.63 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1124, 372, 83, 339])).
% 2.44/2.64 tff(10418,plain,
% 2.44/2.64 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[523, 10415])).
% 2.44/2.64 tff(10419,plain,
% 2.44/2.64 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[821, 10418, 10417])).
% 2.44/2.64 tff(10420,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[924, 10419, 10416, 225, 287])).
% 2.44/2.64 tff(10421,plain,((~b(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(10422,plain,
% 2.44/2.64 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10421, 10315, 10119, 372, 10407, 83, 2718])).
% 2.44/2.64 tff(10423,plain,
% 2.44/2.64 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[336, 10422])).
% 2.44/2.64 tff(10424,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[317, 10423, 10413, 3, 10407, 10315])).
% 2.44/2.64 tff(10425,plain,(b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(10426,plain,
% 2.44/2.64 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10425, 4937, 3, 83, 1702, 61, 2597, 204, 5941, 10303])).
% 2.44/2.64 tff(10427,plain,
% 2.44/2.64 (~b(s(z), s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1710, 193, 1139, 1702])).
% 2.44/2.64 tff(10428,plain,
% 2.44/2.64 (r(s(z), s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[253, 10427])).
% 2.44/2.64 tff(10429,plain,
% 2.44/2.64 (~r(s(s(z)), s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2940, 10428, 2, 2597])).
% 2.44/2.64 tff(10430,plain,
% 2.44/2.64 (b(s(s(z)), s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[437, 10429])).
% 2.44/2.64 tff(10431,plain,
% 2.44/2.64 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[8976, 97, 10430, 1331, 5941])).
% 2.44/2.64 tff(10432,plain,
% 2.44/2.64 (r(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[143, 10431])).
% 2.44/2.64 tff(10433,plain,
% 2.44/2.64 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10331, 97, 204, 83, 10430, 1331, 5941])).
% 2.44/2.64 tff(10434,plain,
% 2.44/2.64 (r(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[58, 10433])).
% 2.44/2.64 tff(10435,plain,
% 2.44/2.64 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10339, 155, 10434, 10432, 10319])).
% 2.44/2.64 tff(10436,plain,
% 2.44/2.64 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10346, 97, 1139, 193, 10217])).
% 2.44/2.64 tff(10437,plain,
% 2.44/2.64 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[7637, 53, 10436, 10435])).
% 2.44/2.64 tff(10438,plain,
% 2.44/2.64 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[10437])).
% 2.44/2.64 tff(10439,plain,
% 2.44/2.64 (s(s(s(z))) = s(s(elem!1))),
% 2.44/2.64 inference(transitivity,[status(thm)],[2792, 10438, 19])).
% 2.44/2.64 tff(10440,plain,
% 2.44/2.64 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[10439])).
% 2.44/2.64 tff(10441,plain,
% 2.44/2.64 (s(s(z)) = s(elem!1)),
% 2.44/2.64 inference(transitivity,[status(thm)],[73, 10440, 29])).
% 2.44/2.64 tff(10442,plain,
% 2.44/2.64 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[10441])).
% 2.44/2.64 tff(10443,plain,
% 2.44/2.64 (s(z) = elem!1),
% 2.44/2.64 inference(transitivity,[status(thm)],[24, 10442, 85])).
% 2.44/2.64 tff(10444,plain,
% 2.44/2.64 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[10443, 10439])).
% 2.44/2.64 tff(10445,plain,
% 2.44/2.64 (r(elem!1, s(s(elem!1)))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[10428, 10444])).
% 2.44/2.64 tff(10446,plain,
% 2.44/2.64 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 2.44/2.64 inference(monotonicity,[status(thm)],[10439, 10443])).
% 2.44/2.64 tff(10447,plain,
% 2.44/2.64 (r(s(s(elem!1)), elem!1)),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[2597, 10446])).
% 2.44/2.64 tff(10448,plain,
% 2.44/2.64 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.64 inference(monotonicity,[status(thm)],[10443])).
% 2.44/2.64 tff(10449,plain,
% 2.44/2.64 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[495, 10448])).
% 2.44/2.64 tff(10450,plain,
% 2.44/2.64 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[10439])).
% 2.44/2.64 tff(10451,plain,
% 2.44/2.64 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[10450])).
% 2.44/2.64 tff(10452,plain,
% 2.44/2.64 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[286, 10451])).
% 2.44/2.64 tff(10453,plain,
% 2.44/2.64 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 2.44/2.64 inference(symmetry,[status(thm)],[10438])).
% 2.44/2.64 tff(10454,plain,
% 2.44/2.64 (s(s(elem!1)) = s(s(s(z)))),
% 2.44/2.64 inference(transitivity,[status(thm)],[167, 10453, 63])).
% 2.44/2.64 tff(10455,plain,
% 2.44/2.64 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[10454])).
% 2.44/2.64 tff(10456,plain,
% 2.44/2.64 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.44/2.64 inference(symmetry,[status(thm)],[10455])).
% 2.44/2.64 tff(10457,plain,
% 2.44/2.64 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[1702, 10456])).
% 2.44/2.64 tff(10458,plain,
% 2.44/2.64 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[10454])).
% 2.44/2.64 tff(10459,plain,
% 2.44/2.64 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.64 inference(symmetry,[status(thm)],[10458])).
% 2.44/2.64 tff(10460,plain,
% 2.44/2.64 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[5941, 10459])).
% 2.44/2.64 tff(10461,plain,
% 2.44/2.64 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[8941, 10460, 473, 10457])).
% 2.44/2.64 tff(10462,plain,
% 2.44/2.64 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1484, 10461, 10452])).
% 2.44/2.64 tff(10463,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[6107, 155, 10462, 10449, 10447, 10445])).
% 2.44/2.64 tff(10464,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(10465,plain,
% 2.44/2.64 (~b(s(z), s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10464, 10426, 2597, 10302, 5941, 1702, 10119, 10300, 204, 83, 10294, 10189])).
% 2.44/2.64 tff(10466,plain,
% 2.44/2.64 (r(s(z), s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[181, 10465])).
% 2.44/2.64 tff(10467,plain,
% 2.44/2.64 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[523, 10303])).
% 2.44/2.64 tff(10468,plain,
% 2.44/2.64 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10311, 155, 10189, 3, 10302])).
% 2.44/2.64 tff(10469,plain,
% 2.44/2.64 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[452, 10468])).
% 2.44/2.64 tff(10470,plain,
% 2.44/2.64 (~b(s(s(s(s(elem!1)))), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1832, 10469, 61, 83])).
% 2.44/2.64 tff(10471,plain,
% 2.44/2.64 (r(s(s(s(s(elem!1)))), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[842, 10470])).
% 2.44/2.64 tff(10472,plain,
% 2.44/2.64 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[4101, 10471, 1702, 10467, 10177, 10409, 10296, 10214])).
% 2.44/2.64 tff(10473,plain,
% 2.44/2.64 (r(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[58, 10472])).
% 2.44/2.64 tff(10474,plain,
% 2.44/2.64 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[5875, 10473, 3, 10466])).
% 2.44/2.64 tff(10475,plain,
% 2.44/2.64 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[832, 10471, 10177, 10214])).
% 2.44/2.64 tff(10476,plain,
% 2.44/2.64 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[821, 10475, 10467])).
% 2.44/2.64 tff(10477,plain,
% 2.44/2.64 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2741, 10476, 10426, 10469])).
% 2.44/2.64 tff(10478,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[143, 10477, 10474])).
% 2.44/2.64 tff(10479,plain,(r(z, s(s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(10480,plain,
% 2.44/2.64 (r(z, s(s(s(s(elem!1)))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10479, 10216, 3, 61, 83, 10141, 10292, 204])).
% 2.44/2.64 tff(10481,assumption,(r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 2.44/2.64 tff(10482,plain,
% 2.44/2.64 (~r(s(s(s(s(z)))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10195, 155, 2, 3, 10481])).
% 2.44/2.64 tff(10483,plain,
% 2.44/2.64 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2807, 10482, 2795])).
% 2.44/2.64 tff(10484,plain,
% 2.44/2.64 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1872, 3226, 288, 463])).
% 2.44/2.64 tff(10485,plain,
% 2.44/2.64 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[486, 10484, 2718])).
% 2.44/2.64 tff(10486,plain,
% 2.44/2.64 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[9942, 10485, 1702])).
% 2.44/2.64 tff(10487,plain,
% 2.44/2.64 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[349, 10485])).
% 2.44/2.64 tff(10488,plain,
% 2.44/2.64 (s(s(s(s(elem!1)))) = elem!1),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1734, 10487])).
% 2.44/2.64 tff(10489,plain,
% 2.44/2.64 (~(s(s(s(s(z)))) = elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2786, 10485])).
% 2.44/2.64 tff(10490,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(10491,plain,
% 2.44/2.64 (((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(10492,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[10491])).
% 2.44/2.64 tff(10493,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[10492, 10490])).
% 2.44/2.64 tff(10494,plain,
% 2.44/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(10495,plain,
% 2.44/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[10494, 10493])).
% 2.44/2.64 tff(10496,plain,
% 2.44/2.64 ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10495, 155, 463, 1170, 10481])).
% 2.44/2.64 tff(10497,plain,
% 2.44/2.64 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10496, 10219])).
% 2.44/2.64 tff(10498,plain,
% 2.44/2.64 (~r(s(s(s(s(z)))), elem!1)),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[10497, 4152])).
% 2.44/2.64 tff(10499,plain,
% 2.44/2.64 ((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[4148])).
% 2.44/2.64 tff(10500,plain,
% 2.44/2.64 (((~![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(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(10501,plain,
% 2.44/2.64 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(10502,plain,
% 2.44/2.64 (((~![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(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[10501])).
% 2.44/2.64 tff(10503,plain,
% 2.44/2.64 (((~![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(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[10502, 10500])).
% 2.44/2.64 tff(10504,plain,
% 2.44/2.64 ((~![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(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(10505,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[10504, 10503])).
% 2.44/2.64 tff(10506,plain,
% 2.44/2.64 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10505, 97, 550, 513, 10217])).
% 2.44/2.64 tff(10507,plain,
% 2.44/2.64 (~b(s(s(s(s(z)))), elem!1)),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[10506, 10499])).
% 2.44/2.64 tff(10508,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2873, 10507, 10498, 4150])).
% 2.44/2.64 tff(10509,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (s(s(s(s(z)))) = elem!1) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(10510,plain,
% 2.44/2.64 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10509, 10489, 10488, 463, 10481, 550, 513, 10217, 61])).
% 2.44/2.64 tff(10511,plain,
% 2.44/2.64 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[452, 10510])).
% 2.44/2.64 tff(10512,plain,
% 2.44/2.64 (((~![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(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(10513,plain,
% 2.44/2.64 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(10514,plain,
% 2.44/2.64 (((~![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)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[10513])).
% 2.44/2.64 tff(10515,plain,
% 2.44/2.64 (((~![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)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[10514, 10512])).
% 2.44/2.64 tff(10516,plain,
% 2.44/2.64 ((~![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)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(10517,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[10516, 10515])).
% 2.44/2.64 tff(10518,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10517, 97, 550, 83, 513, 10511, 1331, 10486])).
% 2.44/2.64 tff(10519,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(10520,plain,
% 2.44/2.64 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10519, 2718, 83, 1331, 463, 10481, 10483, 61, 1702, 2589, 288])).
% 2.44/2.64 tff(10521,plain,
% 2.44/2.64 (r(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[511, 10520])).
% 2.44/2.64 tff(10522,plain,
% 2.44/2.64 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1154, 10520, 10119])).
% 2.44/2.64 tff(10523,plain,
% 2.44/2.64 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[486, 10522, 2718])).
% 2.44/2.64 tff(10524,plain,
% 2.44/2.64 (~r(s(s(s(s(elem!1)))), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1872, 10523, 288, 463])).
% 2.44/2.64 tff(10525,plain,
% 2.44/2.64 (b(s(s(s(s(elem!1)))), z)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[842, 10524])).
% 2.44/2.64 tff(10526,plain,
% 2.44/2.64 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1832, 10525, 61, 83])).
% 2.44/2.64 tff(10527,plain,
% 2.44/2.64 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[452, 10526])).
% 2.44/2.64 tff(10528,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10311, 155, 10527, 2, 3, 10521])).
% 2.44/2.64 tff(10529,plain,(b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(10530,plain,
% 2.44/2.64 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10529, 10189, 3, 61, 83, 10214, 10480, 10151, 10187, 10216])).
% 2.44/2.64 tff(10531,plain,
% 2.44/2.64 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10464, 10287, 10141, 10530, 10292, 10216, 10119, 10197, 204, 83, 10151, 10189])).
% 2.44/2.64 tff(10532,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[511, 10531, 10288])).
% 2.44/2.64 tff(10533,plain,((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~r(s(z), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(10534,plain,
% 2.44/2.64 (~b(z, s(s(z)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10533, 83, 61, 3, 1])).
% 2.44/2.64 tff(10535,plain,
% 2.44/2.64 (r(z, s(s(z)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[222, 10534])).
% 2.44/2.64 tff(10536,plain,
% 2.44/2.64 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[8976, 97, 1361, 1331, 5941])).
% 2.44/2.64 tff(10537,plain,
% 2.44/2.64 (r(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[143, 10536])).
% 2.44/2.64 tff(10538,plain,
% 2.44/2.64 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[9378, 97, 1361, 1331, 5941])).
% 2.44/2.64 tff(10539,plain,
% 2.44/2.64 (r(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[58, 10538])).
% 2.44/2.64 tff(10540,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[5182, 155, 570, 226, 10539, 10537])).
% 2.44/2.64 tff(10541,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(10542,plain,
% 2.44/2.64 (~b(s(s(z)), s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10541, 10535, 10177, 10151, 10175])).
% 2.44/2.64 tff(10543,plain,
% 2.44/2.64 (r(s(s(z)), s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[437, 10542])).
% 2.44/2.64 tff(10544,plain,
% 2.44/2.64 (~r(s(z), s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2940, 10543, 10149, 10141])).
% 2.44/2.64 tff(10545,plain,
% 2.44/2.64 (b(s(z), s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[253, 10544])).
% 2.44/2.64 tff(10546,plain,
% 2.44/2.64 (((~![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(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(10547,plain,
% 2.44/2.65 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(10548,plain,
% 2.44/2.65 (((~![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(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(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(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[10547])).
% 2.44/2.65 tff(10549,plain,
% 2.44/2.65 (((~![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(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(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(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[10548, 10546])).
% 2.44/2.65 tff(10550,plain,
% 2.44/2.65 ((~![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(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(10551,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[10550, 10549])).
% 2.44/2.65 tff(10552,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[10551, 97, 10119, 10151, 10545, 10175])).
% 2.44/2.65 tff(10553,plain,((~b(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~b(z, s(z))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(10554,plain,
% 2.44/2.65 (~b(s(s(z)), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[10553, 1, 61, 3])).
% 2.44/2.65 tff(10555,plain,
% 2.44/2.65 (r(s(s(z)), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[625, 10554])).
% 2.44/2.65 tff(10556,plain,
% 2.44/2.65 (((~![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(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), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(10557,plain,
% 2.44/2.65 (((~b(s(z), z)) | (~b(s(z), z)) | (~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), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(10558,plain,
% 2.44/2.65 (((~![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(s(z), z)) | (~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), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[10557])).
% 2.44/2.65 tff(10559,plain,
% 2.44/2.65 (((~![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(s(z), z)) | (~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), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.44/2.65 inference(transitivity,[status(thm)],[10558, 10556])).
% 2.44/2.65 tff(10560,plain,
% 2.44/2.65 ((~![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(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(10561,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[10560, 10559])).
% 2.44/2.65 tff(10562,plain,
% 2.44/2.65 (~b(s(s(s(elem!1))), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[10561, 97, 10119, 2589, 61])).
% 2.44/2.65 tff(10563,plain,
% 2.44/2.65 (r(s(s(s(elem!1))), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[246, 10562])).
% 2.44/2.65 tff(10564,plain,
% 2.44/2.65 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[735, 155, 10177, 10563, 10555])).
% 2.44/2.65 tff(10565,plain,
% 2.44/2.65 (b(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[143, 10564])).
% 2.44/2.65 tff(10566,plain,
% 2.44/2.65 (~r(s(s(z)), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[2930, 2591, 3, 6691])).
% 2.44/2.65 tff(10567,plain,
% 2.44/2.65 (b(s(s(z)), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[122, 10566])).
% 2.44/2.65 tff(10568,plain,
% 2.44/2.65 (~b(z, s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[7811, 10567, 61, 2589])).
% 2.44/2.65 tff(10569,plain,
% 2.44/2.65 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[6945, 2590, 3, 2589, 10177, 1843])).
% 2.44/2.65 tff(10570,plain,
% 2.44/2.65 (b(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[280, 10569])).
% 2.44/2.65 tff(10571,plain,
% 2.44/2.65 (~r(z, s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[5184, 10567, 10119, 10177, 10570])).
% 2.44/2.65 tff(10572,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[222, 10571, 10568])).
% 2.44/2.65 tff(10573,plain,(b(s(s(s(z))), s(s(z))) | (~b(z, s(z))) | (~r(s(z), s(s(z)))) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(10574,plain,
% 2.44/2.65 (b(s(s(s(z))), s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[10573, 10140, 3, 61])).
% 2.44/2.65 tff(10575,plain,
% 2.44/2.65 (~r(s(z), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[2452, 61, 1331, 3])).
% 2.44/2.65 tff(10576,plain,
% 2.44/2.65 (b(s(z), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[568, 10575])).
% 2.44/2.65 tff(10577,plain,
% 2.44/2.65 (~b(s(s(s(elem!1))), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[10212, 10576, 1139, 204])).
% 2.44/2.65 tff(10578,plain,
% 2.44/2.65 (r(s(s(s(elem!1))), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[246, 10577])).
% 2.44/2.65 tff(10579,plain,
% 2.44/2.65 (~b(z, s(s(s(elem!1))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1164, 10576, 1139, 61])).
% 2.44/2.65 tff(10580,plain,
% 2.44/2.65 (r(z, s(s(s(elem!1))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[590, 10579])).
% 2.44/2.65 tff(10581,plain,
% 2.44/2.65 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[735, 155, 10580, 10578, 645])).
% 2.44/2.65 tff(10582,plain,
% 2.44/2.65 (b(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[143, 10581])).
% 2.44/2.65 tff(10583,plain,
% 2.44/2.65 (((~![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(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(10584,plain,
% 2.44/2.65 (((~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(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(10585,plain,
% 2.44/2.65 (((~![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(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~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(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[10584])).
% 2.44/2.65 tff(10586,plain,
% 2.44/2.65 (((~![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(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~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(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 2.44/2.65 inference(transitivity,[status(thm)],[10585, 10583])).
% 2.44/2.65 tff(10587,plain,
% 2.44/2.65 ((~![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(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(10588,plain,
% 2.44/2.65 ((~![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(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[10587, 10586])).
% 2.44/2.65 tff(10589,plain,
% 2.44/2.65 (~b(s(s(s(z))), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[10588, 97, 204, 1331, 10582])).
% 2.44/2.65 tff(10590,plain,
% 2.44/2.65 (r(s(s(s(z))), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[402, 10589])).
% 2.44/2.65 tff(10591,plain,
% 2.44/2.65 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1674, 155, 10580, 10578, 10590])).
% 2.44/2.65 tff(10592,plain,
% 2.44/2.65 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[3089, 10591, 1])).
% 2.44/2.65 tff(10593,plain,
% 2.44/2.65 (((~![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(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(10594,plain,
% 2.44/2.65 (((~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(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(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(10595,plain,
% 2.44/2.65 (((~![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(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), 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(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[10594])).
% 2.44/2.65 tff(10596,plain,
% 2.44/2.65 (((~![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(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), 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(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[10595, 10593])).
% 2.44/2.65 tff(10597,plain,
% 2.44/2.65 ((~![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(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), 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)))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(10598,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[10597, 10596])).
% 2.44/2.65 tff(10599,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[10598, 97, 1139, 1331, 10582, 10592])).
% 2.44/2.65 tff(10600,plain,((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(10601,plain,
% 2.44/2.65 (~b(z, s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[10600, 10574, 61, 10119, 1, 10555, 3])).
% 2.44/2.65 tff(10602,plain,
% 2.44/2.65 (r(z, s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[222, 10601])).
% 2.44/2.65 tff(10603,plain,
% 2.44/2.65 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[2671, 10563, 10555, 10602])).
% 2.44/2.65 tff(10604,plain,
% 2.44/2.65 (b(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[58, 10603])).
% 2.44/2.65 tff(10605,plain,
% 2.44/2.65 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[2270, 97, 10604, 10574, 10565])).
% 2.44/2.65 tff(10606,plain,
% 2.44/2.65 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[3089, 10605, 1])).
% 2.44/2.65 tff(10607,plain,
% 2.44/2.65 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(10608,plain,
% 2.44/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[10607])).
% 2.44/2.65 tff(10609,plain,
% 2.44/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[10608, 1669])).
% 2.44/2.65 tff(10610,plain,
% 2.44/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(10611,plain,
% 2.44/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[10610, 10609])).
% 2.44/2.65 tff(10612,plain,
% 2.44/2.65 (~r(s(s(s(z))), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[10611, 155, 10177, 10563, 10606])).
% 2.44/2.65 tff(10613,plain,
% 2.44/2.65 (b(s(s(s(z))), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[402, 10612])).
% 2.44/2.65 tff(10614,plain,
% 2.44/2.65 (~b(s(s(s(s(z)))), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[2853, 10613, 61, 2589, 10141])).
% 2.44/2.65 tff(10615,plain,
% 2.44/2.65 (r(s(s(s(s(z)))), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[2860, 10614])).
% 2.44/2.65 tff(10616,plain,
% 2.44/2.65 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[2881, 155, 10602, 10555, 10615])).
% 2.44/2.65 tff(10617,plain,
% 2.44/2.65 (b(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[2886, 10616, 80])).
% 2.44/2.65 tff(10618,plain,
% 2.44/2.65 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[7861, 97, 10604, 10574, 10565])).
% 2.44/2.65 tff(10619,plain,
% 2.44/2.65 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[2687, 10618, 4228])).
% 2.44/2.65 tff(10620,plain,
% 2.44/2.65 (~r(z, s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[5852, 10605, 1, 10618, 10177])).
% 2.44/2.65 tff(10621,plain,
% 2.44/2.65 (b(z, s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1318, 10620])).
% 2.44/2.65 tff(10622,plain,
% 2.44/2.65 (~b(s(z), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[7835, 10621, 10574, 2589])).
% 2.44/2.65 tff(10623,plain,
% 2.44/2.65 (r(s(z), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[253, 10622])).
% 2.44/2.65 tff(10624,plain,
% 2.44/2.65 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(10625,plain,
% 2.44/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[10624])).
% 2.44/2.65 tff(10626,plain,
% 2.44/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[10625, 7664])).
% 2.44/2.65 tff(10627,plain,
% 2.44/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(10628,plain,
% 2.44/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[10627, 10626])).
% 2.44/2.65 tff(10629,plain,
% 2.44/2.65 (~r(s(z), s(s(s(elem!1))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[10628, 155, 10623, 10619, 10606])).
% 2.44/2.65 tff(10630,plain,
% 2.44/2.65 (b(s(z), s(s(s(elem!1))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[181, 10629])).
% 2.44/2.65 tff(10631,plain,
% 2.44/2.65 (((~![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(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(10632,plain,
% 2.44/2.65 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(10633,plain,
% 2.44/2.65 (((~![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(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[10632])).
% 2.44/2.65 tff(10634,plain,
% 2.44/2.65 (((~![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(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[10633, 10631])).
% 2.44/2.65 tff(10635,plain,
% 2.44/2.65 ((~![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(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(10636,plain,
% 2.44/2.66 ((~![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(z))) | (~b(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(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[10635, 10634])).
% 2.44/2.66 tff(10637,plain,
% 2.44/2.66 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10636, 97, 10119, 10630, 10604, 10565, 10617])).
% 2.44/2.66 tff(10638,plain,
% 2.44/2.66 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10227, 155, 10177, 10563, 10615])).
% 2.44/2.66 tff(10639,plain,
% 2.44/2.66 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[7637, 53, 10638, 10637])).
% 2.44/2.66 tff(10640,plain,
% 2.44/2.66 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10639])).
% 2.44/2.66 tff(10641,plain,
% 2.44/2.66 (s(s(s(z))) = s(s(elem!1))),
% 2.44/2.66 inference(transitivity,[status(thm)],[2792, 10640, 19])).
% 2.44/2.66 tff(10642,plain,
% 2.44/2.66 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10641])).
% 2.44/2.66 tff(10643,plain,
% 2.44/2.66 (s(s(z)) = s(elem!1)),
% 2.44/2.66 inference(transitivity,[status(thm)],[73, 10642, 29])).
% 2.44/2.66 tff(10644,plain,
% 2.44/2.66 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10643])).
% 2.44/2.66 tff(10645,plain,
% 2.44/2.66 ((~r(s(s(s(s(elem!1)))), s(s(z)))) <=> (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10644])).
% 2.44/2.66 tff(10646,plain,
% 2.44/2.66 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10641])).
% 2.44/2.66 tff(10647,plain,
% 2.44/2.66 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10646])).
% 2.44/2.66 tff(10648,plain,
% 2.44/2.66 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[286, 10647])).
% 2.44/2.66 tff(10649,plain,
% 2.44/2.66 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[349, 10648])).
% 2.44/2.66 tff(10650,plain,
% 2.44/2.66 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[523, 10649])).
% 2.44/2.66 tff(10651,plain,
% 2.44/2.66 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1808, 10650, 61, 10119, 10563, 10177, 10630])).
% 2.44/2.66 tff(10652,plain,
% 2.44/2.66 (r(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[511, 10651])).
% 2.44/2.66 tff(10653,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[6916, 97, 1139, 550, 60, 87])).
% 2.44/2.66 tff(10654,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(10655,plain,
% 2.44/2.66 (~b(s(s(z)), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10654, 10604, 10119, 2589])).
% 2.44/2.66 tff(10656,plain,
% 2.44/2.66 (r(s(s(z)), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[122, 10655])).
% 2.44/2.66 tff(10657,plain,
% 2.44/2.66 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10643])).
% 2.44/2.66 tff(10658,plain,
% 2.44/2.66 (s(z) = elem!1),
% 2.44/2.66 inference(transitivity,[status(thm)],[24, 10657, 85])).
% 2.44/2.66 tff(10659,plain,
% 2.44/2.66 (b(z, s(z)) <=> b(z, elem!1)),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10658])).
% 2.44/2.66 tff(10660,plain,
% 2.44/2.66 (b(z, elem!1)),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[61, 10659])).
% 2.44/2.66 tff(10661,plain,
% 2.44/2.66 (b(s(z), z) <=> b(elem!1, z)),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10658])).
% 2.44/2.66 tff(10662,plain,
% 2.44/2.66 (b(elem!1, z)),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[2589, 10661])).
% 2.44/2.66 tff(10663,plain,
% 2.44/2.66 (r(s(z), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10658])).
% 2.44/2.66 tff(10664,plain,
% 2.44/2.66 (r(s(z), s(s(z))) <=> r(s(z), s(elem!1))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10643])).
% 2.44/2.66 tff(10665,plain,
% 2.44/2.66 (r(s(z), s(elem!1))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[3, 10664])).
% 2.44/2.66 tff(10666,plain,
% 2.44/2.66 (r(elem!1, s(elem!1))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[10665, 10663])).
% 2.44/2.66 tff(10667,plain,
% 2.44/2.66 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[7701])).
% 2.44/2.66 tff(10668,plain,
% 2.44/2.66 (s(s(z)) = s(elem!1)),
% 2.44/2.66 inference(transitivity,[status(thm)],[73, 10667, 29])).
% 2.44/2.66 tff(10669,plain,
% 2.44/2.66 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10668])).
% 2.44/2.66 tff(10670,plain,
% 2.44/2.66 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.66 inference(symmetry,[status(thm)],[10669])).
% 2.44/2.66 tff(10671,plain,
% 2.44/2.66 ((~r(s(s(s(s(elem!1)))), s(elem!1))) <=> (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10670])).
% 2.44/2.66 tff(10672,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 2.44/2.66 tff(10673,plain,
% 2.44/2.66 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10668])).
% 2.44/2.66 tff(10674,plain,
% 2.44/2.66 (s(z) = elem!1),
% 2.44/2.66 inference(transitivity,[status(thm)],[24, 10673, 85])).
% 2.44/2.66 tff(10675,plain,
% 2.44/2.66 (r(s(s(z)), s(z)) <=> r(s(elem!1), elem!1)),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10668, 10674])).
% 2.44/2.66 tff(10676,plain,
% 2.44/2.66 (r(s(elem!1), elem!1)),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[2, 10675])).
% 2.44/2.66 tff(10677,plain,
% 2.44/2.66 ((s(z) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10674])).
% 2.44/2.66 tff(10678,plain,
% 2.44/2.66 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.44/2.66 inference(transitivity,[status(thm)],[10677, 1900])).
% 2.44/2.66 tff(10679,plain,
% 2.44/2.66 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10678])).
% 2.44/2.66 tff(10680,plain,
% 2.44/2.66 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[275, 10679])).
% 2.44/2.66 tff(10681,assumption,(b(z, elem!1)), introduced(assumption)).
% 2.44/2.66 tff(10682,assumption,(b(elem!1, z)), introduced(assumption)).
% 2.44/2.66 tff(10683,plain,
% 2.44/2.66 (~r(s(s(s(s(elem!1)))), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[3278, 1170, 226, 2, 495])).
% 2.44/2.66 tff(10684,plain,
% 2.44/2.66 (b(s(s(s(s(elem!1)))), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[842, 10683])).
% 2.44/2.66 tff(10685,plain,
% 2.44/2.66 (((~![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, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(10686,plain,
% 2.44/2.66 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(10687,plain,
% 2.44/2.66 (((~![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(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10686])).
% 2.44/2.66 tff(10688,plain,
% 2.44/2.66 (((~![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(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.44/2.66 inference(transitivity,[status(thm)],[10687, 10685])).
% 2.44/2.66 tff(10689,plain,
% 2.44/2.66 ((~![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(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(10690,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[10689, 10688])).
% 2.44/2.66 tff(10691,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10690, 97, 10681, 10682, 1458, 876])).
% 2.44/2.66 tff(10692,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(10693,plain,
% 2.44/2.66 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10692, 10684, 10682, 10681])).
% 2.44/2.66 tff(10694,plain,
% 2.44/2.66 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1471, 10693, 10680])).
% 2.44/2.66 tff(10695,plain,
% 2.44/2.66 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4437, 155, 10694, 10676, 10672])).
% 2.44/2.66 tff(10696,plain,
% 2.44/2.66 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[10695, 10671])).
% 2.44/2.66 tff(10697,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1170, 10696])).
% 2.44/2.66 tff(10698,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~(s(s(s(s(z)))) = s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(10699,plain,
% 2.44/2.66 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10698, 10639, 10666, 10662, 10660, 10602, 10656, 10652])).
% 2.44/2.66 tff(10700,plain,
% 2.44/2.66 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[10699, 10645])).
% 2.44/2.66 tff(10701,plain,
% 2.44/2.66 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 2.44/2.66 inference(symmetry,[status(thm)],[10642])).
% 2.44/2.66 tff(10702,plain,
% 2.44/2.66 (s(elem!1) = s(s(z))),
% 2.44/2.66 inference(transitivity,[status(thm)],[30, 10701, 72])).
% 2.44/2.66 tff(10703,plain,
% 2.44/2.66 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(s(z)))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10702])).
% 2.44/2.66 tff(10704,plain,
% 2.44/2.66 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[10703, 319])).
% 2.44/2.66 tff(10705,plain,
% 2.44/2.66 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.44/2.66 inference(symmetry,[status(thm)],[10704])).
% 2.44/2.66 tff(10706,plain,
% 2.44/2.66 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10705])).
% 2.44/2.66 tff(10707,plain,
% 2.44/2.66 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[331, 10706])).
% 2.44/2.66 tff(10708,plain,
% 2.44/2.66 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1615, 53, 10707, 10700])).
% 2.44/2.66 tff(10709,plain,
% 2.44/2.66 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10643, 10641])).
% 2.44/2.66 tff(10710,plain,
% 2.44/2.66 (~r(s(s(z)), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2940, 10623, 10656, 10141])).
% 2.44/2.66 tff(10711,plain,
% 2.44/2.66 (b(s(s(z)), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[437, 10710])).
% 2.44/2.66 tff(10712,plain,
% 2.44/2.66 (b(s(elem!1), s(s(elem!1)))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[10711, 10709])).
% 2.44/2.66 tff(10713,plain,
% 2.44/2.66 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10641])).
% 2.44/2.66 tff(10714,plain,
% 2.44/2.66 (b(s(s(elem!1)), z)),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[10613, 10713])).
% 2.44/2.66 tff(10715,plain,
% 2.44/2.66 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10658, 10641])).
% 2.44/2.66 tff(10716,plain,
% 2.44/2.66 (r(elem!1, s(s(elem!1)))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[10623, 10715])).
% 2.44/2.66 tff(10717,plain,
% 2.44/2.66 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10641, 10658])).
% 2.44/2.66 tff(10718,plain,
% 2.44/2.66 (r(s(s(elem!1)), elem!1)),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[10141, 10717])).
% 2.44/2.66 tff(10719,plain,
% 2.44/2.66 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10658])).
% 2.44/2.66 tff(10720,plain,
% 2.44/2.66 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[10652, 10719])).
% 2.44/2.66 tff(10721,plain,
% 2.44/2.66 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[6107, 155, 10720, 10718, 10716])).
% 2.44/2.66 tff(10722,plain,
% 2.44/2.66 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1484, 10721, 10648])).
% 2.44/2.66 tff(10723,plain,
% 2.44/2.66 (((~![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(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(10724,plain,
% 2.44/2.66 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~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(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(s(elem!1)))), s(s(elem!1)))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(10725,plain,
% 2.44/2.66 (((~![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)), z)) | (~b(s(s(elem!1)), z)) | (~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(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(s(elem!1)))), s(s(elem!1))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10724])).
% 2.44/2.66 tff(10726,plain,
% 2.44/2.66 (((~![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)), z)) | (~b(s(s(elem!1)), z)) | (~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(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(s(elem!1)))), s(s(elem!1)))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[10725, 10723])).
% 2.44/2.66 tff(10727,plain,
% 2.44/2.66 ((~![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)), z)) | (~b(s(s(elem!1)), z)) | (~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))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(10728,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[10727, 10726])).
% 2.44/2.66 tff(10729,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10728, 97, 10722, 10714, 10712, 10708])).
% 2.44/2.66 tff(10730,plain,((s(s(s(z))) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(10731,plain,
% 2.44/2.66 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10730, 3, 61])).
% 2.44/2.66 tff(10732,plain,
% 2.44/2.66 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10731])).
% 2.44/2.66 tff(10733,plain,
% 2.44/2.66 (s(s(z)) = s(s(elem!1))),
% 2.44/2.66 inference(transitivity,[status(thm)],[73, 10732, 19])).
% 2.44/2.66 tff(10734,plain,
% 2.44/2.66 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10733])).
% 2.44/2.66 tff(10735,plain,
% 2.44/2.66 (s(z) = s(elem!1)),
% 2.44/2.66 inference(transitivity,[status(thm)],[24, 10734, 29])).
% 2.44/2.66 tff(10736,plain,
% 2.44/2.66 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10733, 10735])).
% 2.44/2.66 tff(10737,plain,
% 2.44/2.66 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10733])).
% 2.44/2.66 tff(10738,plain,
% 2.44/2.66 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 2.44/2.66 inference(symmetry,[status(thm)],[10737])).
% 2.44/2.66 tff(10739,plain,
% 2.44/2.66 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10735])).
% 2.44/2.66 tff(10740,plain,
% 2.44/2.66 (z = elem!1),
% 2.44/2.66 inference(transitivity,[status(thm)],[1443, 10739, 85])).
% 2.44/2.66 tff(10741,plain,
% 2.44/2.66 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10740])).
% 2.44/2.66 tff(10742,plain,
% 2.44/2.66 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 2.44/2.66 inference(symmetry,[status(thm)],[10741])).
% 2.44/2.66 tff(10743,plain,
% 2.44/2.66 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(z)))),
% 2.44/2.66 inference(transitivity,[status(thm)],[10742, 10738])).
% 2.44/2.66 tff(10744,plain,
% 2.44/2.66 ((~b(elem!1, s(s(elem!1)))) <=> (~b(z, s(s(z))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10743])).
% 2.44/2.66 tff(10745,plain,
% 2.44/2.66 (elem!1 = z),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1888, 10740])).
% 2.44/2.66 tff(10746,plain,
% 2.44/2.66 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[1976])).
% 2.44/2.66 tff(10747,plain,
% 2.44/2.66 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 2.44/2.66 inference(symmetry,[status(thm)],[10746])).
% 2.44/2.66 tff(10748,plain,
% 2.44/2.66 (b(s(s(s(z))), s(s(z)))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[60, 10747])).
% 2.44/2.66 tff(10749,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2590, 10748])).
% 2.44/2.66 tff(10750,plain,(b(s(s(s(z))), s(s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(10751,plain,
% 2.44/2.66 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10750, 2590, 10745])).
% 2.44/2.66 tff(10752,plain,
% 2.44/2.66 (r(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[58, 10751])).
% 2.44/2.66 tff(10753,plain,
% 2.44/2.66 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10731])).
% 2.44/2.66 tff(10754,plain,
% 2.44/2.66 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[10753, 1414])).
% 2.44/2.66 tff(10755,plain,
% 2.44/2.66 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[10754, 2507])).
% 2.44/2.66 tff(10756,plain,
% 2.44/2.66 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10755])).
% 2.44/2.66 tff(10757,plain,
% 2.44/2.66 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[286, 10756])).
% 2.44/2.66 tff(10758,plain,
% 2.44/2.66 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10740])).
% 2.44/2.66 tff(10759,plain,
% 2.44/2.66 (r(elem!1, s(s(s(elem!1))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[10177, 10758])).
% 2.44/2.66 tff(10760,plain,
% 2.44/2.66 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10740])).
% 2.44/2.66 tff(10761,plain,
% 2.44/2.66 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[10760, 6776])).
% 2.44/2.66 tff(10762,plain,
% 2.44/2.66 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.44/2.66 inference(transitivity,[status(thm)],[10761, 6777])).
% 2.44/2.66 tff(10763,plain,
% 2.44/2.66 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10762])).
% 2.44/2.66 tff(10764,plain,
% 2.44/2.66 (~(s(s(s(elem!1))) = elem!1)),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[241, 10763])).
% 2.44/2.66 tff(10765,plain,
% 2.44/2.66 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10735, 10740])).
% 2.44/2.66 tff(10766,plain,
% 2.44/2.66 (b(s(elem!1), elem!1)),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[2589, 10765])).
% 2.44/2.66 tff(10767,plain,
% 2.44/2.66 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10740, 10735])).
% 2.44/2.66 tff(10768,plain,
% 2.44/2.66 (b(elem!1, s(elem!1))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[61, 10767])).
% 2.44/2.66 tff(10769,plain,
% 2.44/2.66 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.44/2.66 inference(symmetry,[status(thm)],[10734])).
% 2.44/2.66 tff(10770,plain,
% 2.44/2.66 (s(elem!1) = s(z)),
% 2.44/2.66 inference(transitivity,[status(thm)],[30, 10769, 23])).
% 2.44/2.66 tff(10771,plain,
% 2.44/2.66 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10770])).
% 2.44/2.66 tff(10772,plain,
% 2.44/2.66 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.66 inference(symmetry,[status(thm)],[10771])).
% 2.44/2.66 tff(10773,plain,
% 2.44/2.66 (b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[10119, 10772])).
% 2.44/2.66 tff(10774,plain,
% 2.44/2.66 (((~![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))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(10775,plain,
% 2.44/2.66 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(10776,plain,
% 2.44/2.66 (((~![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), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(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(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10775])).
% 2.44/2.66 tff(10777,plain,
% 2.44/2.66 (((~![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), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(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(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 2.44/2.66 inference(transitivity,[status(thm)],[10776, 10774])).
% 2.44/2.66 tff(10778,plain,
% 2.44/2.66 ((~![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), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(10779,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[10778, 10777])).
% 2.44/2.66 tff(10780,plain,
% 2.44/2.66 (~b(s(s(s(elem!1))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10779, 97, 10773, 10768, 10766])).
% 2.44/2.66 tff(10781,plain,
% 2.44/2.66 (r(s(s(s(elem!1))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[6862, 10780, 10764])).
% 2.44/2.66 tff(10782,plain,
% 2.44/2.66 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10740])).
% 2.44/2.66 tff(10783,plain,
% 2.44/2.66 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10731])).
% 2.44/2.66 tff(10784,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10783])).
% 2.44/2.66 tff(10785,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.66 inference(transitivity,[status(thm)],[10784, 10782])).
% 2.44/2.66 tff(10786,plain,
% 2.44/2.66 (b(s(s(s(z))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1846, 10731, 10119])).
% 2.44/2.66 tff(10787,plain,
% 2.44/2.66 (~b(z, s(s(z)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[7811, 87, 61, 550])).
% 2.44/2.66 tff(10788,plain,
% 2.44/2.66 (r(z, s(s(z)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[222, 10787])).
% 2.44/2.66 tff(10789,plain,
% 2.44/2.66 (~b(s(s(z)), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[7010, 87, 1360, 550])).
% 2.44/2.66 tff(10790,plain,
% 2.44/2.66 (r(s(s(z)), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[437, 10789])).
% 2.44/2.66 tff(10791,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1969, 10790, 10788, 7018, 1960])).
% 2.44/2.66 tff(10792,plain,((~b(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(10793,plain,
% 2.44/2.66 (~b(s(s(z)), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10792, 1960, 10786, 2589, 61])).
% 2.44/2.66 tff(10794,plain,
% 2.44/2.66 (r(s(s(z)), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[122, 10793])).
% 2.44/2.66 tff(10795,plain,
% 2.44/2.66 (r(s(s(elem!1)), s(elem!1))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[10794, 10736])).
% 2.44/2.66 tff(10796,plain,
% 2.44/2.66 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10733])).
% 2.44/2.66 tff(10797,plain,
% 2.44/2.66 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(z)))),
% 2.44/2.66 inference(symmetry,[status(thm)],[10796])).
% 2.44/2.66 tff(10798,plain,
% 2.44/2.66 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10735, 10733])).
% 2.44/2.66 tff(10799,plain,
% 2.44/2.66 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 2.44/2.66 inference(transitivity,[status(thm)],[10798, 10797])).
% 2.44/2.66 tff(10800,plain,
% 2.44/2.66 (r(s(elem!1), s(s(z)))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[3, 10799])).
% 2.44/2.66 tff(10801,plain,
% 2.44/2.66 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10740])).
% 2.44/2.66 tff(10802,plain,
% 2.44/2.66 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10733])).
% 2.44/2.66 tff(10803,plain,
% 2.44/2.66 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.44/2.66 inference(transitivity,[status(thm)],[10802, 10801])).
% 2.44/2.66 tff(10804,plain,
% 2.44/2.66 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 2.44/2.66 inference(monotonicity,[status(thm)],[1401, 1444])).
% 2.44/2.66 tff(10805,plain,
% 2.44/2.66 (b(s(elem!1), elem!1)),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[550, 10804])).
% 2.44/2.66 tff(10806,plain,
% 2.44/2.66 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[1411])).
% 2.44/2.66 tff(10807,plain,
% 2.44/2.66 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.66 inference(symmetry,[status(thm)],[10806])).
% 2.44/2.66 tff(10808,plain,
% 2.44/2.66 (b(s(s(s(elem!1))), s(elem!1))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[10119, 10807])).
% 2.44/2.66 tff(10809,plain,
% 2.44/2.66 (~b(s(s(s(elem!1))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10779, 97, 10808, 7275, 10805])).
% 2.44/2.66 tff(10810,plain,
% 2.44/2.66 (~b(s(s(s(elem!1))), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8380, 10809, 1889])).
% 2.44/2.66 tff(10811,plain,
% 2.44/2.66 (r(s(s(s(elem!1))), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[246, 10810])).
% 2.44/2.66 tff(10812,plain,
% 2.44/2.66 (s(s(z)) = s(s(elem!1))),
% 2.44/2.66 inference(symmetry,[status(thm)],[1974])).
% 2.44/2.66 tff(10813,plain,
% 2.44/2.66 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[10812])).
% 2.44/2.66 tff(10814,plain,
% 2.44/2.66 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.66 inference(symmetry,[status(thm)],[10813])).
% 2.44/2.66 tff(10815,plain,
% 2.44/2.66 (r(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[6277, 10814])).
% 2.44/2.66 tff(10816,plain,
% 2.44/2.66 ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[735, 155, 570, 288])).
% 2.44/2.66 tff(10817,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10816, 10815, 645])).
% 2.44/2.66 tff(10818,plain,((~r(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(10819,plain,
% 2.44/2.66 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10818, 645, 1889, 10811, 10221])).
% 2.44/2.66 tff(10820,plain,
% 2.44/2.66 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8079, 10819, 8063])).
% 2.44/2.66 tff(10821,plain,
% 2.44/2.66 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[3326, 3226, 645, 1393, 7716])).
% 2.44/2.66 tff(10822,plain,
% 2.44/2.66 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[336, 10821])).
% 2.44/2.66 tff(10823,plain,
% 2.44/2.66 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[1393])).
% 2.44/2.66 tff(10824,plain,
% 2.44/2.66 (b(s(s(s(z))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1846, 1393, 10119])).
% 2.44/2.66 tff(10825,plain,
% 2.44/2.66 (~b(z, s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[6364, 10824, 61, 550])).
% 2.44/2.66 tff(10826,plain,
% 2.44/2.66 (r(z, s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1318, 10825])).
% 2.44/2.66 tff(10827,plain,
% 2.44/2.66 (~b(s(s(s(z))), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9913, 10810, 1393])).
% 2.44/2.66 tff(10828,plain,
% 2.44/2.66 (r(s(s(s(z))), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[402, 10827])).
% 2.44/2.66 tff(10829,plain,
% 2.44/2.66 (~r(s(s(z)), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[6410, 645, 10828, 10826])).
% 2.44/2.66 tff(10830,plain,
% 2.44/2.66 (b(s(s(z)), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[437, 10829])).
% 2.44/2.66 tff(10831,plain,
% 2.44/2.66 (b(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[10830, 10823])).
% 2.44/2.66 tff(10832,plain,
% 2.44/2.66 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[832, 3226, 10221, 10811])).
% 2.44/2.66 tff(10833,plain,
% 2.44/2.66 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1872, 7716, 10811, 3226])).
% 2.44/2.66 tff(10834,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4129, 10833, 10832, 10831, 1418, 10822])).
% 2.44/2.66 tff(10835,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), z)) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(10836,plain,
% 2.44/2.66 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10835, 645, 1393, 550, 61])).
% 2.44/2.66 tff(10837,plain,
% 2.44/2.66 (r(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[511, 10836])).
% 2.44/2.66 tff(10838,plain,
% 2.44/2.66 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1816, 10837, 1520, 1393, 1812])).
% 2.44/2.66 tff(10839,plain,
% 2.44/2.66 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1484, 10838, 1432])).
% 2.44/2.66 tff(10840,plain,
% 2.44/2.66 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2431, 10839, 10808, 10820])).
% 2.44/2.66 tff(10841,plain,
% 2.44/2.66 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[821, 10840, 4451])).
% 2.44/2.66 tff(10842,plain,
% 2.44/2.66 (~r(s(s(s(s(elem!1)))), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[832, 10841, 10221, 10811])).
% 2.44/2.66 tff(10843,plain,
% 2.44/2.66 (b(s(s(s(s(elem!1)))), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[842, 10842])).
% 2.44/2.66 tff(10844,plain,
% 2.44/2.66 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4474, 10843, 1444])).
% 2.44/2.66 tff(10845,plain,
% 2.44/2.67 (((~![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(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(10846,plain,
% 2.44/2.67 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), 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)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(10847,plain,
% 2.44/2.67 (((~![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)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), 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)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10846])).
% 2.44/2.67 tff(10848,plain,
% 2.44/2.67 (((~![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)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), 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)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[10847, 10845])).
% 2.44/2.67 tff(10849,plain,
% 2.44/2.67 ((~![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)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), 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)))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(10850,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[10849, 10848])).
% 2.44/2.67 tff(10851,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[10850, 97, 10839, 10844, 10820, 1914])).
% 2.44/2.67 tff(10852,plain,((~r(s(s(z)), z)) | (~b(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(10853,plain,
% 2.44/2.67 (~r(s(s(z)), z)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[10852, 1914, 10800, 10731, 10795, 2589, 61])).
% 2.44/2.67 tff(10854,plain,
% 2.44/2.67 (b(s(s(z)), z)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[625, 10853])).
% 2.44/2.67 tff(10855,plain,
% 2.44/2.67 (b(s(s(elem!1)), elem!1)),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[10854, 10803])).
% 2.44/2.67 tff(10856,plain,
% 2.44/2.67 (~b(s(s(s(s(z)))), z)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[7293, 10855, 10731, 10800, 2589, 61, 10795])).
% 2.44/2.67 tff(10857,plain,
% 2.44/2.67 (r(s(s(s(s(z)))), z)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[2860, 10856])).
% 2.44/2.67 tff(10858,plain,
% 2.44/2.67 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[10857, 10785])).
% 2.44/2.67 tff(10859,plain,
% 2.44/2.67 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[7302, 155, 10858, 10781, 10759])).
% 2.44/2.67 tff(10860,plain,
% 2.44/2.67 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[821, 10859, 10757])).
% 2.44/2.67 tff(10861,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[2745, 1979])).
% 2.44/2.67 tff(10862,plain,(b(s(s(s(s(elem!1)))), s(s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(10863,plain,
% 2.44/2.67 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[10862, 10860, 10745])).
% 2.44/2.67 tff(10864,plain,
% 2.44/2.67 (r(s(s(s(s(elem!1)))), z)),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[10857, 10784])).
% 2.44/2.67 tff(10865,plain,
% 2.44/2.67 (r(s(s(s(s(s(elem!1))))), s(elem!1)) <=> r(s(s(s(s(s(elem!1))))), s(z))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10770])).
% 2.44/2.67 tff(10866,plain,
% 2.44/2.67 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.44/2.67 inference(symmetry,[status(thm)],[10865])).
% 2.44/2.67 tff(10867,plain,
% 2.44/2.67 (~(s(s(s(s(s(elem!1))))) = s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[6222, 10731])).
% 2.44/2.67 tff(10868,plain,
% 2.44/2.67 (b(s(s(s(s(s(elem!1))))), s(elem!1)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10770])).
% 2.44/2.67 tff(10869,plain,
% 2.44/2.67 ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) <=> (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10868])).
% 2.44/2.67 tff(10870,plain,
% 2.44/2.67 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.44/2.67 inference(symmetry,[status(thm)],[10731])).
% 2.44/2.67 tff(10871,plain,
% 2.44/2.67 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10870])).
% 2.44/2.67 tff(10872,plain,
% 2.44/2.67 (b(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.44/2.67 inference(symmetry,[status(thm)],[10871])).
% 2.44/2.67 tff(10873,plain,
% 2.44/2.67 (~(s(s(s(s(s(elem!1))))) = s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[7491, 10731])).
% 2.44/2.67 tff(10874,plain,
% 2.44/2.67 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10870])).
% 2.44/2.67 tff(10875,plain,
% 2.44/2.67 ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10874])).
% 2.44/2.67 tff(10876,plain,
% 2.44/2.67 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.44/2.67 inference(symmetry,[status(thm)],[10732])).
% 2.44/2.67 tff(10877,plain,
% 2.44/2.67 (s(s(elem!1)) = s(s(z))),
% 2.44/2.67 inference(transitivity,[status(thm)],[167, 10876, 72])).
% 2.44/2.67 tff(10878,plain,
% 2.44/2.67 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10877])).
% 2.44/2.67 tff(10879,plain,
% 2.44/2.67 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.67 inference(symmetry,[status(thm)],[10878])).
% 2.44/2.67 tff(10880,plain,
% 2.44/2.67 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[145, 10879])).
% 2.44/2.67 tff(10881,plain,
% 2.44/2.67 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10740])).
% 2.44/2.67 tff(10882,plain,
% 2.44/2.67 ((s(s(s(s(s(elem!1))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[10881, 6292])).
% 2.44/2.67 tff(10883,plain,
% 2.44/2.67 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.44/2.67 inference(transitivity,[status(thm)],[10882, 6293])).
% 2.44/2.67 tff(10884,plain,
% 2.44/2.67 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10883])).
% 2.44/2.67 tff(10885,plain,
% 2.44/2.67 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[6299, 10884])).
% 2.44/2.67 tff(10886,plain,
% 2.44/2.67 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(z))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10770])).
% 2.44/2.67 tff(10887,plain,
% 2.44/2.67 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(z) = s(s(s(s(elem!1)))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[10886, 265])).
% 2.44/2.67 tff(10888,plain,
% 2.44/2.67 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.44/2.67 inference(symmetry,[status(thm)],[10887])).
% 2.44/2.67 tff(10889,plain,
% 2.44/2.67 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10888])).
% 2.44/2.67 tff(10890,plain,
% 2.44/2.67 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[275, 10889])).
% 2.44/2.67 tff(10891,plain,
% 2.44/2.67 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[6172, 10890])).
% 2.44/2.67 tff(10892,plain,
% 2.44/2.67 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10877])).
% 2.44/2.67 tff(10893,plain,
% 2.44/2.67 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.44/2.67 inference(symmetry,[status(thm)],[10892])).
% 2.44/2.67 tff(10894,plain,
% 2.44/2.67 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[10893, 1531])).
% 2.44/2.67 tff(10895,plain,
% 2.44/2.67 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10894])).
% 2.44/2.67 tff(10896,plain,
% 2.44/2.67 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[43, 10895])).
% 2.44/2.67 tff(10897,plain,
% 2.44/2.67 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10733])).
% 2.44/2.67 tff(10898,plain,
% 2.44/2.67 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.44/2.67 inference(transitivity,[status(thm)],[10897, 1428])).
% 2.44/2.67 tff(10899,plain,
% 2.44/2.67 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10898])).
% 2.44/2.67 tff(10900,plain,
% 2.44/2.67 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[331, 10899])).
% 2.44/2.67 tff(10901,plain,
% 2.44/2.67 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[1484, 1820, 10900])).
% 2.44/2.67 tff(10902,plain,
% 2.44/2.67 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[2431, 10901, 10773, 805])).
% 2.44/2.67 tff(10903,plain,
% 2.44/2.67 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[8079, 10902, 10896])).
% 2.44/2.67 tff(10904,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))), introduced(assumption)).
% 2.44/2.67 tff(10905,assumption,(r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))), introduced(assumption)).
% 2.44/2.67 tff(10906,plain,
% 2.44/2.67 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(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)))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(10907,plain,
% 2.44/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10906])).
% 2.44/2.67 tff(10908,plain,
% 2.44/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[10907, 6278])).
% 2.44/2.67 tff(10909,plain,
% 2.44/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(10910,plain,
% 2.44/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[10909, 10908])).
% 2.44/2.67 tff(10911,plain,
% 2.44/2.67 ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[10910, 155, 4497, 6277])).
% 2.44/2.67 tff(10912,plain,
% 2.44/2.67 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[10911, 10905])).
% 2.44/2.67 tff(10913,plain,
% 2.44/2.67 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[6269, 10912, 10904])).
% 2.44/2.67 tff(10914,plain,
% 2.44/2.67 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(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)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(10915,plain,
% 2.44/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10914])).
% 2.44/2.67 tff(10916,plain,
% 2.44/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.44/2.67 inference(transitivity,[status(thm)],[10915, 7512])).
% 2.44/2.67 tff(10917,plain,
% 2.44/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(10918,plain,
% 2.44/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[10917, 10916])).
% 2.44/2.67 tff(10919,plain,
% 2.44/2.67 ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[10918, 155, 1528, 1523])).
% 2.44/2.67 tff(10920,plain,
% 2.44/2.67 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[10919, 10905])).
% 2.44/2.67 tff(10921,plain,
% 2.44/2.67 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[6313, 10920, 9196])).
% 2.44/2.67 tff(10922,plain,
% 2.44/2.67 (((~![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(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)))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(10923,plain,
% 2.44/2.67 (((~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)))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(10924,plain,
% 2.44/2.67 (((~![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(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))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10923])).
% 2.44/2.67 tff(10925,plain,
% 2.44/2.67 (((~![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(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)))),
% 2.44/2.67 inference(transitivity,[status(thm)],[10924, 10922])).
% 2.44/2.67 tff(10926,plain,
% 2.44/2.67 ((~![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(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)))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(10927,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[10926, 10925])).
% 2.44/2.67 tff(10928,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[10927, 97, 1915, 9575, 10921, 10913])).
% 2.44/2.67 tff(10929,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (s(s(s(s(s(elem!1))))) = elem!1) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(10930,plain,
% 2.44/2.67 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[10929, 10903, 10768, 10891, 10885, 10880, 1915, 10781, 10759])).
% 2.44/2.67 tff(10931,plain,
% 2.44/2.67 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[10930, 10875])).
% 2.44/2.67 tff(10932,plain,
% 2.44/2.67 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[6289, 10931, 10873])).
% 2.44/2.67 tff(10933,plain,
% 2.44/2.67 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[10932, 10872])).
% 2.44/2.67 tff(10934,plain,
% 2.44/2.67 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10770])).
% 2.44/2.67 tff(10935,plain,
% 2.44/2.67 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.44/2.67 inference(symmetry,[status(thm)],[10934])).
% 2.44/2.67 tff(10936,plain,
% 2.44/2.67 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[1822, 1820, 10731])).
% 2.44/2.67 tff(10937,plain,
% 2.44/2.67 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[452, 10936])).
% 2.44/2.67 tff(10938,plain,
% 2.44/2.67 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[10754])).
% 2.44/2.67 tff(10939,plain,
% 2.44/2.67 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[286, 10938])).
% 2.44/2.67 tff(10940,plain,
% 2.44/2.67 (~b(s(s(s(elem!1))), z)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[8380, 10780, 10745])).
% 2.44/2.67 tff(10941,plain,
% 2.44/2.67 (r(s(s(s(elem!1))), z)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[246, 10940])).
% 2.44/2.67 tff(10942,plain,
% 2.44/2.67 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[1921, 97, 10901, 1915, 1914])).
% 2.44/2.67 tff(10943,plain,
% 2.44/2.67 (~b(z, s(s(s(s(elem!1)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[2407, 10942, 10745])).
% 2.44/2.67 tff(10944,plain,
% 2.44/2.67 (r(z, s(s(s(s(elem!1)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[1093, 10943])).
% 2.44/2.67 tff(10945,plain,
% 2.44/2.67 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[1872, 10944, 10941, 824])).
% 2.44/2.67 tff(10946,plain,
% 2.44/2.67 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[486, 10945, 10939])).
% 2.44/2.67 tff(10947,plain,
% 2.44/2.67 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[2741, 10946, 805, 10937])).
% 2.44/2.67 tff(10948,plain,
% 2.44/2.67 (r(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[143, 10947])).
% 2.44/2.67 tff(10949,plain,
% 2.44/2.67 (~r(s(z), s(s(s(elem!1))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[5875, 10948, 3, 145])).
% 2.44/2.67 tff(10950,plain,
% 2.44/2.67 (b(s(z), s(s(s(elem!1))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[181, 10949])).
% 2.44/2.67 tff(10951,plain,
% 2.44/2.67 (b(s(elem!1), s(s(s(elem!1))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[10950, 10935])).
% 2.44/2.67 tff(10952,plain,
% 2.44/2.67 (((~![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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(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))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(10953,plain,
% 2.44/2.67 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(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(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(10954,plain,
% 2.44/2.67 (((~![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(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(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[10953])).
% 2.44/2.68 tff(10955,plain,
% 2.44/2.68 (((~![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(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(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[10954, 10952])).
% 2.44/2.68 tff(10956,plain,
% 2.44/2.68 ((~![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(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(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(10957,plain,
% 2.44/2.68 ((~![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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[10956, 10955])).
% 2.44/2.68 tff(10958,plain,
% 2.44/2.68 ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[10957, 97, 10946, 10951])).
% 2.44/2.68 tff(10959,plain,
% 2.44/2.68 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[10958, 10933])).
% 2.44/2.68 tff(10960,plain,
% 2.44/2.68 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[10959, 10869])).
% 2.44/2.68 tff(10961,plain,
% 2.44/2.68 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[6239, 10960, 10867])).
% 2.44/2.68 tff(10962,plain,
% 2.44/2.68 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[10961, 10866])).
% 2.44/2.68 tff(10963,plain,
% 2.44/2.68 (((~![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(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(10964,plain,
% 2.44/2.68 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(10965,plain,
% 2.44/2.68 (((~![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(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(s(s(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[10964])).
% 2.44/2.68 tff(10966,plain,
% 2.44/2.68 (((~![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(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(s(s(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[10965, 10963])).
% 2.44/2.68 tff(10967,plain,
% 2.44/2.68 ((~![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(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(s(s(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))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(10968,plain,
% 2.44/2.68 ((~![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(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[10967, 10966])).
% 2.44/2.68 tff(10969,plain,
% 2.44/2.68 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[10968, 97, 10946, 805, 10951])).
% 2.44/2.68 tff(10970,plain,
% 2.44/2.68 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1615, 53, 10890, 10969])).
% 2.44/2.68 tff(10971,plain,
% 2.44/2.68 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[6197, 10939, 10731])).
% 2.44/2.68 tff(10972,plain,
% 2.44/2.68 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[7544, 10971])).
% 2.44/2.68 tff(10973,plain,
% 2.44/2.68 (((~![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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(10974,plain,
% 2.44/2.68 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(10975,plain,
% 2.44/2.68 (((~![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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[10974])).
% 2.44/2.68 tff(10976,plain,
% 2.44/2.68 (((~![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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[10975, 10973])).
% 2.44/2.68 tff(10977,plain,
% 2.44/2.68 ((~![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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(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)))))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(10978,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[10977, 10976])).
% 2.44/2.68 tff(10979,plain,
% 2.44/2.68 ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[10978, 97, 10946, 805])).
% 2.44/2.68 tff(10980,plain,
% 2.44/2.68 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[10979, 10933])).
% 2.44/2.68 tff(10981,plain,
% 2.44/2.68 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[6254, 10980, 10972])).
% 2.44/2.68 tff(10982,plain,
% 2.44/2.68 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1874, 10937, 61, 10119, 10941, 824, 10901, 10939])).
% 2.44/2.68 tff(10983,plain,
% 2.44/2.68 (r(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[280, 10982])).
% 2.44/2.68 tff(10984,plain,
% 2.44/2.68 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1909, 10983, 10731])).
% 2.44/2.68 tff(10985,plain,
% 2.44/2.68 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[6261, 155, 10984, 10981, 10970])).
% 2.44/2.68 tff(10986,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[10985, 10962])).
% 2.44/2.68 tff(10987,plain,(r(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)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(10988,plain,
% 2.44/2.68 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[10987, 10860, 10855, 3, 145, 10864, 1914, 61])).
% 2.44/2.68 tff(10989,plain,
% 2.44/2.68 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1816, 10988, 10800, 10731, 10795])).
% 2.44/2.68 tff(10990,plain,
% 2.44/2.68 (b(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[511, 10989])).
% 2.44/2.68 tff(10991,plain,
% 2.44/2.68 (((~![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(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(10992,plain,
% 2.44/2.68 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(10993,plain,
% 2.44/2.68 (((~![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(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[10992])).
% 2.44/2.68 tff(10994,plain,
% 2.44/2.68 (((~![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(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[10993, 10991])).
% 2.44/2.68 tff(10995,plain,
% 2.44/2.68 ((~![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(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(10996,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[10995, 10994])).
% 2.44/2.68 tff(10997,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[10996, 97, 255, 513, 1360, 371])).
% 2.44/2.68 tff(10998,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(10999,plain,
% 2.44/2.68 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[10998, 10990, 10786, 10863])).
% 2.44/2.68 tff(11000,plain,
% 2.44/2.68 (r(s(z), s(s(s(s(elem!1)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[280, 10999])).
% 2.44/2.68 tff(11001,plain,
% 2.44/2.68 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[10731, 6631])).
% 2.44/2.68 tff(11002,plain,
% 2.44/2.68 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[7352, 10988, 10731])).
% 2.44/2.68 tff(11003,plain,
% 2.44/2.68 (~b(s(z), s(s(s(elem!1))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2535, 11002, 10119, 10177, 61, 3, 11001, 10794])).
% 2.44/2.68 tff(11004,plain,
% 2.44/2.68 (~b(s(z), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[6628, 11003, 10731])).
% 2.44/2.68 tff(11005,plain,
% 2.44/2.68 (r(s(z), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[253, 11004])).
% 2.44/2.68 tff(11006,plain,
% 2.44/2.68 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2171, 11005, 3, 1960, 11000])).
% 2.44/2.68 tff(11007,plain,
% 2.44/2.68 (~b(z, s(s(s(s(elem!1)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[558, 10990, 2589, 61])).
% 2.44/2.68 tff(11008,plain,
% 2.44/2.68 (r(z, s(s(s(s(elem!1)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1093, 11007])).
% 2.44/2.68 tff(11009,plain,
% 2.44/2.68 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1872, 11008, 10941, 10864])).
% 2.44/2.68 tff(11010,plain,
% 2.44/2.68 (r(s(z), s(s(s(elem!1))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[181, 11003])).
% 2.44/2.68 tff(11011,plain,
% 2.44/2.68 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[5875, 11010, 3, 145])).
% 2.44/2.68 tff(11012,plain,
% 2.44/2.68 (b(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[143, 11011])).
% 2.44/2.68 tff(11013,plain,
% 2.44/2.68 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[4129, 11012, 10859, 10939, 11009])).
% 2.44/2.68 tff(11014,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[336, 11013, 11006])).
% 2.44/2.68 tff(11015,plain,((~b(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(11016,plain,
% 2.44/2.68 (~b(elem!1, s(s(elem!1)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[11015, 2591, 3, 10752, 61])).
% 2.44/2.68 tff(11017,plain,
% 2.44/2.68 (~b(z, s(s(z)))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[11016, 10744])).
% 2.44/2.68 tff(11018,plain,
% 2.44/2.68 (r(z, s(s(z)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[222, 11017])).
% 2.44/2.68 tff(11019,plain,
% 2.44/2.68 (~b(z, s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[6364, 10786, 61, 2589])).
% 2.44/2.68 tff(11020,plain,
% 2.44/2.68 (r(z, s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1318, 11019])).
% 2.44/2.68 tff(11021,plain,
% 2.44/2.68 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[10740])).
% 2.44/2.68 tff(11022,plain,
% 2.44/2.68 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[10733])).
% 2.44/2.68 tff(11023,plain,
% 2.44/2.68 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 2.44/2.68 inference(transitivity,[status(thm)],[11022, 11021])).
% 2.44/2.68 tff(11024,plain,
% 2.44/2.68 (r(elem!1, s(s(elem!1)))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[11018, 11023])).
% 2.44/2.68 tff(11025,plain,
% 2.44/2.68 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[10752, 10879])).
% 2.44/2.68 tff(11026,plain,
% 2.44/2.68 (~b(s(s(z)), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[10792, 2591, 10786, 2589, 61])).
% 2.44/2.68 tff(11027,plain,
% 2.44/2.68 (r(s(s(z)), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[122, 11026])).
% 2.44/2.68 tff(11028,plain,
% 2.44/2.68 (r(s(s(elem!1)), s(elem!1))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[11027, 10736])).
% 2.44/2.68 tff(11029,plain,
% 2.44/2.68 ((s(s(elem!1)) = elem!1) <=> (s(s(z)) = elem!1)),
% 2.44/2.68 inference(monotonicity,[status(thm)],[10877])).
% 2.44/2.68 tff(11030,plain,
% 2.44/2.68 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 2.44/2.68 inference(monotonicity,[status(thm)],[10740])).
% 2.44/2.68 tff(11031,plain,
% 2.44/2.68 ((s(s(elem!1)) = z) <=> (s(s(z)) = elem!1)),
% 2.44/2.68 inference(transitivity,[status(thm)],[11030, 11029])).
% 2.44/2.68 tff(11032,plain,
% 2.44/2.68 ((~(s(s(elem!1)) = z)) <=> (~(s(s(z)) = elem!1))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[11031])).
% 2.44/2.68 tff(11033,plain,
% 2.44/2.68 (~(s(s(z)) = elem!1)),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[170, 11032])).
% 2.44/2.68 tff(11034,plain,
% 2.44/2.68 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.44/2.68 inference(monotonicity,[status(thm)],[10731])).
% 2.44/2.68 tff(11035,plain,
% 2.44/2.68 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.44/2.68 inference(symmetry,[status(thm)],[11034])).
% 2.44/2.68 tff(11036,plain,
% 2.44/2.68 (r(s(s(s(z))), elem!1)),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[10781, 11035])).
% 2.44/2.68 tff(11037,plain,
% 2.44/2.68 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(z)))),
% 2.44/2.68 inference(transitivity,[status(thm)],[11030, 11029, 6823])).
% 2.44/2.68 tff(11038,plain,
% 2.44/2.68 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(z))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[11037])).
% 2.44/2.68 tff(11039,plain,
% 2.44/2.68 (~(elem!1 = s(s(z)))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[170, 11038])).
% 2.44/2.68 tff(11040,plain,
% 2.44/2.68 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[10733])).
% 2.44/2.68 tff(11041,plain,
% 2.44/2.68 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 2.44/2.68 inference(symmetry,[status(thm)],[11040])).
% 2.44/2.68 tff(11042,plain,
% 2.44/2.68 ((~b(elem!1, s(s(elem!1)))) <=> (~b(elem!1, s(s(z))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[11041])).
% 2.44/2.68 tff(11043,plain,
% 2.44/2.68 (~b(elem!1, s(s(z)))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[11016, 11042])).
% 2.44/2.68 tff(11044,plain,
% 2.44/2.68 (r(elem!1, s(s(z)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[6842, 11043, 11039])).
% 2.44/2.68 tff(11045,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 2.44/2.68 tff(11046,plain,
% 2.44/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(11047,plain,
% 2.44/2.68 (((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(11048,plain,
% 2.44/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[11047])).
% 2.44/2.68 tff(11049,plain,
% 2.44/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)))),
% 2.44/2.68 inference(transitivity,[status(thm)],[11048, 11046])).
% 2.44/2.68 tff(11050,plain,
% 2.44/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(11051,plain,
% 2.44/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[11050, 11049])).
% 2.44/2.68 tff(11052,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[11051, 155, 6845, 6844, 11045, 1960])).
% 2.44/2.68 tff(11053,plain,((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(11054,plain,
% 2.44/2.68 (~r(s(s(z)), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[11053, 11044, 11036, 2591])).
% 2.44/2.68 tff(11055,plain,
% 2.44/2.68 (b(s(s(z)), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1563, 11054, 11033])).
% 2.44/2.68 tff(11056,plain,
% 2.44/2.68 (b(s(s(elem!1)), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[6819, 11055, 10745])).
% 2.44/2.68 tff(11057,plain,
% 2.44/2.68 (~b(s(s(s(s(z)))), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[7293, 11056, 10731, 10800, 2589, 61, 11028])).
% 2.44/2.68 tff(11058,plain,
% 2.44/2.68 (r(s(s(s(s(z)))), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2860, 11057])).
% 2.44/2.68 tff(11059,plain,
% 2.44/2.68 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[11058, 10785])).
% 2.44/2.68 tff(11060,plain,
% 2.44/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(11061,plain,
% 2.44/2.68 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(11062,plain,
% 2.44/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[11061])).
% 2.44/2.68 tff(11063,plain,
% 2.44/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.44/2.68 inference(transitivity,[status(thm)],[11062, 11060])).
% 2.44/2.68 tff(11064,plain,
% 2.44/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(11065,plain,
% 2.44/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[11064, 11063])).
% 2.44/2.68 tff(11066,plain,
% 2.44/2.68 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[11065, 155, 11059, 11025, 10781, 11024])).
% 2.44/2.68 tff(11067,plain,
% 2.44/2.68 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[5949, 11018, 11020, 10177, 2591])).
% 2.44/2.68 tff(11068,plain,
% 2.44/2.68 (b(s(s(z)), s(s(s(elem!1))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[143, 11067])).
% 2.44/2.68 tff(11069,plain,
% 2.44/2.68 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[7302, 155, 11059, 10781, 10759])).
% 2.44/2.68 tff(11070,plain,
% 2.44/2.68 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[4129, 11069, 11068, 10939, 11066])).
% 2.44/2.68 tff(11071,plain,
% 2.44/2.68 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[336, 11070])).
% 2.44/2.68 tff(11072,plain,
% 2.44/2.68 (~r(z, s(s(s(s(elem!1)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[6995, 11071, 2591, 11020, 11018])).
% 2.44/2.69 tff(11073,plain,
% 2.44/2.69 (b(z, s(s(s(s(elem!1)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1093, 11072])).
% 2.44/2.69 tff(11074,plain,
% 2.44/2.69 (r(s(s(s(s(elem!1)))), z)),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[11058, 10784])).
% 2.44/2.69 tff(11075,plain,
% 2.44/2.69 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[821, 11069, 10757])).
% 2.44/2.69 tff(11076,plain,
% 2.44/2.69 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[486, 11066, 10939])).
% 2.44/2.69 tff(11077,plain,
% 2.44/2.69 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2741, 11076, 11075, 11068])).
% 2.44/2.69 tff(11078,plain,
% 2.44/2.69 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[452, 11077])).
% 2.44/2.69 tff(11079,plain,
% 2.44/2.69 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[3278, 11078, 11018, 11027, 11074])).
% 2.44/2.69 tff(11080,plain,
% 2.44/2.69 (b(s(s(s(s(elem!1)))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[511, 11079])).
% 2.44/2.69 tff(11081,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[558, 11080, 11073, 2589, 61])).
% 2.44/2.69 tff(11082,plain,(b(s(s(s(z))), s(s(z))) | (~b(z, s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(11083,plain,
% 2.44/2.69 (b(s(s(s(z))), s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[11082, 3, 61])).
% 2.44/2.69 tff(11084,plain,
% 2.44/2.69 (b(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1995, 11083, 10731])).
% 2.44/2.69 tff(11085,plain,
% 2.44/2.69 (~b(s(s(z)), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[10654, 11084, 10119, 2589])).
% 2.44/2.69 tff(11086,plain,
% 2.44/2.69 (r(s(s(z)), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[122, 11085])).
% 2.44/2.69 tff(11087,plain,
% 2.44/2.69 (r(s(s(elem!1)), s(elem!1))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[11086, 10736])).
% 2.44/2.69 tff(11088,plain,
% 2.44/2.69 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[10877])).
% 2.44/2.69 tff(11089,plain,
% 2.44/2.69 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.69 inference(symmetry,[status(thm)],[11088])).
% 2.44/2.69 tff(11090,plain,
% 2.44/2.69 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[11084, 11089])).
% 2.44/2.69 tff(11091,plain,
% 2.44/2.69 (r(s(elem!1), s(s(elem!1)))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[3, 10798])).
% 2.44/2.69 tff(11092,plain,
% 2.44/2.69 (r(elem!1, s(s(s(elem!1))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[10221, 1509])).
% 2.44/2.69 tff(11093,plain,
% 2.44/2.69 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.44/2.69 inference(monotonicity,[status(thm)],[1444])).
% 2.44/2.69 tff(11094,plain,
% 2.44/2.69 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[11093, 6776])).
% 2.44/2.69 tff(11095,plain,
% 2.44/2.69 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.44/2.69 inference(transitivity,[status(thm)],[11094, 6777])).
% 2.44/2.69 tff(11096,plain,
% 2.44/2.69 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[11095])).
% 2.44/2.69 tff(11097,plain,
% 2.44/2.69 (~(s(s(s(elem!1))) = elem!1)),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[241, 11096])).
% 2.44/2.69 tff(11098,plain,
% 2.44/2.69 (r(s(s(s(elem!1))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6862, 10809, 11097])).
% 2.44/2.69 tff(11099,plain,
% 2.44/2.69 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1816, 3438, 1520, 1393, 1812])).
% 2.44/2.69 tff(11100,plain,
% 2.44/2.69 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1484, 11099, 1432])).
% 2.44/2.69 tff(11101,plain,
% 2.44/2.69 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1822, 11099, 1393])).
% 2.44/2.69 tff(11102,plain,
% 2.44/2.69 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[452, 11101])).
% 2.44/2.69 tff(11103,plain,
% 2.44/2.69 (~b(s(s(z)), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1832, 11102, 61, 876])).
% 2.44/2.69 tff(11104,plain,
% 2.44/2.69 (r(s(s(z)), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[625, 11103])).
% 2.44/2.69 tff(11105,plain,
% 2.44/2.69 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[10818, 11104, 1889, 10811, 10221])).
% 2.44/2.69 tff(11106,plain,
% 2.44/2.69 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[8079, 11105, 8063])).
% 2.44/2.69 tff(11107,plain,
% 2.44/2.69 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2431, 11106, 10808, 11100])).
% 2.44/2.69 tff(11108,plain,
% 2.44/2.69 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[821, 11107, 4451])).
% 2.44/2.69 tff(11109,plain,
% 2.44/2.69 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1586, 11100, 11098, 11092, 1527, 1529, 1444])).
% 2.44/2.69 tff(11110,plain,
% 2.44/2.69 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[486, 11109, 1418])).
% 2.44/2.69 tff(11111,plain,
% 2.44/2.69 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2439, 11108, 1889])).
% 2.44/2.69 tff(11112,plain,
% 2.44/2.69 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[11110, 8360])).
% 2.44/2.69 tff(11113,plain,
% 2.44/2.69 (~r(z, s(s(s(s(elem!1)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2449, 11112, 10826, 11111])).
% 2.44/2.69 tff(11114,plain,
% 2.44/2.69 (b(z, s(s(s(s(elem!1)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1093, 11113])).
% 2.44/2.69 tff(11115,plain,
% 2.44/2.69 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2407, 11114, 1889])).
% 2.44/2.69 tff(11116,plain,
% 2.44/2.69 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[4474, 876, 1444])).
% 2.44/2.69 tff(11117,plain,
% 2.44/2.69 (((~![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(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $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)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(11118,plain,
% 2.44/2.69 (((~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(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(11119,plain,
% 2.44/2.69 (((~![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(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(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[11118])).
% 2.44/2.69 tff(11120,plain,
% 2.44/2.69 (((~![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(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(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.44/2.69 inference(transitivity,[status(thm)],[11119, 11117])).
% 2.44/2.69 tff(11121,plain,
% 2.44/2.69 ((~![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(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))))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(11122,plain,
% 2.44/2.69 ((~![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(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[11121, 11120])).
% 2.44/2.69 tff(11123,plain,
% 2.44/2.69 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[11122, 97, 11116, 7275, 10805])).
% 2.44/2.69 tff(11124,plain,
% 2.44/2.69 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1615, 53, 1612, 11123])).
% 2.44/2.69 tff(11125,plain,
% 2.44/2.69 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1909, 3442, 1393])).
% 2.44/2.69 tff(11126,plain,
% 2.44/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(11127,plain,
% 2.44/2.69 (((~r(s(s(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)))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(11128,plain,
% 2.44/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[11127])).
% 2.44/2.69 tff(11129,plain,
% 2.44/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[11128, 11126])).
% 2.44/2.69 tff(11130,plain,
% 2.44/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(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))))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(11131,plain,
% 2.44/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[11130, 11129])).
% 2.44/2.69 tff(11132,plain,
% 2.44/2.69 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[11131, 155, 1812, 11125, 11124])).
% 2.44/2.69 tff(11133,plain,
% 2.44/2.69 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1631, 11132, 1508])).
% 2.44/2.69 tff(11134,plain,
% 2.44/2.69 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(11135,plain,
% 2.44/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[11134])).
% 2.44/2.69 tff(11136,plain,
% 2.44/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[11135, 8194])).
% 2.44/2.69 tff(11137,plain,
% 2.44/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(11138,plain,
% 2.44/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[11137, 11136])).
% 2.44/2.69 tff(11139,plain,
% 2.44/2.69 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[11138, 155, 488, 823, 10905])).
% 2.44/2.69 tff(11140,plain,
% 2.44/2.69 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6254, 11139, 6243])).
% 2.44/2.69 tff(11141,plain,
% 2.44/2.69 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[10918, 155, 1528, 1523, 10905])).
% 2.44/2.69 tff(11142,plain,
% 2.44/2.69 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6313, 11141, 9196])).
% 2.44/2.69 tff(11143,plain,
% 2.44/2.69 (((~![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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(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(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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(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(s(elem!1))))), elem!1)))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(11144,plain,
% 2.44/2.69 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(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(s(elem!1))))), elem!1)))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(11145,plain,
% 2.44/2.69 (((~![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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(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(s(elem!1))))), elem!1))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[11144])).
% 2.44/2.69 tff(11146,plain,
% 2.44/2.69 (((~![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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(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(s(elem!1))))), elem!1)))),
% 2.44/2.69 inference(transitivity,[status(thm)],[11145, 11143])).
% 2.44/2.69 tff(11147,plain,
% 2.44/2.69 ((~![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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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)))))))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(11148,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[11147, 11146])).
% 2.44/2.69 tff(11149,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[11148, 97, 1545, 1633, 1458, 2392, 11142, 11140])).
% 2.44/2.69 tff(11150,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | (s(s(s(s(s(elem!1))))) = elem!1) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(11151,plain,
% 2.44/2.69 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[11150, 11100, 11133, 11116, 11115, 8167, 6300, 11110, 11108, 11098, 11092])).
% 2.44/2.69 tff(11152,plain,
% 2.44/2.69 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[11151, 6275])).
% 2.44/2.69 tff(11153,plain,
% 2.44/2.69 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6289, 11152, 7492])).
% 2.44/2.69 tff(11154,plain,
% 2.44/2.69 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[11153, 6272])).
% 2.44/2.69 tff(11155,plain,
% 2.44/2.69 ((~r(s(z), s(s(s(elem!1))))) <=> (~r(s(elem!1), s(s(s(elem!1)))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[8169])).
% 2.44/2.69 tff(11156,plain,
% 2.44/2.69 (~r(s(z), s(s(s(elem!1))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[924, 11108, 11110, 3442])).
% 2.44/2.69 tff(11157,plain,
% 2.44/2.69 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[11156, 11155])).
% 2.44/2.69 tff(11158,plain,
% 2.44/2.69 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[1411])).
% 2.44/2.69 tff(11159,plain,
% 2.44/2.69 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 2.44/2.69 inference(transitivity,[status(thm)],[11158, 592])).
% 2.44/2.69 tff(11160,plain,
% 2.44/2.69 ((s(s(s(elem!1))) = s(z)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.44/2.69 inference(symmetry,[status(thm)],[11159])).
% 2.44/2.69 tff(11161,plain,
% 2.44/2.69 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[11160])).
% 2.44/2.69 tff(11162,plain,
% 2.44/2.69 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[172, 11161])).
% 2.44/2.69 tff(11163,plain,
% 2.44/2.69 (((~![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)))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(11164,plain,
% 2.44/2.69 ((~![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)))))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(11165,plain,
% 2.44/2.69 ((~![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))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[11164, 11163])).
% 2.44/2.69 tff(11166,plain,
% 2.44/2.69 (b(s(elem!1), s(s(s(elem!1))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[11165, 53, 11162, 11157])).
% 2.44/2.69 tff(11167,plain,
% 2.44/2.69 (((~![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(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(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(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(11168,plain,
% 2.44/2.69 (((~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(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(s(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(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(11169,plain,
% 2.44/2.69 (((~![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(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(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[11168])).
% 2.44/2.69 tff(11170,plain,
% 2.44/2.69 (((~![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(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(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.44/2.70 inference(transitivity,[status(thm)],[11169, 11167])).
% 2.44/2.70 tff(11171,plain,
% 2.44/2.70 ((~![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(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(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.44/2.70 inference(quant_inst,[status(thm)],[])).
% 2.44/2.70 tff(11172,plain,
% 2.44/2.70 ((~![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(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(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.44/2.70 inference(modus_ponens,[status(thm)],[11171, 11170])).
% 2.44/2.70 tff(11173,plain,
% 2.44/2.70 ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[11172, 97, 1529, 11166])).
% 2.44/2.70 tff(11174,plain,
% 2.44/2.70 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[11173, 11154])).
% 2.44/2.70 tff(11175,plain,
% 2.44/2.70 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.44/2.70 inference(modus_ponens,[status(thm)],[11174, 6225])).
% 2.44/2.70 tff(11176,plain,
% 2.44/2.70 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[6239, 11175, 6223])).
% 2.44/2.70 tff(11177,plain,
% 2.44/2.70 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.44/2.70 inference(modus_ponens,[status(thm)],[11176, 6213])).
% 2.44/2.70 tff(11178,plain,
% 2.44/2.70 (((~![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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(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(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(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.44/2.70 inference(rewrite,[status(thm)],[])).
% 2.44/2.70 tff(11179,plain,
% 2.44/2.70 (((~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(elem!1))))) | (~b(s(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(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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(s(elem!1))))), s(s(s(elem!1))))))),
% 2.44/2.70 inference(rewrite,[status(thm)],[])).
% 2.44/2.70 tff(11180,plain,
% 2.44/2.70 (((~![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(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(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(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[11179])).
% 2.54/2.70 tff(11181,plain,
% 2.54/2.70 (((~![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(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(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(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.54/2.70 inference(transitivity,[status(thm)],[11180, 11178])).
% 2.54/2.70 tff(11182,plain,
% 2.54/2.70 ((~![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(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(11183,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[11182, 11181])).
% 2.54/2.70 tff(11184,plain,
% 2.54/2.70 ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11183, 97, 11100, 11133, 1529, 11106])).
% 2.54/2.70 tff(11185,plain,
% 2.54/2.70 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11184, 11154])).
% 2.54/2.70 tff(11186,plain,
% 2.54/2.70 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[6269, 11185, 8108])).
% 2.54/2.70 tff(11187,plain,
% 2.54/2.70 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[7529, 155, 1812, 8103, 11186])).
% 2.54/2.70 tff(11188,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11187, 11177])).
% 2.54/2.70 tff(11189,plain,((~b(s(s(s(s(elem!1)))), z)) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(elem!1), s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(11190,plain,
% 2.54/2.70 (~b(s(s(s(s(elem!1)))), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11189, 10731, 11087, 11091, 11090, 61, 10800, 2589])).
% 2.54/2.70 tff(11191,plain,
% 2.54/2.70 (r(s(s(s(s(elem!1)))), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[842, 11190])).
% 2.54/2.70 tff(11192,plain,
% 2.54/2.70 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[832, 11191, 10177, 10941])).
% 2.54/2.70 tff(11193,plain,
% 2.54/2.70 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[821, 11192, 10757])).
% 2.54/2.70 tff(11194,plain,
% 2.54/2.70 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.54/2.70 inference(transitivity,[status(thm)],[10898, 1505])).
% 2.54/2.70 tff(11195,plain,
% 2.54/2.70 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[11194])).
% 2.54/2.70 tff(11196,plain,
% 2.54/2.70 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[331, 11195])).
% 2.54/2.70 tff(11197,plain,
% 2.54/2.70 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[10893])).
% 2.54/2.70 tff(11198,plain,
% 2.54/2.70 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[43, 11197])).
% 2.54/2.70 tff(11199,plain,
% 2.54/2.70 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1586, 1545, 1528, 1523, 352, 1529, 1534])).
% 2.54/2.70 tff(11200,plain,
% 2.54/2.70 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[486, 11199, 472])).
% 2.54/2.70 tff(11201,plain,
% 2.54/2.70 (~r(z, s(s(s(s(elem!1)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1872, 11200, 288, 824])).
% 2.54/2.70 tff(11202,plain,
% 2.54/2.70 (elem!1 = z),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1888, 1534])).
% 2.54/2.70 tff(11203,assumption,(~(s(s(elem!1)) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.54/2.70 tff(11204,plain,
% 2.54/2.70 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[10812])).
% 2.54/2.70 tff(11205,plain,
% 2.54/2.70 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.70 inference(symmetry,[status(thm)],[11204])).
% 2.54/2.70 tff(11206,plain,
% 2.54/2.70 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[1545, 11205])).
% 2.54/2.70 tff(11207,plain,
% 2.54/2.70 ((s(s(z)) = elem!1) <=> (s(s(z)) = z)),
% 2.54/2.70 inference(monotonicity,[status(thm)],[1972])).
% 2.54/2.70 tff(11208,plain,
% 2.54/2.70 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 2.54/2.70 inference(symmetry,[status(thm)],[11207])).
% 2.54/2.70 tff(11209,plain,
% 2.54/2.70 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[11208])).
% 2.54/2.70 tff(11210,plain,
% 2.54/2.70 (~(s(s(z)) = elem!1)),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[76, 11209])).
% 2.54/2.70 tff(11211,plain,
% 2.54/2.70 (z = elem!1),
% 2.54/2.70 inference(symmetry,[status(thm)],[1972])).
% 2.54/2.70 tff(11212,plain,
% 2.54/2.70 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 2.54/2.70 inference(monotonicity,[status(thm)],[11211])).
% 2.54/2.70 tff(11213,plain,
% 2.54/2.70 ((~r(s(s(z)), z)) <=> (~r(s(s(z)), elem!1))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[11212])).
% 2.54/2.70 tff(11214,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 2.54/2.70 tff(11215,plain,
% 2.54/2.70 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.54/2.70 inference(symmetry,[status(thm)],[11214])).
% 2.54/2.70 tff(11216,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[352, 11215])).
% 2.54/2.70 tff(11217,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(11218,plain,
% 2.54/2.70 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11217, 352])).
% 2.54/2.70 tff(11219,plain,
% 2.54/2.70 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2431, 1545, 805, 2423])).
% 2.54/2.70 tff(11220,plain,
% 2.54/2.70 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[8079, 11219, 11218])).
% 2.54/2.70 tff(11221,plain,
% 2.54/2.70 (~r(s(s(z)), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[10818, 11220, 288, 570, 1972])).
% 2.54/2.70 tff(11222,plain,
% 2.54/2.70 (~r(s(s(z)), elem!1)),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[11221, 11213])).
% 2.54/2.70 tff(11223,plain,
% 2.54/2.70 (b(s(s(z)), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1563, 11222, 11210])).
% 2.54/2.70 tff(11224,plain,
% 2.54/2.70 (b(s(s(z)), z)),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[11223, 6814])).
% 2.54/2.70 tff(11225,plain,
% 2.54/2.70 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[1974])).
% 2.54/2.70 tff(11226,plain,
% 2.54/2.70 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[1972])).
% 2.54/2.70 tff(11227,plain,
% 2.54/2.70 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.54/2.70 inference(symmetry,[status(thm)],[11226])).
% 2.54/2.70 tff(11228,plain,
% 2.54/2.70 (r(elem!1, s(s(s(elem!1))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[570, 11227])).
% 2.54/2.70 tff(11229,plain,
% 2.54/2.70 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[10812])).
% 2.54/2.70 tff(11230,plain,
% 2.54/2.70 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.70 inference(symmetry,[status(thm)],[11229])).
% 2.54/2.70 tff(11231,plain,
% 2.54/2.70 (r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[4497, 11230])).
% 2.54/2.70 tff(11232,plain,
% 2.54/2.70 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[1974])).
% 2.54/2.70 tff(11233,plain,
% 2.54/2.70 (z = elem!1),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[1972, 1883])).
% 2.54/2.70 tff(11234,assumption,(~(z = elem!1)), introduced(assumption)).
% 2.54/2.70 tff(11235,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11234, 11233])).
% 2.54/2.70 tff(11236,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(11237,plain,
% 2.54/2.70 (z = elem!1),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11236, 1972])).
% 2.54/2.70 tff(11238,plain,
% 2.54/2.70 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 2.54/2.70 inference(monotonicity,[status(thm)],[1972])).
% 2.54/2.70 tff(11239,plain,
% 2.54/2.70 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 2.54/2.70 inference(symmetry,[status(thm)],[11238])).
% 2.54/2.70 tff(11240,plain,
% 2.54/2.70 (r(s(s(s(elem!1))), elem!1)),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[288, 11239])).
% 2.54/2.70 tff(11241,plain,
% 2.54/2.70 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[1537])).
% 2.54/2.70 tff(11242,plain,
% 2.54/2.70 (r(elem!1, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 2.54/2.70 inference(symmetry,[status(thm)],[11241])).
% 2.54/2.70 tff(11243,plain,
% 2.54/2.70 (r(z, s(s(z))) <=> r(elem!1, s(s(z)))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[1534])).
% 2.54/2.70 tff(11244,plain,
% 2.54/2.70 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[1534])).
% 2.54/2.70 tff(11245,plain,
% 2.54/2.70 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 2.54/2.70 inference(symmetry,[status(thm)],[11244])).
% 2.54/2.70 tff(11246,plain,
% 2.54/2.70 ((~b(elem!1, s(s(z)))) <=> (~b(z, s(s(z))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[11245])).
% 2.54/2.70 tff(11247,plain,
% 2.54/2.70 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1572, 6302])).
% 2.54/2.70 tff(11248,plain,
% 2.54/2.70 ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1576, 53, 11247])).
% 2.54/2.70 tff(11249,plain,
% 2.54/2.70 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11248, 1533])).
% 2.54/2.70 tff(11250,plain,
% 2.54/2.70 (~b(elem!1, s(s(z)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2401, 11249, 1545, 2392, 1534])).
% 2.54/2.70 tff(11251,plain,
% 2.54/2.70 (~b(z, s(s(z)))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[11250, 11246])).
% 2.54/2.70 tff(11252,plain,
% 2.54/2.70 (r(z, s(s(z)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[222, 11251])).
% 2.54/2.70 tff(11253,plain,
% 2.54/2.70 (r(elem!1, s(s(z)))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[11252, 11243])).
% 2.54/2.70 tff(11254,plain,
% 2.54/2.70 (r(elem!1, s(s(elem!1)))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[11253, 11242])).
% 2.54/2.70 tff(11255,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(11256,plain,
% 2.54/2.70 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(11257,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[11256])).
% 2.54/2.70 tff(11258,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.54/2.70 inference(transitivity,[status(thm)],[11257, 11255])).
% 2.54/2.70 tff(11259,plain,
% 2.54/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(11260,plain,
% 2.54/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[11259, 11258])).
% 2.54/2.70 tff(11261,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11260, 155, 4497, 1528, 6302, 11254])).
% 2.54/2.70 tff(11262,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(11263,plain,
% 2.54/2.70 (~r(s(s(elem!1)), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11262, 4497, 11237, 1523, 11240, 2392, 352, 1545])).
% 2.54/2.70 tff(11264,plain,
% 2.54/2.70 (r(s(s(elem!1)), elem!1)),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[6845, 1539])).
% 2.54/2.70 tff(11265,assumption,(~r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 2.54/2.70 tff(11266,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11265, 11264])).
% 2.54/2.70 tff(11267,plain,((~r(s(s(z)), elem!1)) | r(s(s(elem!1)), elem!1) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(11268,plain,
% 2.54/2.70 (~r(s(s(z)), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11267, 11263, 11237])).
% 2.54/2.70 tff(11269,plain,
% 2.54/2.70 (b(s(s(z)), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1563, 11268, 11210])).
% 2.54/2.70 tff(11270,plain,
% 2.54/2.70 (b(s(s(elem!1)), elem!1)),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[11269, 6815])).
% 2.54/2.70 tff(11271,plain,
% 2.54/2.70 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[7800, 11270, 2392, 1545])).
% 2.54/2.70 tff(11272,plain,
% 2.54/2.70 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1631, 11271, 11203])).
% 2.54/2.70 tff(11273,plain,
% 2.54/2.70 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[11272, 11232])).
% 2.54/2.70 tff(11274,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(11275,plain,
% 2.54/2.70 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(11276,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[11275])).
% 2.54/2.70 tff(11277,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.54/2.70 inference(transitivity,[status(thm)],[11276, 11274])).
% 2.54/2.70 tff(11278,plain,
% 2.54/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(11279,plain,
% 2.54/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[11278, 11277])).
% 2.54/2.70 tff(11280,plain,
% 2.54/2.70 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11279, 155, 488, 11273, 288, 824])).
% 2.54/2.70 tff(11281,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11280, 11231])).
% 2.54/2.70 tff(11282,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(elem!1 = z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (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)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(11283,plain,
% 2.54/2.70 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11282, 1545, 488, 288, 824, 11203, 2392, 1972, 11228, 352])).
% 2.54/2.70 tff(11284,plain,
% 2.54/2.70 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(11285,plain,
% 2.54/2.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(11286,plain,
% 2.54/2.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[11285, 11284])).
% 2.54/2.70 tff(11287,plain,
% 2.54/2.70 ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11286, 53])).
% 2.54/2.70 tff(11288,plain,
% 2.54/2.70 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11287, 11283, 352])).
% 2.54/2.70 tff(11289,plain,
% 2.54/2.70 (b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[11288, 11225])).
% 2.54/2.70 tff(11290,plain,
% 2.54/2.70 (((~![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)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(11291,plain,
% 2.54/2.70 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(11292,plain,
% 2.54/2.70 (((~![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)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[11291])).
% 2.54/2.70 tff(11293,plain,
% 2.54/2.70 (((~![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)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.54/2.70 inference(transitivity,[status(thm)],[11292, 11290])).
% 2.54/2.70 tff(11294,plain,
% 2.54/2.70 ((~![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)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(11295,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[11294, 11293])).
% 2.54/2.70 tff(11296,plain,
% 2.54/2.70 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11295, 97, 805, 11289, 11224])).
% 2.54/2.70 tff(11297,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11296, 11206])).
% 2.54/2.70 tff(11298,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~(elem!1 = z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (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(s(elem!1)))), z)) | (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(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(11299,plain,
% 2.54/2.70 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11298, 11200, 570, 288, 2423, 352, 824, 1545, 11203, 805, 11202])).
% 2.54/2.70 tff(11300,plain,
% 2.54/2.70 (~b(z, s(s(s(s(elem!1)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2407, 11299, 11202])).
% 2.54/2.70 tff(11301,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1093, 11300, 11201])).
% 2.54/2.70 tff(11302,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(11303,plain,
% 2.54/2.71 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[11302, 10941, 11191, 10177, 10773, 11198, 11196, 11193, 10939, 10781, 10759, 11090, 10740])).
% 2.54/2.71 tff(11304,plain,
% 2.54/2.71 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1484, 11303, 10900])).
% 2.54/2.71 tff(11305,plain,
% 2.54/2.71 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1816, 11304, 10800, 10731, 11087])).
% 2.54/2.71 tff(11306,plain,
% 2.54/2.71 (b(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[511, 11305])).
% 2.54/2.71 tff(11307,plain,
% 2.54/2.71 (~b(z, s(s(s(s(elem!1)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[558, 11306, 2589, 61])).
% 2.54/2.71 tff(11308,plain,
% 2.54/2.71 (r(z, s(s(s(s(elem!1)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1093, 11307])).
% 2.54/2.71 tff(11309,plain,
% 2.54/2.71 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1872, 11308, 10941, 11191])).
% 2.54/2.71 tff(11310,plain,
% 2.54/2.71 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[486, 11309, 10939])).
% 2.54/2.71 tff(11311,plain,
% 2.54/2.71 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[10862, 11193, 10745])).
% 2.54/2.71 tff(11312,plain,
% 2.54/2.71 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[10998, 11306, 10786, 11311])).
% 2.54/2.71 tff(11313,plain,
% 2.54/2.71 (r(s(z), s(s(s(s(elem!1)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[280, 11312])).
% 2.54/2.71 tff(11314,plain,
% 2.54/2.71 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[4669, 11313, 10731, 10800, 11304])).
% 2.54/2.71 tff(11315,plain,
% 2.54/2.71 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1631, 11314, 11196])).
% 2.54/2.71 tff(11316,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1641, 11315, 11310, 11090, 11306])).
% 2.54/2.71 tff(11317,plain,((~r(s(z), s(s(z)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(11318,plain,
% 2.54/2.71 (~r(s(z), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[11317, 61])).
% 2.54/2.71 tff(11319,plain,
% 2.54/2.71 (b(s(z), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[548, 11318])).
% 2.54/2.71 tff(11320,plain,
% 2.54/2.71 (((~![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(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), 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(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(11321,plain,
% 2.54/2.71 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~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(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(11322,plain,
% 2.54/2.71 (((~![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(z)))) | (~b(s(z), s(s(z)))) | (~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(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[11321])).
% 2.54/2.71 tff(11323,plain,
% 2.54/2.71 (((~![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(z)))) | (~b(s(z), s(s(z)))) | (~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(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[11322, 11320])).
% 2.54/2.71 tff(11324,plain,
% 2.54/2.71 ((~![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(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(11325,plain,
% 2.54/2.71 ((~![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(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[11324, 11323])).
% 2.54/2.71 tff(11326,plain,
% 2.54/2.71 (~b(s(s(s(elem!1))), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[11325, 97, 10119, 61, 11319])).
% 2.54/2.71 tff(11327,plain,
% 2.54/2.71 (r(s(s(s(elem!1))), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[246, 11326])).
% 2.54/2.71 tff(11328,plain,
% 2.54/2.71 (~b(z, s(s(s(elem!1))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1147, 11319, 61, 10119])).
% 2.54/2.71 tff(11329,plain,
% 2.54/2.71 (r(z, s(s(s(elem!1))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[590, 11328])).
% 2.54/2.71 tff(11330,plain,
% 2.54/2.71 (~r(s(z), s(s(s(elem!1))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1423, 155, 11329, 81, 11327])).
% 2.54/2.71 tff(11331,plain,
% 2.54/2.71 (b(s(z), s(s(s(elem!1))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[181, 11330])).
% 2.54/2.71 tff(11332,plain,
% 2.54/2.71 (((~![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(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(11333,plain,
% 2.54/2.71 (((~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(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(11334,plain,
% 2.54/2.71 (((~![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(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(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[11333])).
% 2.54/2.71 tff(11335,plain,
% 2.54/2.71 (((~![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(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(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[11334, 11332])).
% 2.54/2.71 tff(11336,plain,
% 2.54/2.71 ((~![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(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)))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(11337,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[11336, 11335])).
% 2.54/2.71 tff(11338,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[11337, 97, 1139, 193, 535, 127])).
% 2.54/2.71 tff(11339,plain,((~b(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(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(11340,plain,
% 2.54/2.71 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[11339, 11331, 10119, 11319])).
% 2.54/2.71 tff(11341,plain,
% 2.54/2.71 (r(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[143, 11340])).
% 2.54/2.71 tff(11342,plain,
% 2.54/2.71 (~b(s(s(z)), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2651, 87, 11319, 61])).
% 2.54/2.71 tff(11343,plain,
% 2.54/2.71 (r(s(s(z)), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[625, 11342])).
% 2.54/2.71 tff(11344,plain,
% 2.54/2.71 (~b(z, s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[8695, 87, 11319, 61])).
% 2.54/2.71 tff(11345,plain,
% 2.54/2.71 (r(z, s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[222, 11344])).
% 2.54/2.71 tff(11346,plain,
% 2.54/2.71 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2671, 11345, 11327, 11343])).
% 2.54/2.71 tff(11347,plain,
% 2.54/2.71 (b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[58, 11346])).
% 2.54/2.71 tff(11348,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[5103, 97, 10119, 193, 11347, 87])).
% 2.54/2.71 tff(11349,plain,((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(11350,plain,
% 2.54/2.71 (~b(s(s(z)), s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[11349, 11331, 61])).
% 2.54/2.71 tff(11351,plain,
% 2.54/2.71 (r(s(s(z)), s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[122, 11350])).
% 2.54/2.71 tff(11352,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(11353,plain,
% 2.54/2.71 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(11354,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[11353])).
% 2.54/2.71 tff(11355,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[11354, 11352])).
% 2.54/2.71 tff(11356,plain,
% 2.54/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(11357,plain,
% 2.54/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[11356, 11355])).
% 2.54/2.71 tff(11358,plain,
% 2.54/2.71 (~r(s(s(z)), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[11357, 155, 11329, 81, 11351, 11341])).
% 2.54/2.71 tff(11359,plain,
% 2.54/2.71 (b(s(s(z)), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[625, 11358])).
% 2.54/2.71 tff(11360,plain,
% 2.54/2.71 (~b(z, s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2962, 11359, 61, 11319])).
% 2.54/2.71 tff(11361,plain,
% 2.54/2.71 (r(z, s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[222, 11360])).
% 2.54/2.71 tff(11362,plain,
% 2.54/2.71 (~r(z, s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[5949, 1960, 11341, 11329, 11361])).
% 2.54/2.71 tff(11363,plain,
% 2.54/2.71 (b(z, s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1318, 11362])).
% 2.54/2.71 tff(11364,plain,
% 2.54/2.71 (~r(s(s(s(z))), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2035, 11363, 61, 81, 1960, 11331, 11359])).
% 2.54/2.71 tff(11365,plain,
% 2.54/2.71 (b(s(s(s(z))), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[402, 11364])).
% 2.54/2.71 tff(11366,plain,
% 2.54/2.71 (~b(s(s(s(z))), s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[9723, 11365, 11319, 61])).
% 2.54/2.71 tff(11367,plain,
% 2.54/2.71 (r(s(s(s(z))), s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1358, 11366])).
% 2.54/2.71 tff(11368,plain,
% 2.54/2.71 (~b(s(z), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2615, 11365, 61, 11363])).
% 2.54/2.71 tff(11369,plain,
% 2.54/2.71 (r(s(z), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[253, 11368])).
% 2.54/2.71 tff(11370,plain,
% 2.54/2.71 (~r(s(s(z)), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2940, 11369, 11351, 11367])).
% 2.54/2.71 tff(11371,plain,
% 2.54/2.71 (b(s(s(z)), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[437, 11370])).
% 2.54/2.71 tff(11372,plain,
% 2.54/2.71 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), 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(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(11373,plain,
% 2.54/2.71 (((~![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(s(z))), z)) | (~b(s(s(s(z))), 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(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[11372])).
% 2.54/2.71 tff(11374,plain,
% 2.54/2.71 (((~![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(s(z))), z)) | (~b(s(s(s(z))), 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(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.54/2.71 inference(transitivity,[status(thm)],[11373, 9404])).
% 2.54/2.71 tff(11375,plain,
% 2.54/2.71 ((~![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(s(z))), z)) | (~b(s(s(s(z))), 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)))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(11376,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[11375, 11374])).
% 2.54/2.71 tff(11377,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[11376, 97, 11359, 11371, 11363, 11365])).
% 2.54/2.71 tff(11378,plain,((~r(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(11379,plain,
% 2.54/2.71 (~r(s(s(s(z))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[11378, 81, 61])).
% 2.54/2.71 tff(11380,plain,
% 2.54/2.71 (b(s(s(s(z))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[421, 11379])).
% 2.54/2.71 tff(11381,plain,
% 2.54/2.71 (~b(s(z), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[9363, 97, 11359, 11319, 11380])).
% 2.54/2.71 tff(11382,plain,
% 2.54/2.71 (r(s(z), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[253, 11381])).
% 2.54/2.71 tff(11383,plain,
% 2.54/2.71 (~b(s(s(s(z))), s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[8531, 11380, 61, 11319])).
% 2.54/2.71 tff(11384,plain,
% 2.54/2.71 (r(s(s(s(z))), s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1358, 11383])).
% 2.54/2.71 tff(11385,plain,
% 2.54/2.71 (~r(s(s(z)), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2940, 11382, 11351, 11384])).
% 2.54/2.71 tff(11386,plain,
% 2.54/2.71 (b(s(s(z)), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[437, 11385])).
% 2.54/2.71 tff(11387,plain,
% 2.54/2.71 (((~![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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(11388,plain,
% 2.54/2.71 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(11389,plain,
% 2.54/2.71 (((~![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(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(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(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[11388])).
% 2.54/2.71 tff(11390,plain,
% 2.54/2.71 (((~![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(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(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(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[11389, 11387])).
% 2.54/2.71 tff(11391,plain,
% 2.54/2.71 ((~![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(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(11392,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[11391, 11390])).
% 2.54/2.71 tff(11393,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[11392, 97, 61, 83, 11319, 1361, 1331, 1330])).
% 2.54/2.71 tff(11394,plain,((~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(11395,plain,
% 2.54/2.71 (~b(z, s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[11394, 11359, 61, 11386, 11380])).
% 2.54/2.71 tff(11396,plain,
% 2.54/2.71 (r(z, s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1318, 11395])).
% 2.54/2.71 tff(11397,plain,
% 2.54/2.71 (~r(s(s(s(z))), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1308, 11396, 81, 11382])).
% 2.54/2.71 tff(11398,plain,
% 2.54/2.71 (b(s(s(s(z))), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[402, 11397])).
% 2.54/2.71 tff(11399,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[409, 97, 61, 11359, 11380, 11398])).
% 2.54/2.71 tff(11400,plain,((~r(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(11401,plain,
% 2.54/2.71 (~r(s(z), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[11400, 61])).
% 2.54/2.71 tff(11402,plain,
% 2.54/2.71 (b(s(z), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[568, 11401])).
% 2.54/2.71 tff(11403,plain,
% 2.54/2.71 (~b(s(s(z)), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[8535, 11402, 61, 11319])).
% 2.54/2.71 tff(11404,plain,
% 2.54/2.71 (r(s(s(z)), z)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[625, 11403])).
% 2.54/2.71 tff(11405,plain,
% 2.54/2.71 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[735, 155, 11329, 11327, 11404])).
% 2.54/2.71 tff(11406,plain,
% 2.54/2.71 (b(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[143, 11405])).
% 2.54/2.71 tff(11407,plain,
% 2.54/2.71 (~b(z, s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2661, 11406, 61, 11319])).
% 2.54/2.71 tff(11408,plain,
% 2.54/2.71 (r(z, s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[222, 11407])).
% 2.54/2.71 tff(11409,plain,
% 2.54/2.71 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2671, 11408, 11327, 11404])).
% 2.54/2.71 tff(11410,plain,
% 2.54/2.71 (b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[58, 11409])).
% 2.54/2.71 tff(11411,plain,
% 2.54/2.71 (((~![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(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(11412,plain,
% 2.54/2.71 (((~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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(11413,plain,
% 2.54/2.72 (((~![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(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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[11412])).
% 2.54/2.72 tff(11414,plain,
% 2.54/2.72 (((~![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(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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[11413, 11411])).
% 2.54/2.72 tff(11415,plain,
% 2.54/2.72 ((~![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(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))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(11416,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[11415, 11414])).
% 2.54/2.72 tff(11417,plain,
% 2.54/2.72 ($false),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[11416, 97, 10119, 11410, 11319, 11406])).
% 2.54/2.72 tff(11418,plain,(~b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.72 tff(11419,plain,
% 2.54/2.72 (r(z, s(z))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[723, 11418])).
% 2.54/2.72 tff(11420,plain,
% 2.54/2.72 (((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(11421,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[11420])).
% 2.54/2.72 tff(11422,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[11421, 866])).
% 2.54/2.72 tff(11423,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(11424,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[11423, 11422])).
% 2.54/2.72 tff(11425,plain,
% 2.54/2.72 ($false),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[11424, 155, 729, 226, 2, 3])).
% 2.54/2.72 tff(11426,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.72 tff(11427,plain,
% 2.54/2.72 ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[11426, 11419])).
% 2.54/2.72 tff(11428,plain,
% 2.54/2.72 (~r(z, s(s(z)))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[11427, 3, 2])).
% 2.54/2.72 tff(11429,plain,
% 2.54/2.72 (b(z, s(s(z)))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[222, 11428])).
% 2.54/2.72 tff(11430,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(11431,plain,
% 2.54/2.72 (((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(11432,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[11431])).
% 2.54/2.72 tff(11433,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[11432, 11430])).
% 2.54/2.72 tff(11434,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(11435,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[11434, 11433])).
% 2.54/2.72 tff(11436,plain,
% 2.54/2.72 ($false),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[11435, 155, 11419, 288, 645, 2, 224])).
% 2.54/2.72 tff(11437,plain,((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.72 tff(11438,plain,
% 2.54/2.72 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[11437, 645, 2, 288])).
% 2.54/2.72 tff(11439,plain,
% 2.54/2.72 (b(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[143, 11438])).
% 2.54/2.72 tff(11440,plain,
% 2.54/2.72 (~r(s(z), s(s(z)))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[11427, 226, 2])).
% 2.54/2.72 tff(11441,plain,
% 2.54/2.72 (b(s(z), s(s(z)))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[548, 11440])).
% 2.54/2.72 tff(11442,plain,
% 2.54/2.72 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[2671, 645, 288, 226])).
% 2.54/2.72 tff(11443,plain,
% 2.54/2.72 (b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[58, 11442])).
% 2.54/2.72 tff(11444,plain,
% 2.54/2.72 ($false),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[11416, 97, 1139, 11443, 11441, 11439])).
% 2.54/2.72 tff(11445,plain,((~r(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.72 tff(11446,plain,
% 2.54/2.72 (~r(s(s(z)), z)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[11445, 1139, 2, 2596, 226])).
% 2.54/2.72 tff(11447,plain,
% 2.54/2.72 (b(s(s(z)), z)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[625, 11446])).
% 2.54/2.72 tff(11448,plain,
% 2.54/2.72 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[11339, 193, 1139, 535])).
% 2.54/2.72 tff(11449,plain,
% 2.54/2.72 (r(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[143, 11448])).
% 2.54/2.72 tff(11450,plain,
% 2.54/2.72 (~r(s(s(s(z))), s(s(z)))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[5949, 1300, 570, 11449, 226])).
% 2.54/2.72 tff(11451,plain,
% 2.54/2.72 (b(s(s(s(z))), s(s(z)))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[421, 11450])).
% 2.54/2.72 tff(11452,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(11453,plain,
% 2.54/2.72 (((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(11454,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[11453])).
% 2.54/2.72 tff(11455,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[11454, 11452])).
% 2.54/2.72 tff(11456,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(11457,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[11456, 11455])).
% 2.54/2.72 tff(11458,plain,
% 2.54/2.72 ($false),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[11457, 155, 729, 226, 1300, 1961, 2597])).
% 2.54/2.72 tff(11459,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.72 tff(11460,plain,
% 2.54/2.72 ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[11459, 11419])).
% 2.54/2.72 tff(11461,plain,
% 2.54/2.72 (~r(s(s(z)), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[11460, 2597, 1300, 226])).
% 2.54/2.72 tff(11462,plain,
% 2.54/2.72 (b(s(s(z)), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[437, 11461])).
% 2.54/2.72 tff(11463,plain,
% 2.54/2.72 (~b(s(z), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[8804, 11462, 535, 1331])).
% 2.54/2.72 tff(11464,plain,
% 2.54/2.72 (r(s(z), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[253, 11463])).
% 2.54/2.72 tff(11465,plain,
% 2.54/2.72 (((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(11466,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[11465])).
% 2.54/2.72 tff(11467,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[11466, 5904])).
% 2.54/2.72 tff(11468,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(11469,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[11468, 11467])).
% 2.54/2.72 tff(11470,plain,
% 2.54/2.72 ($false),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[11469, 155, 11419, 1300, 11464, 2597])).
% 2.54/2.72 tff(11471,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.72 tff(11472,plain,
% 2.54/2.72 (~r(s(s(s(z))), s(z))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[11471, 1300, 535, 11451, 226])).
% 2.54/2.72 tff(11473,plain,
% 2.54/2.72 (b(s(s(s(z))), s(z))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[1358, 11472])).
% 2.54/2.72 tff(11474,plain,
% 2.54/2.72 (((~![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(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(11475,plain,
% 2.54/2.72 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(11476,plain,
% 2.54/2.72 (((~![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(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[11475])).
% 2.54/2.72 tff(11477,plain,
% 2.54/2.72 (((~![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(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[11476, 11474])).
% 2.54/2.72 tff(11478,plain,
% 2.54/2.72 ((~![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(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(11479,plain,
% 2.54/2.72 ((~![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(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[11478, 11477])).
% 2.54/2.72 tff(11480,plain,
% 2.54/2.72 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[11479, 97, 1139, 535, 1360])).
% 2.54/2.72 tff(11481,plain,
% 2.54/2.72 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[3089, 11480, 1])).
% 2.54/2.72 tff(11482,plain,
% 2.54/2.72 (((~![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(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(11483,plain,
% 2.54/2.72 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(11484,plain,
% 2.54/2.72 (((~![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(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[11483])).
% 2.54/2.72 tff(11485,plain,
% 2.54/2.72 (((~![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(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[11484, 11482])).
% 2.54/2.72 tff(11486,plain,
% 2.54/2.72 ((~![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(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(11487,plain,
% 2.54/2.72 ((~![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(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[11486, 11485])).
% 2.54/2.72 tff(11488,plain,
% 2.54/2.72 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[11487, 97, 1139, 535, 1360])).
% 2.54/2.72 tff(11489,plain,
% 2.54/2.72 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[2687, 11488, 4228])).
% 2.54/2.72 tff(11490,plain,
% 2.54/2.72 (~b(s(s(z)), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[3585, 535, 1360, 1331])).
% 2.54/2.73 tff(11491,plain,
% 2.54/2.73 (r(s(s(z)), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[437, 11490])).
% 2.54/2.73 tff(11492,plain,
% 2.54/2.73 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[5749, 155, 11491, 11489, 11481])).
% 2.54/2.73 tff(11493,plain,
% 2.54/2.73 (b(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[143, 11492])).
% 2.54/2.73 tff(11494,plain,
% 2.54/2.73 (((~![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), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(11495,plain,
% 2.54/2.73 (((~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(z))), s(s(z)))) | (~b(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(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(11496,plain,
% 2.54/2.73 (((~![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(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[11495])).
% 2.54/2.73 tff(11497,plain,
% 2.54/2.73 (((~![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(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.54/2.73 inference(transitivity,[status(thm)],[11496, 11494])).
% 2.54/2.73 tff(11498,plain,
% 2.54/2.73 ((~![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(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~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))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(11499,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[11498, 11497])).
% 2.54/2.73 tff(11500,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11499, 97, 535, 1360, 1331, 11493])).
% 2.54/2.73 tff(11501,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(11502,plain,
% 2.54/2.73 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11501, 11473, 535, 11451, 1139])).
% 2.54/2.73 tff(11503,plain,
% 2.54/2.73 (~b(s(s(s(z))), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[9913, 11502, 239])).
% 2.54/2.73 tff(11504,plain,
% 2.54/2.73 (~b(s(s(s(z))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8529, 97, 83, 535, 1331])).
% 2.54/2.73 tff(11505,plain,
% 2.54/2.73 (r(s(s(s(z))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1358, 11504])).
% 2.54/2.73 tff(11506,plain,
% 2.54/2.73 (~b(s(z), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[9363, 97, 83, 535, 1331])).
% 2.54/2.73 tff(11507,plain,
% 2.54/2.73 (r(s(z), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[253, 11506])).
% 2.54/2.73 tff(11508,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11469, 155, 11419, 1300, 11507, 11505])).
% 2.54/2.73 tff(11509,plain,((~b(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(11510,plain,
% 2.54/2.73 (~b(s(s(z)), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11509, 1300, 535, 11451])).
% 2.54/2.73 tff(11511,plain,
% 2.54/2.73 (r(s(s(z)), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[625, 11510])).
% 2.54/2.73 tff(11512,plain,
% 2.54/2.73 (r(z, s(s(s(z))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[570, 1958])).
% 2.54/2.73 tff(11513,plain,
% 2.54/2.73 (~r(s(s(z)), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[6410, 11512, 645, 386])).
% 2.54/2.73 tff(11514,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[437, 9781, 11513])).
% 2.54/2.73 tff(11515,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(11516,plain,
% 2.54/2.73 (~r(s(s(s(z))), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11515, 11502, 535, 11451, 193, 11511, 570])).
% 2.54/2.73 tff(11517,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[402, 11516, 11503])).
% 2.54/2.73 tff(11518,plain,((~r(z, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), z) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(11519,plain,
% 2.54/2.73 (~r(z, s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11518, 193, 11441, 570, 239, 1139, 226])).
% 2.54/2.73 tff(11520,plain,
% 2.54/2.73 (b(z, s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1318, 11519])).
% 2.54/2.73 tff(11521,plain,
% 2.54/2.73 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11339, 193, 1139, 11441])).
% 2.54/2.73 tff(11522,plain,
% 2.54/2.73 (r(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[143, 11521])).
% 2.54/2.73 tff(11523,plain,
% 2.54/2.73 (~r(s(s(z)), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11437, 11522, 2, 2596])).
% 2.54/2.73 tff(11524,plain,
% 2.54/2.73 (b(s(s(z)), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[625, 11523])).
% 2.54/2.73 tff(11525,plain,
% 2.54/2.73 (~b(s(z), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[2972, 11524, 11441, 11520])).
% 2.54/2.73 tff(11526,plain,
% 2.54/2.73 (r(s(z), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[568, 11525])).
% 2.54/2.73 tff(11527,plain,
% 2.54/2.73 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[6374, 11519, 570])).
% 2.54/2.73 tff(11528,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[2466, 8026])).
% 2.54/2.73 tff(11529,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(11530,plain,
% 2.54/2.73 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11529, 11527])).
% 2.54/2.73 tff(11531,plain,
% 2.54/2.73 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1674, 155, 570, 288, 386])).
% 2.54/2.73 tff(11532,plain,
% 2.54/2.73 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[3089, 11531, 1])).
% 2.54/2.73 tff(11533,plain,
% 2.54/2.73 (~r(s(s(s(z))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[4334, 155, 11419, 81, 386])).
% 2.54/2.73 tff(11534,plain,
% 2.54/2.73 (b(s(s(s(z))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1358, 11533])).
% 2.54/2.73 tff(11535,plain,
% 2.54/2.73 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), 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))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(11536,plain,
% 2.54/2.73 (((~![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), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[11535])).
% 2.54/2.73 tff(11537,plain,
% 2.54/2.73 (((~![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), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.54/2.73 inference(transitivity,[status(thm)],[11536, 5384])).
% 2.54/2.73 tff(11538,plain,
% 2.54/2.73 ((~![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), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(11539,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[11538, 11537])).
% 2.54/2.73 tff(11540,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11539, 97, 1139, 193, 11534, 11532])).
% 2.54/2.73 tff(11541,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(11542,plain,
% 2.54/2.73 (~r(s(s(s(z))), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11541, 193, 1139, 11530, 570, 2596, 11526])).
% 2.54/2.73 tff(11543,plain,
% 2.54/2.73 (b(s(s(s(z))), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[402, 11542])).
% 2.54/2.73 tff(11544,plain,
% 2.54/2.73 (~b(s(s(z)), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[9409, 97, 83, 1330, 1216])).
% 2.54/2.73 tff(11545,plain,
% 2.54/2.73 (r(s(s(z)), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[437, 11544])).
% 2.54/2.73 tff(11546,plain,
% 2.54/2.73 (((~![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(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(11547,plain,
% 2.54/2.73 (((~b(z, s(s(s(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(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(11548,plain,
% 2.54/2.73 (((~![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(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), 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(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[11547])).
% 2.54/2.73 tff(11549,plain,
% 2.54/2.73 (((~![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(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), 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(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.54/2.73 inference(transitivity,[status(thm)],[11548, 11546])).
% 2.54/2.73 tff(11550,plain,
% 2.54/2.73 ((~![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(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(11551,plain,
% 2.54/2.73 ((~![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(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[11550, 11549])).
% 2.54/2.73 tff(11552,plain,
% 2.54/2.73 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11551, 97, 876, 1330, 1216])).
% 2.54/2.73 tff(11553,plain,
% 2.54/2.73 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[2747, 11552])).
% 2.54/2.73 tff(11554,plain,
% 2.54/2.73 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[5010, 97, 83, 876, 1330])).
% 2.54/2.73 tff(11555,plain,
% 2.54/2.73 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[452, 11554])).
% 2.54/2.73 tff(11556,plain,
% 2.54/2.73 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~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))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(11557,plain,
% 2.54/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[11556])).
% 2.54/2.73 tff(11558,plain,
% 2.54/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.73 inference(transitivity,[status(thm)],[11557, 454])).
% 2.54/2.73 tff(11559,plain,
% 2.54/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~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)))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(11560,plain,
% 2.54/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[11559, 11558])).
% 2.54/2.73 tff(11561,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11560, 155, 11555, 11553, 11545, 1960])).
% 2.54/2.73 tff(11562,plain,((~b(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(11563,plain,
% 2.54/2.73 (~b(s(s(s(s(elem!1)))), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11562, 83, 1330, 1216, 1960])).
% 2.54/2.73 tff(11564,plain,
% 2.54/2.73 (r(s(s(s(s(elem!1)))), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[842, 11563])).
% 2.54/2.73 tff(11565,plain,
% 2.54/2.73 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[832, 11564, 570, 288])).
% 2.54/2.73 tff(11566,plain,
% 2.54/2.73 (~b(s(z), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[2972, 83, 11441, 1330])).
% 2.54/2.73 tff(11567,plain,
% 2.54/2.73 (r(s(z), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[568, 11566])).
% 2.54/2.73 tff(11568,plain,
% 2.54/2.73 ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[4414, 11419])).
% 2.54/2.73 tff(11569,plain,
% 2.54/2.73 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11568, 11564, 11567])).
% 2.54/2.73 tff(11570,plain,
% 2.54/2.73 (b(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[511, 11569])).
% 2.54/2.73 tff(11571,plain,
% 2.54/2.73 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1804, 11570, 1139, 193])).
% 2.54/2.73 tff(11572,plain,
% 2.54/2.73 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[821, 11571, 11565])).
% 2.54/2.73 tff(11573,plain,
% 2.54/2.73 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[523, 11572])).
% 2.54/2.73 tff(11574,plain,
% 2.54/2.73 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[349, 11573])).
% 2.54/2.73 tff(11575,plain,
% 2.54/2.73 (s(s(s(s(elem!1)))) = elem!1),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1734, 11574])).
% 2.54/2.73 tff(11576,plain,
% 2.54/2.73 (elem!1 = s(s(s(s(elem!1))))),
% 2.54/2.73 inference(symmetry,[status(thm)],[11575])).
% 2.54/2.73 tff(11577,plain,
% 2.54/2.73 (r(z, elem!1) <=> r(z, s(s(s(s(elem!1)))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[11576])).
% 2.54/2.73 tff(11578,plain,
% 2.54/2.73 (r(z, s(s(s(s(elem!1))))) <=> r(z, elem!1)),
% 2.54/2.73 inference(symmetry,[status(thm)],[11577])).
% 2.54/2.73 tff(11579,plain,
% 2.54/2.73 (r(z, s(s(s(s(elem!1)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[4141, 11573, 570])).
% 2.54/2.73 tff(11580,plain,
% 2.54/2.73 (r(z, elem!1)),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[11579, 11578])).
% 2.54/2.73 tff(11581,plain,
% 2.54/2.73 (r(elem!1, s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[11576])).
% 2.54/2.73 tff(11582,plain,
% 2.54/2.73 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 2.54/2.73 inference(symmetry,[status(thm)],[11581])).
% 2.54/2.73 tff(11583,plain,
% 2.54/2.73 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[11573])).
% 2.54/2.73 tff(11584,plain,
% 2.54/2.73 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11568, 824, 81])).
% 2.54/2.73 tff(11585,plain,
% 2.54/2.73 (b(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[511, 11584])).
% 2.54/2.73 tff(11586,plain,
% 2.54/2.73 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1804, 11585, 1139, 193])).
% 2.54/2.73 tff(11587,plain,
% 2.54/2.73 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[821, 11586, 4082])).
% 2.54/2.73 tff(11588,plain,
% 2.54/2.73 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[523, 11587])).
% 2.54/2.73 tff(11589,plain,
% 2.54/2.73 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[3169, 11588, 4])).
% 2.54/2.73 tff(11590,plain,
% 2.54/2.73 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[452, 11589])).
% 2.54/2.73 tff(11591,plain,
% 2.54/2.73 (((~![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), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(11592,plain,
% 2.54/2.73 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(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(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(11593,plain,
% 2.54/2.73 (((~![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)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[11592])).
% 2.54/2.73 tff(11594,plain,
% 2.54/2.73 (((~![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)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.54/2.73 inference(transitivity,[status(thm)],[11593, 11591])).
% 2.54/2.73 tff(11595,plain,
% 2.54/2.73 ((~![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)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(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(z))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(11596,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[11595, 11594])).
% 2.54/2.73 tff(11597,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11596, 97, 83, 11585, 11590, 535])).
% 2.54/2.73 tff(11598,plain,((~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | r(s(s(s(elem!1))), s(s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(11599,plain,
% 2.54/2.73 (r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11598, 11564, 11441, 83, 1139, 193, 570, 288, 11567])).
% 2.54/2.73 tff(11600,plain,
% 2.54/2.73 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[11599, 11583])).
% 2.54/2.73 tff(11601,plain,
% 2.54/2.73 (r(elem!1, s(s(z)))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[11600, 11582])).
% 2.54/2.73 tff(11602,assumption,(r(z, elem!1)), introduced(assumption)).
% 2.54/2.73 tff(11603,plain,
% 2.54/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(11604,plain,
% 2.54/2.73 (((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, elem!1))) <=> ((~r(s(s(z)), s(z))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(11605,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z))))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[11604])).
% 2.54/2.74 tff(11606,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[11605, 11603])).
% 2.54/2.74 tff(11607,plain,
% 2.54/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, elem!1)))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(11608,plain,
% 2.54/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[11607, 11606])).
% 2.54/2.74 tff(11609,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11608, 155, 11602, 729, 226, 6844, 2])).
% 2.54/2.74 tff(11610,plain,((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(11611,plain,
% 2.54/2.74 ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11610, 11419])).
% 2.54/2.74 tff(11612,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11611, 11601, 11580, 226, 2])).
% 2.54/2.74 tff(11613,plain,((~b(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(11614,plain,
% 2.54/2.74 (~r(s(s(s(z))), s(s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11613, 11543, 2, 570, 1139, 193, 2596, 11520, 226, 11524])).
% 2.54/2.74 tff(11615,plain,
% 2.54/2.74 (b(s(s(s(z))), s(s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[421, 11614])).
% 2.54/2.74 tff(11616,plain,
% 2.54/2.74 (((~![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)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(11617,plain,
% 2.54/2.74 (((~b(z, s(s(s(z))))) | (~b(z, s(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(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(11618,plain,
% 2.54/2.74 (((~![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(z, s(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(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[11617])).
% 2.54/2.74 tff(11619,plain,
% 2.54/2.74 (((~![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(z, s(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(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.54/2.74 inference(transitivity,[status(thm)],[11618, 11616])).
% 2.54/2.74 tff(11620,plain,
% 2.54/2.74 ((~![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(z, s(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)))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(11621,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[11620, 11619])).
% 2.54/2.74 tff(11622,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11621, 97, 11524, 11615, 11520, 11543])).
% 2.54/2.74 tff(11623,plain,((~b(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(11624,plain,
% 2.54/2.74 (~b(s(z), s(s(s(elem!1))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11623, 570, 2, 1139, 226, 239])).
% 2.54/2.74 tff(11625,plain,
% 2.54/2.74 (r(s(z), s(s(s(elem!1))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[181, 11624])).
% 2.54/2.74 tff(11626,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(11627,plain,
% 2.54/2.74 (((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(11628,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(z))))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[11627])).
% 2.54/2.74 tff(11629,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[11628, 11626])).
% 2.54/2.74 tff(11630,plain,
% 2.54/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(11631,plain,
% 2.54/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(z))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[11630, 11629])).
% 2.54/2.74 tff(11632,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11631, 155, 11419, 570, 226, 2, 11625])).
% 2.54/2.74 tff(11633,plain,((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(11634,plain,
% 2.54/2.74 (~r(z, s(s(s(elem!1))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11633, 1139, 2, 226, 239])).
% 2.54/2.74 tff(11635,plain,
% 2.54/2.74 (~r(s(s(z)), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11445, 1139, 2, 288, 226])).
% 2.54/2.74 tff(11636,plain,
% 2.54/2.74 (b(s(s(z)), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[625, 11635])).
% 2.54/2.74 tff(11637,plain,
% 2.54/2.74 (((~![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(elem!1))), s(z))) | (~b(s(z), s(s(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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(11638,plain,
% 2.54/2.74 (((~b(s(s(z)), z)) | (~b(s(s(z)), 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(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(11639,plain,
% 2.54/2.74 (((~![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)), z)) | (~b(s(s(z)), 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(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[11638])).
% 2.54/2.74 tff(11640,plain,
% 2.54/2.74 (((~![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)), z)) | (~b(s(s(z)), 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(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[11639, 11637])).
% 2.54/2.74 tff(11641,plain,
% 2.54/2.74 ((~![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)), z)) | (~b(s(s(z)), 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))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(11642,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[11641, 11640])).
% 2.54/2.74 tff(11643,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11642, 97, 1139, 60, 83, 535])).
% 2.54/2.74 tff(11644,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(11645,plain,
% 2.54/2.74 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11644, 1139, 11636, 11441])).
% 2.54/2.74 tff(11646,plain,
% 2.54/2.74 (r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[58, 11645])).
% 2.54/2.74 tff(11647,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(11648,plain,
% 2.54/2.74 (((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(11649,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[11648])).
% 2.54/2.74 tff(11650,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[11649, 11647])).
% 2.54/2.74 tff(11651,plain,
% 2.54/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(11652,plain,
% 2.54/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[11651, 11650])).
% 2.54/2.74 tff(11653,plain,
% 2.54/2.74 (~r(z, s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11652, 155, 11419, 226, 2, 1960])).
% 2.54/2.74 tff(11654,plain,
% 2.54/2.74 (b(z, s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1318, 11653])).
% 2.54/2.74 tff(11655,plain,
% 2.54/2.74 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11644, 1139, 83, 535])).
% 2.54/2.74 tff(11656,plain,
% 2.54/2.74 (r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[58, 11655])).
% 2.54/2.74 tff(11657,plain,
% 2.54/2.74 (~b(s(s(s(s(elem!1)))), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11562, 1216, 1960, 83, 1330])).
% 2.54/2.74 tff(11658,plain,
% 2.54/2.74 (r(s(s(s(s(elem!1)))), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[842, 11657])).
% 2.54/2.74 tff(11659,plain,
% 2.54/2.74 (~b(s(z), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2972, 1330, 535, 83])).
% 2.54/2.74 tff(11660,plain,
% 2.54/2.74 (r(s(z), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[568, 11659])).
% 2.54/2.74 tff(11661,plain,
% 2.54/2.74 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11568, 11658, 11660])).
% 2.54/2.74 tff(11662,plain,
% 2.54/2.74 (b(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[511, 11661])).
% 2.54/2.74 tff(11663,plain,
% 2.54/2.74 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2129, 11662, 1139, 535])).
% 2.54/2.74 tff(11664,plain,
% 2.54/2.74 (~r(z, s(s(s(s(elem!1)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[3464, 11663, 288, 585, 11658])).
% 2.54/2.74 tff(11665,plain,
% 2.54/2.74 (b(z, s(s(s(s(elem!1)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1093, 11664])).
% 2.54/2.74 tff(11666,plain,
% 2.54/2.74 (~b(s(s(z)), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[5232, 11665, 1216, 83])).
% 2.54/2.74 tff(11667,plain,
% 2.54/2.74 (r(s(s(z)), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[437, 11666])).
% 2.54/2.74 tff(11668,plain,
% 2.54/2.74 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[5794, 11667, 11656, 1960])).
% 2.54/2.74 tff(11669,plain,
% 2.54/2.74 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[669, 11665, 83, 11662])).
% 2.54/2.74 tff(11670,plain,
% 2.54/2.74 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[336, 11669])).
% 2.54/2.74 tff(11671,plain,
% 2.54/2.74 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[5339, 11670, 288, 11656, 226])).
% 2.54/2.74 tff(11672,plain,
% 2.54/2.74 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[486, 11671, 11663])).
% 2.54/2.74 tff(11673,plain,
% 2.54/2.74 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2729, 11672, 11668])).
% 2.54/2.74 tff(11674,plain,
% 2.54/2.74 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2747, 11673])).
% 2.54/2.74 tff(11675,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2763, 97, 11665, 11674, 1330, 1216])).
% 2.54/2.74 tff(11676,plain,((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | r(z, s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(11677,plain,
% 2.54/2.74 (~b(s(s(s(z))), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11676, 11654, 288, 226, 1960, 11636, 585, 1139, 11441])).
% 2.54/2.74 tff(11678,plain,
% 2.54/2.74 (r(s(s(s(z))), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[402, 11677])).
% 2.54/2.74 tff(11679,plain,
% 2.54/2.74 (~b(s(z), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2972, 11654, 11441, 11636])).
% 2.54/2.74 tff(11680,plain,
% 2.54/2.74 (r(s(z), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[568, 11679])).
% 2.54/2.74 tff(11681,plain,
% 2.54/2.74 ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[4290, 155, 226, 11680, 1960])).
% 2.54/2.74 tff(11682,plain,
% 2.54/2.74 (~r(s(s(s(z))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11681, 11678])).
% 2.54/2.74 tff(11683,plain,
% 2.54/2.74 (b(s(s(s(z))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1358, 11682])).
% 2.54/2.74 tff(11684,plain,
% 2.54/2.74 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11479, 97, 1139, 11441, 11683])).
% 2.54/2.74 tff(11685,plain,
% 2.54/2.74 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11487, 97, 1139, 11441, 11683])).
% 2.54/2.74 tff(11686,plain,
% 2.54/2.74 (~r(s(s(z)), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[5794, 2630, 1960, 145])).
% 2.54/2.74 tff(11687,plain,
% 2.54/2.74 (b(s(s(z)), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[437, 11686])).
% 2.54/2.74 tff(11688,plain,
% 2.54/2.74 (~b(z, s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1369, 11687, 1139, 124, 83, 1360])).
% 2.54/2.74 tff(11689,plain,
% 2.54/2.74 (r(z, s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1318, 11688])).
% 2.54/2.74 tff(11690,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(11691,plain,
% 2.54/2.74 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(11692,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[11691])).
% 2.54/2.74 tff(11693,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[11692, 11690])).
% 2.54/2.74 tff(11694,plain,
% 2.54/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(11695,plain,
% 2.54/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[11694, 11693])).
% 2.54/2.74 tff(11696,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11695, 155, 288, 11689, 145, 1960, 2630])).
% 2.54/2.74 tff(11697,plain,((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(11698,plain,
% 2.54/2.74 (~r(s(s(s(elem!1))), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11697, 5842, 1360, 1960, 1139, 124, 83, 145])).
% 2.54/2.74 tff(11699,plain,
% 2.54/2.74 (b(s(s(s(elem!1))), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[246, 11698])).
% 2.54/2.74 tff(11700,plain,
% 2.54/2.74 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[4987, 11699, 83, 124])).
% 2.54/2.74 tff(11701,plain,
% 2.54/2.74 (r(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[143, 11700])).
% 2.54/2.74 tff(11702,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[4382, 155, 145, 11701, 1960, 5841])).
% 2.54/2.74 tff(11703,plain,((s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | b(s(s(s(elem!1))), s(s(s(z)))) | b(s(s(s(z))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(11704,plain,
% 2.54/2.74 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11703, 11685, 1139, 3008, 11636, 1960, 11683, 11646, 11684])).
% 2.54/2.74 tff(11705,plain,
% 2.54/2.74 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[11704])).
% 2.54/2.74 tff(11706,plain,
% 2.54/2.74 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[11705, 1414])).
% 2.54/2.74 tff(11707,plain,
% 2.54/2.74 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[11706])).
% 2.54/2.74 tff(11708,plain,
% 2.54/2.74 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[286, 11707])).
% 2.54/2.74 tff(11709,plain,
% 2.54/2.74 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[11704])).
% 2.54/2.74 tff(11710,plain,
% 2.54/2.74 (s(s(z)) = s(s(elem!1))),
% 2.54/2.74 inference(transitivity,[status(thm)],[73, 11709, 19])).
% 2.54/2.75 tff(11711,plain,
% 2.54/2.75 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[11710])).
% 2.54/2.75 tff(11712,plain,
% 2.54/2.75 (s(z) = s(elem!1)),
% 2.54/2.75 inference(transitivity,[status(thm)],[24, 11711, 29])).
% 2.54/2.75 tff(11713,plain,
% 2.54/2.75 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[11712])).
% 2.54/2.75 tff(11714,plain,
% 2.54/2.75 (z = elem!1),
% 2.54/2.75 inference(transitivity,[status(thm)],[1443, 11713, 85])).
% 2.54/2.75 tff(11715,plain,
% 2.54/2.75 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.54/2.75 inference(monotonicity,[status(thm)],[11714])).
% 2.54/2.75 tff(11716,plain,
% 2.54/2.75 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 2.54/2.75 inference(monotonicity,[status(thm)],[11710])).
% 2.54/2.75 tff(11717,plain,
% 2.54/2.75 (b(s(s(elem!1)), z)),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[11636, 11716])).
% 2.54/2.75 tff(11718,plain,
% 2.54/2.75 (b(s(s(elem!1)), elem!1)),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[11717, 11715])).
% 2.54/2.75 tff(11719,plain,
% 2.54/2.75 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.54/2.75 inference(symmetry,[status(thm)],[11709])).
% 2.54/2.75 tff(11720,plain,
% 2.54/2.75 (s(s(elem!1)) = s(s(z))),
% 2.54/2.75 inference(transitivity,[status(thm)],[167, 11719, 72])).
% 2.54/2.75 tff(11721,plain,
% 2.54/2.75 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[11720])).
% 2.54/2.75 tff(11722,plain,
% 2.54/2.75 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.54/2.75 inference(symmetry,[status(thm)],[11721])).
% 2.54/2.75 tff(11723,plain,
% 2.54/2.75 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[11646, 11722])).
% 2.54/2.75 tff(11724,plain,
% 2.54/2.75 (b(elem!1, s(s(s(elem!1))))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[124, 8104])).
% 2.54/2.75 tff(11725,plain,
% 2.54/2.75 (((~![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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(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(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(11726,plain,
% 2.54/2.75 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(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(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(11727,plain,
% 2.54/2.75 (((~![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(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(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(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[11726])).
% 2.54/2.75 tff(11728,plain,
% 2.54/2.75 (((~![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(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(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(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.54/2.75 inference(transitivity,[status(thm)],[11727, 11725])).
% 2.54/2.75 tff(11729,plain,
% 2.54/2.75 ((~![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(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(11730,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[11729, 11728])).
% 2.54/2.75 tff(11731,plain,
% 2.54/2.75 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11730, 97, 11724, 11116, 1915])).
% 2.54/2.75 tff(11732,plain,
% 2.54/2.75 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1484, 11731, 1432])).
% 2.54/2.75 tff(11733,plain,
% 2.54/2.75 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[4515, 97, 11724, 11116, 1915])).
% 2.54/2.75 tff(11734,plain,
% 2.54/2.75 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1631, 11733, 1508])).
% 2.54/2.75 tff(11735,plain,
% 2.54/2.75 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[4505, 11734, 4497, 11732])).
% 2.54/2.75 tff(11736,plain,
% 2.54/2.75 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[7352, 11732, 1393])).
% 2.54/2.75 tff(11737,plain,
% 2.54/2.75 ((~b(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[3825, 11419])).
% 2.54/2.75 tff(11738,plain,
% 2.54/2.75 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11737, 11736, 226, 535, 124, 876])).
% 2.54/2.75 tff(11739,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[486, 11738, 11735, 1418])).
% 2.54/2.75 tff(11740,plain,((~b(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(11741,plain,
% 2.54/2.75 (~b(s(s(s(s(elem!1)))), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11740, 11723, 11441, 3008, 226, 11704, 11718])).
% 2.54/2.75 tff(11742,plain,
% 2.54/2.75 (r(s(s(s(s(elem!1)))), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[842, 11741])).
% 2.54/2.75 tff(11743,plain,
% 2.54/2.75 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11568, 11742, 11680])).
% 2.54/2.75 tff(11744,plain,
% 2.54/2.75 (b(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[511, 11743])).
% 2.54/2.75 tff(11745,plain,
% 2.54/2.75 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[2129, 11744, 1139, 11441])).
% 2.54/2.75 tff(11746,plain,
% 2.54/2.75 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[486, 11745, 11708])).
% 2.54/2.75 tff(11747,plain,
% 2.54/2.75 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[5339, 11746, 288, 11646, 226])).
% 2.54/2.75 tff(11748,plain,
% 2.54/2.75 (~r(z, s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[3464, 11745, 288, 585, 11742])).
% 2.54/2.75 tff(11749,plain,
% 2.54/2.75 (b(z, s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1093, 11748])).
% 2.54/2.75 tff(11750,plain,
% 2.54/2.75 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[669, 11749, 11636, 11744])).
% 2.54/2.75 tff(11751,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[336, 11750, 11747])).
% 2.54/2.75 tff(11752,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | r(z, s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(11753,plain,
% 2.54/2.75 (~r(s(s(s(z))), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11752, 11634, 226, 2596, 1139, 2])).
% 2.54/2.75 tff(11754,plain,
% 2.54/2.75 (b(s(s(s(z))), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[421, 11753])).
% 2.54/2.75 tff(11755,plain,
% 2.54/2.75 (~r(z, s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11509, 11754, 11441, 11447])).
% 2.54/2.75 tff(11756,plain,
% 2.54/2.75 (b(z, s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1318, 11755])).
% 2.54/2.75 tff(11757,plain,
% 2.54/2.75 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11644, 1139, 11447, 11441])).
% 2.54/2.75 tff(11758,plain,
% 2.54/2.75 (r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[58, 11757])).
% 2.54/2.75 tff(11759,plain,
% 2.54/2.75 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[8734, 11753, 11758])).
% 2.54/2.75 tff(11760,plain,
% 2.54/2.75 (~b(s(s(s(z))), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11501, 11754, 11441, 11759, 1139])).
% 2.54/2.75 tff(11761,plain,
% 2.54/2.75 (r(s(s(s(z))), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1358, 11760])).
% 2.54/2.75 tff(11762,plain,
% 2.54/2.75 (~b(s(z), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9363, 97, 11447, 11441, 11754])).
% 2.54/2.75 tff(11763,plain,
% 2.54/2.75 (r(s(z), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[253, 11762])).
% 2.54/2.75 tff(11764,plain,
% 2.54/2.75 (~r(s(s(z)), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[2940, 11763, 2, 11761])).
% 2.54/2.75 tff(11765,plain,
% 2.54/2.75 (b(s(s(z)), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[437, 11764])).
% 2.54/2.75 tff(11766,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[10159, 97, 11447, 11765, 11754, 11756])).
% 2.54/2.75 tff(11767,plain,((~b(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(11768,plain,
% 2.54/2.75 (~b(s(s(s(elem!1))), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11767, 226, 2, 239])).
% 2.54/2.75 tff(11769,plain,
% 2.54/2.75 (r(s(s(s(elem!1))), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[493, 11768])).
% 2.54/2.75 tff(11770,plain,
% 2.54/2.75 ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[791, 11419])).
% 2.54/2.75 tff(11771,plain,
% 2.54/2.75 (~r(s(z), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11770, 494, 288])).
% 2.54/2.75 tff(11772,plain,
% 2.54/2.75 (b(s(z), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[568, 11771])).
% 2.54/2.75 tff(11773,plain,
% 2.54/2.75 (~r(s(s(z)), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[3956, 585, 288, 82, 11441, 11772, 226])).
% 2.54/2.75 tff(11774,plain,
% 2.54/2.75 (b(s(s(z)), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[625, 11773])).
% 2.54/2.75 tff(11775,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[799, 97, 550, 372, 83, 535])).
% 2.54/2.75 tff(11776,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(11777,plain,
% 2.54/2.75 (~b(z, s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11776, 11774, 11441, 11772])).
% 2.54/2.75 tff(11778,plain,
% 2.54/2.75 (r(z, s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1093, 11777])).
% 2.54/2.75 tff(11779,plain,
% 2.54/2.75 (~b(z, s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[2972, 11774, 11441, 11772])).
% 2.54/2.75 tff(11780,plain,
% 2.54/2.75 (r(z, s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1318, 11779])).
% 2.54/2.75 tff(11781,plain,
% 2.54/2.75 (~b(s(s(s(z))), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11509, 11780, 11441, 11774])).
% 2.54/2.75 tff(11782,plain,
% 2.54/2.75 (r(s(s(s(z))), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[421, 11781])).
% 2.54/2.75 tff(11783,plain,
% 2.54/2.75 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[6995, 11782, 11780, 11778, 226])).
% 2.54/2.75 tff(11784,plain,
% 2.54/2.75 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[336, 11783])).
% 2.54/2.75 tff(11785,plain,
% 2.54/2.75 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[857, 155, 494, 226, 288, 2])).
% 2.54/2.75 tff(11786,plain,
% 2.54/2.75 (b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[58, 11785])).
% 2.54/2.75 tff(11787,plain,
% 2.54/2.75 ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[3746, 11419])).
% 2.54/2.75 tff(11788,plain,
% 2.54/2.75 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11787, 11778, 2, 226])).
% 2.54/2.75 tff(11789,plain,
% 2.54/2.75 (b(s(z), s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[280, 11788])).
% 2.54/2.75 tff(11790,plain,
% 2.54/2.75 (~b(s(s(s(s(elem!1)))), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[3812, 11784, 11441, 11789])).
% 2.54/2.75 tff(11791,plain,
% 2.54/2.75 (r(s(s(s(s(elem!1)))), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[842, 11790])).
% 2.54/2.75 tff(11792,plain,
% 2.54/2.75 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[3464, 11791, 288, 585, 11778])).
% 2.54/2.75 tff(11793,plain,
% 2.54/2.75 (~r(s(s(z)), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1969, 11782, 226, 11780])).
% 2.54/2.75 tff(11794,plain,
% 2.54/2.75 (b(s(s(z)), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[437, 11793])).
% 2.54/2.75 tff(11795,plain,
% 2.54/2.75 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[3067, 11794, 11441, 11789])).
% 2.54/2.75 tff(11796,plain,
% 2.54/2.75 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[452, 11795])).
% 2.54/2.75 tff(11797,plain,
% 2.54/2.75 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[3278, 11791, 2, 11796, 226])).
% 2.54/2.75 tff(11798,plain,
% 2.54/2.75 (b(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[511, 11797])).
% 2.54/2.75 tff(11799,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[753, 11798, 11792, 11786, 11784])).
% 2.54/2.75 tff(11800,plain,(r(z, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(11801,plain,
% 2.54/2.75 (r(z, s(s(s(elem!1))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11800, 226, 2, 2596, 11768])).
% 2.54/2.75 tff(11802,plain,
% 2.54/2.75 ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[4539, 11419])).
% 2.54/2.75 tff(11803,plain,
% 2.54/2.75 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11802, 11801, 11769, 226])).
% 2.54/2.75 tff(11804,plain,
% 2.54/2.75 (b(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[143, 11803])).
% 2.54/2.75 tff(11805,plain,
% 2.54/2.75 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[857, 155, 11769, 226, 2596, 2])).
% 2.54/2.75 tff(11806,plain,
% 2.54/2.75 (b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[58, 11805])).
% 2.54/2.75 tff(11807,plain,
% 2.54/2.75 ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[771, 11419])).
% 2.54/2.75 tff(11808,plain,
% 2.54/2.75 (~r(s(z), s(s(s(elem!1))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11807, 11801, 11769])).
% 2.54/2.75 tff(11809,plain,
% 2.54/2.75 (b(s(z), s(s(s(elem!1))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[181, 11808])).
% 2.54/2.75 tff(11810,plain,
% 2.54/2.75 (((~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(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(11811,plain,
% 2.54/2.75 (((~![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(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[11810])).
% 2.54/2.75 tff(11812,plain,
% 2.54/2.75 (((~![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(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.54/2.75 inference(transitivity,[status(thm)],[11811, 1068])).
% 2.54/2.75 tff(11813,plain,
% 2.54/2.75 ((~![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(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(11814,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[11813, 11812])).
% 2.54/2.75 tff(11815,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11814, 97, 11809, 11806, 11441, 11804])).
% 2.54/2.75 tff(11816,plain,((~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(11817,plain,
% 2.54/2.75 (~r(z, s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11816, 2, 239])).
% 2.54/2.75 tff(11818,plain,
% 2.54/2.75 (b(z, s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[222, 11817])).
% 2.54/2.75 tff(11819,plain,
% 2.54/2.75 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.54/2.75 inference(commutativity,[status(thm)],[])).
% 2.54/2.75 tff(11820,plain,
% 2.54/2.75 (r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[58, 5])).
% 2.54/2.75 tff(11821,plain,
% 2.54/2.75 (~b(s(s(z)), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[5591, 81, 645, 3])).
% 2.54/2.75 tff(11822,plain,
% 2.54/2.75 (r(s(s(z)), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[122, 11821])).
% 2.54/2.75 tff(11823,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[966, 155, 729, 81, 645, 11822])).
% 2.54/2.75 tff(11824,plain,((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(11825,plain,
% 2.54/2.75 ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11824, 11419])).
% 2.54/2.75 tff(11826,plain,
% 2.54/2.75 (~r(s(z), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11825, 645, 3])).
% 2.54/2.75 tff(11827,plain,
% 2.54/2.75 (b(s(z), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[568, 11826])).
% 2.54/2.75 tff(11828,plain,
% 2.54/2.75 ((~r(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[3615, 11419])).
% 2.54/2.75 tff(11829,plain,
% 2.54/2.75 (~r(s(s(z)), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11828, 11827, 2, 3008, 645])).
% 2.54/2.75 tff(11830,plain,
% 2.54/2.75 (b(s(s(z)), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[437, 11829])).
% 2.54/2.75 tff(11831,plain,
% 2.54/2.75 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[2313, 494, 2, 3])).
% 2.54/2.75 tff(11832,plain,
% 2.54/2.75 (b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[58, 11831])).
% 2.54/2.75 tff(11833,plain,
% 2.54/2.75 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[2077, 124, 204, 60])).
% 2.54/2.75 tff(11834,plain,
% 2.54/2.75 (r(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[143, 11833])).
% 2.54/2.75 tff(11835,plain,
% 2.54/2.75 (~b(s(s(z)), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[306, 124, 204, 60])).
% 2.54/2.75 tff(11836,plain,
% 2.54/2.75 (r(s(s(z)), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[625, 11835])).
% 2.54/2.75 tff(11837,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11437, 11836, 11834, 2, 288])).
% 2.54/2.75 tff(11838,plain,((~b(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(11839,plain,
% 2.54/2.75 (~b(z, s(s(s(elem!1))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11838, 11832, 288, 204, 2])).
% 2.54/2.75 tff(11840,plain,
% 2.54/2.75 (r(z, s(s(s(elem!1))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[590, 11839])).
% 2.54/2.75 tff(11841,plain,
% 2.54/2.75 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[11832, 1501])).
% 2.54/2.75 tff(11842,plain,
% 2.54/2.75 (r(elem!1, s(s(s(elem!1))))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[11840, 1509])).
% 2.54/2.75 tff(11843,plain,
% 2.54/2.75 (b(s(elem!1), elem!1)),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[11772, 10804])).
% 2.54/2.75 tff(11844,plain,
% 2.54/2.75 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[1444])).
% 2.54/2.75 tff(11845,plain,
% 2.54/2.75 (b(z, s(s(elem!1)))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[204, 1890])).
% 2.54/2.75 tff(11846,plain,
% 2.54/2.75 (b(elem!1, s(s(elem!1)))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[11845, 11844])).
% 2.54/2.75 tff(11847,plain,
% 2.54/2.75 (~r(s(z), s(s(s(elem!1))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11807, 11840, 494])).
% 2.54/2.75 tff(11848,plain,
% 2.54/2.75 (b(s(z), s(s(s(elem!1))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[181, 11847])).
% 2.54/2.75 tff(11849,plain,
% 2.54/2.75 (b(s(elem!1), s(s(s(elem!1))))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[11848, 1514])).
% 2.54/2.75 tff(11850,plain,
% 2.54/2.75 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[1399])).
% 2.54/2.75 tff(11851,plain,
% 2.54/2.75 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(z)))),
% 2.54/2.75 inference(symmetry,[status(thm)],[11850])).
% 2.54/2.75 tff(11852,plain,
% 2.54/2.75 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[1401, 1399])).
% 2.54/2.75 tff(11853,plain,
% 2.54/2.75 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 2.54/2.75 inference(transitivity,[status(thm)],[11852, 11851])).
% 2.54/2.75 tff(11854,plain,
% 2.54/2.75 (r(s(elem!1), s(s(z)))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[3, 11853])).
% 2.54/2.75 tff(11855,plain,
% 2.54/2.75 (r(s(s(elem!1)), s(elem!1))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[2, 8023])).
% 2.54/2.75 tff(11856,plain,
% 2.54/2.75 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[7334, 11855, 494, 11841, 11842, 1393, 11854, 11849, 1512])).
% 2.54/2.75 tff(11857,plain,
% 2.54/2.75 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[821, 11856, 4451])).
% 2.54/2.75 tff(11858,plain,
% 2.54/2.75 (~r(s(s(s(s(elem!1)))), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[832, 11857, 11840, 288])).
% 2.54/2.75 tff(11859,plain,
% 2.54/2.75 (b(s(s(s(s(elem!1)))), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[842, 11858])).
% 2.54/2.75 tff(11860,plain,
% 2.54/2.75 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[4474, 11859, 1444])).
% 2.54/2.75 tff(11861,plain,
% 2.54/2.75 (((~![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(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(11862,plain,
% 2.54/2.75 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, 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), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(11863,plain,
% 2.54/2.75 (((~![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(elem!1, s(s(elem!1)))) | (~b(elem!1, 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), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[11862])).
% 2.54/2.75 tff(11864,plain,
% 2.54/2.75 (((~![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(elem!1, s(s(elem!1)))) | (~b(elem!1, 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), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.54/2.75 inference(transitivity,[status(thm)],[11863, 11861])).
% 2.54/2.75 tff(11865,plain,
% 2.54/2.75 ((~![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(elem!1, s(s(elem!1)))) | (~b(elem!1, 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)))))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(11866,plain,
% 2.54/2.75 ((~![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(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[11865, 11864])).
% 2.54/2.75 tff(11867,plain,
% 2.54/2.75 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11866, 97, 11860, 11846, 11843])).
% 2.54/2.75 tff(11868,plain,
% 2.54/2.75 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[11867, 7308])).
% 2.54/2.75 tff(11869,plain,
% 2.54/2.75 (r(s(z), s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[280, 11868])).
% 2.54/2.75 tff(11870,plain,
% 2.54/2.75 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[503, 287, 494, 488])).
% 2.54/2.75 tff(11871,plain,
% 2.54/2.75 (b(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[511, 11870])).
% 2.54/2.75 tff(11872,plain,
% 2.54/2.75 (~b(z, s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1083, 11871, 82, 287])).
% 2.54/2.75 tff(11873,plain,
% 2.54/2.75 (r(z, s(s(s(s(elem!1)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1093, 11872])).
% 2.54/2.75 tff(11874,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(11875,plain,
% 2.54/2.75 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(11876,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[11875])).
% 2.54/2.75 tff(11877,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[11876, 11874])).
% 2.54/2.76 tff(11878,plain,
% 2.54/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(11879,plain,
% 2.54/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[11878, 11877])).
% 2.54/2.76 tff(11880,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11879, 155, 494, 729, 570, 287, 11873])).
% 2.54/2.76 tff(11881,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(11882,plain,
% 2.54/2.76 ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11881, 11419])).
% 2.54/2.76 tff(11883,plain,
% 2.54/2.76 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11882, 11869, 82, 11840])).
% 2.54/2.76 tff(11884,plain,
% 2.54/2.76 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[486, 11883, 1418])).
% 2.54/2.76 tff(11885,plain,
% 2.54/2.76 (((~![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(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(11886,plain,
% 2.54/2.76 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(11887,plain,
% 2.54/2.76 (((~![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(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[11886])).
% 2.54/2.76 tff(11888,plain,
% 2.54/2.76 (((~![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(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 2.54/2.76 inference(transitivity,[status(thm)],[11887, 11885])).
% 2.54/2.76 tff(11889,plain,
% 2.54/2.76 ((~![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(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(11890,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[11889, 11888])).
% 2.54/2.76 tff(11891,plain,
% 2.54/2.76 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11890, 97, 11860, 11841, 11849, 11846, 11843])).
% 2.54/2.76 tff(11892,plain,
% 2.54/2.76 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[11891, 7319])).
% 2.54/2.76 tff(11893,plain,
% 2.54/2.76 (r(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[511, 11892])).
% 2.54/2.76 tff(11894,plain,
% 2.54/2.76 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1816, 11893, 1393, 11854, 11855])).
% 2.54/2.76 tff(11895,plain,
% 2.54/2.76 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1484, 11894, 1432])).
% 2.54/2.76 tff(11896,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1586, 11895, 11884, 1512, 11842, 1527, 11841, 1444])).
% 2.54/2.76 tff(11897,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(11898,plain,
% 2.54/2.76 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11897, 82, 288, 3, 2, 204])).
% 2.54/2.76 tff(11899,plain,
% 2.54/2.76 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2682, 11898])).
% 2.54/2.76 tff(11900,plain,
% 2.54/2.76 (~r(s(z), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11770, 125, 288])).
% 2.54/2.76 tff(11901,plain,
% 2.54/2.76 (b(s(z), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[568, 11900])).
% 2.54/2.76 tff(11902,plain,
% 2.54/2.76 (~r(s(s(s(z))), s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2930, 1960, 2, 3])).
% 2.54/2.76 tff(11903,plain,
% 2.54/2.76 (b(s(s(s(z))), s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1358, 11902])).
% 2.54/2.76 tff(11904,plain,
% 2.54/2.76 (((~![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(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(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(11905,plain,
% 2.54/2.76 (((~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(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(11906,plain,
% 2.54/2.76 (((~![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(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(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[11905])).
% 2.54/2.76 tff(11907,plain,
% 2.54/2.76 (((~![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(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(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.54/2.76 inference(transitivity,[status(thm)],[11906, 11904])).
% 2.54/2.76 tff(11908,plain,
% 2.54/2.76 ((~![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(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(11909,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[11908, 11907])).
% 2.54/2.76 tff(11910,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11909, 97, 550, 204, 1360, 1216])).
% 2.54/2.76 tff(11911,plain,((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(11912,plain,
% 2.54/2.76 (~b(s(s(s(z))), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11911, 11903, 204, 11901])).
% 2.54/2.76 tff(11913,plain,
% 2.54/2.76 (r(s(s(s(z))), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[402, 11912])).
% 2.54/2.76 tff(11914,plain,
% 2.54/2.76 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[4280, 155, 125, 11419, 288, 11913])).
% 2.54/2.76 tff(11915,plain,
% 2.54/2.76 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2687, 11914, 2466])).
% 2.54/2.76 tff(11916,plain,
% 2.54/2.76 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2313, 125, 2, 3])).
% 2.54/2.76 tff(11917,plain,
% 2.54/2.76 (b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[58, 11916])).
% 2.54/2.76 tff(11918,plain,
% 2.54/2.76 (~b(z, s(s(s(elem!1))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11838, 11917, 288, 204, 2])).
% 2.54/2.76 tff(11919,plain,
% 2.54/2.76 (r(z, s(s(s(elem!1))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[590, 11918])).
% 2.54/2.76 tff(11920,plain,
% 2.54/2.76 (~r(s(z), s(s(s(elem!1))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11807, 11919, 125])).
% 2.54/2.76 tff(11921,plain,
% 2.54/2.76 (b(s(z), s(s(s(elem!1))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[181, 11920])).
% 2.54/2.76 tff(11922,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[4071, 97, 193, 1360, 86, 5941])).
% 2.54/2.76 tff(11923,plain,((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(11924,plain,
% 2.54/2.76 (~b(s(z), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11923, 11903, 11921, 11915])).
% 2.54/2.76 tff(11925,plain,
% 2.54/2.76 (r(s(z), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[253, 11924])).
% 2.54/2.76 tff(11926,plain,
% 2.54/2.76 (~r(s(s(z)), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2641, 11925, 3, 1960])).
% 2.54/2.76 tff(11927,plain,
% 2.54/2.76 (b(s(s(z)), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[437, 11926])).
% 2.54/2.76 tff(11928,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[7048, 97, 11917, 11927, 11903, 11915])).
% 2.54/2.76 tff(11929,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(11930,plain,
% 2.54/2.76 (~r(s(s(s(z))), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11929, 11899, 3, 494, 288, 204, 2])).
% 2.54/2.76 tff(11931,plain,
% 2.54/2.76 (b(s(s(s(z))), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[421, 11930])).
% 2.54/2.76 tff(11932,plain,
% 2.54/2.76 (~b(z, s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1339, 83, 204, 1331])).
% 2.54/2.76 tff(11933,plain,
% 2.54/2.76 (r(z, s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1318, 11932])).
% 2.54/2.76 tff(11934,plain,
% 2.54/2.76 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[7213, 97, 60, 83, 1331])).
% 2.54/2.76 tff(11935,plain,
% 2.54/2.76 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[7147, 97, 60, 83, 1331])).
% 2.54/2.76 tff(11936,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[5852, 11935, 11934, 570, 1, 11933])).
% 2.54/2.76 tff(11937,plain,((~b(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(11938,plain,
% 2.54/2.76 (~b(s(s(z)), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11937, 11840, 11898, 11832, 11931, 204])).
% 2.54/2.76 tff(11939,plain,
% 2.54/2.76 (r(s(s(z)), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[625, 11938])).
% 2.54/2.76 tff(11940,plain,
% 2.54/2.76 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2253, 11939, 2, 494, 11840])).
% 2.54/2.76 tff(11941,plain,
% 2.54/2.76 (b(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[143, 11940])).
% 2.54/2.76 tff(11942,plain,
% 2.54/2.76 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2270, 97, 11832, 11931, 11941])).
% 2.54/2.76 tff(11943,plain,
% 2.54/2.76 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[7861, 97, 11832, 11931, 11941])).
% 2.54/2.76 tff(11944,plain,
% 2.54/2.76 (~b(z, s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2415, 97, 204, 11931, 11941])).
% 2.54/2.76 tff(11945,plain,
% 2.54/2.76 (r(z, s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1318, 11944])).
% 2.54/2.76 tff(11946,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[5852, 11945, 11943, 11840, 11898, 11942])).
% 2.54/2.76 tff(11947,plain,(b(s(s(s(elem!1))), s(z)) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(11948,plain,
% 2.54/2.76 (b(s(s(s(elem!1))), s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11947, 3, 2, 204, 288])).
% 2.54/2.76 tff(11949,plain,
% 2.54/2.76 (~r(s(z), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[5665, 87, 3])).
% 2.54/2.76 tff(11950,plain,
% 2.54/2.76 (b(s(z), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[568, 11949])).
% 2.54/2.76 tff(11951,plain,
% 2.54/2.76 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[10654, 11950, 1139, 87])).
% 2.54/2.76 tff(11952,plain,
% 2.54/2.76 (r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[58, 11951])).
% 2.54/2.76 tff(11953,plain,
% 2.54/2.76 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[10132, 97, 1139, 11950, 1360])).
% 2.54/2.76 tff(11954,plain,
% 2.54/2.76 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2687, 11953, 2466])).
% 2.54/2.76 tff(11955,plain,
% 2.54/2.76 (~b(s(s(z)), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[6489, 97, 11950, 87, 1360])).
% 2.54/2.76 tff(11956,plain,
% 2.54/2.76 (r(s(s(z)), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[437, 11955])).
% 2.54/2.76 tff(11957,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[5794, 11956, 11954, 1960, 11952])).
% 2.54/2.76 tff(11958,plain,((~b(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(11959,plain,
% 2.54/2.76 (~b(s(s(z)), s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11958, 4228, 2591, 1360, 1139, 3])).
% 2.54/2.76 tff(11960,plain,
% 2.54/2.76 (r(s(s(z)), s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[122, 11959])).
% 2.54/2.76 tff(11961,plain,
% 2.54/2.76 (~r(z, s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11426, 11960, 729, 3])).
% 2.54/2.76 tff(11962,plain,
% 2.54/2.76 (b(z, s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[222, 11961])).
% 2.54/2.76 tff(11963,plain,
% 2.54/2.76 (((~![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(s(s(z)), s(s(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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(11964,plain,
% 2.54/2.76 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(11965,plain,
% 2.54/2.76 (((~![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))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(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(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[11964])).
% 2.54/2.76 tff(11966,plain,
% 2.54/2.76 (((~![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))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(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(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[11965, 11963])).
% 2.54/2.76 tff(11967,plain,
% 2.54/2.76 ((~![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))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(11968,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[11967, 11966])).
% 2.54/2.76 tff(11969,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11968, 97, 204, 1361, 1360, 1330])).
% 2.54/2.76 tff(11970,plain,((~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(11971,plain,
% 2.54/2.76 (~b(z, s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11970, 1361, 11962, 1360])).
% 2.54/2.76 tff(11972,plain,
% 2.54/2.76 (r(z, s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1318, 11971])).
% 2.54/2.76 tff(11973,plain,
% 2.54/2.76 (((~![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(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(11974,plain,
% 2.54/2.76 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(11975,plain,
% 2.54/2.76 (((~![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), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[11974])).
% 2.54/2.76 tff(11976,plain,
% 2.54/2.76 (((~![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), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[11975, 11973])).
% 2.54/2.76 tff(11977,plain,
% 2.54/2.76 ((~![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), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(11978,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[11977, 11976])).
% 2.54/2.76 tff(11979,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11978, 97, 1139, 255, 1360, 1702])).
% 2.54/2.76 tff(11980,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(11981,plain,
% 2.54/2.76 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11980, 255, 1139, 1360])).
% 2.54/2.76 tff(11982,plain,
% 2.54/2.76 (((~![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(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(11983,plain,
% 2.54/2.76 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(11984,plain,
% 2.54/2.76 (((~![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), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[11983])).
% 2.54/2.76 tff(11985,plain,
% 2.54/2.76 (((~![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), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[11984, 11982])).
% 2.54/2.77 tff(11986,plain,
% 2.54/2.77 ((~![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(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(11987,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[11986, 11985])).
% 2.54/2.77 tff(11988,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[11987, 97, 1139, 255, 1360, 5941])).
% 2.54/2.77 tff(11989,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(11990,plain,
% 2.54/2.77 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[11989, 255, 1139, 1360])).
% 2.54/2.77 tff(11991,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5852, 11990, 11981, 1300, 1, 570])).
% 2.54/2.77 tff(11992,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(11993,plain,
% 2.54/2.77 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[11992, 570, 1, 1300, 1139, 1360])).
% 2.54/2.77 tff(11994,plain,
% 2.54/2.77 (~b(z, s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2587, 81, 3])).
% 2.54/2.77 tff(11995,plain,
% 2.54/2.77 (r(z, s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[723, 11994])).
% 2.54/2.77 tff(11996,plain,
% 2.54/2.77 (~r(s(s(s(elem!1))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5675, 81, 3])).
% 2.54/2.77 tff(11997,plain,
% 2.54/2.77 (b(s(s(s(elem!1))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[493, 11996])).
% 2.54/2.77 tff(11998,plain,
% 2.54/2.77 (~b(s(s(s(elem!1))), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[4567, 60, 83, 204])).
% 2.54/2.77 tff(11999,plain,
% 2.54/2.77 (r(s(s(s(elem!1))), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[246, 11998])).
% 2.54/2.77 tff(12000,plain,
% 2.54/2.77 (~b(z, s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[306, 60, 204, 83])).
% 2.54/2.77 tff(12001,plain,
% 2.54/2.77 (r(z, s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[590, 12000])).
% 2.54/2.77 tff(12002,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[709, 155, 12001, 81, 11999, 225])).
% 2.54/2.77 tff(12003,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(12004,plain,
% 2.54/2.77 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12003, 3009, 81, 5669, 5671])).
% 2.54/2.77 tff(12005,plain,
% 2.54/2.77 (r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[58, 12004])).
% 2.54/2.77 tff(12006,plain,
% 2.54/2.77 (~r(s(s(s(elem!1))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5675, 3, 81])).
% 2.54/2.77 tff(12007,plain,
% 2.54/2.77 (b(s(s(s(elem!1))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[493, 12006])).
% 2.54/2.77 tff(12008,plain,
% 2.54/2.77 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[6631])).
% 2.54/2.77 tff(12009,plain,
% 2.54/2.77 (~b(z, s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1339, 1331, 5669, 5671])).
% 2.54/2.77 tff(12010,plain,
% 2.54/2.77 (r(z, s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1318, 12009])).
% 2.54/2.77 tff(12011,plain,
% 2.54/2.77 (~b(s(s(s(z))), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[10183, 97, 5669, 5671, 1331])).
% 2.54/2.77 tff(12012,plain,
% 2.54/2.77 (r(s(s(s(z))), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[402, 12011])).
% 2.54/2.77 tff(12013,plain,
% 2.54/2.77 (~r(s(z), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1308, 12012, 12010, 81])).
% 2.54/2.77 tff(12014,plain,
% 2.54/2.77 (b(s(z), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[253, 12013])).
% 2.54/2.77 tff(12015,plain,
% 2.54/2.77 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[6628, 12014, 176])).
% 2.54/2.77 tff(12016,plain,
% 2.54/2.77 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[12015, 12008])).
% 2.54/2.77 tff(12017,plain,
% 2.54/2.77 (~r(s(s(s(z))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[4334, 155, 4300, 81, 12012])).
% 2.54/2.77 tff(12018,plain,
% 2.54/2.77 (b(s(s(s(z))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1358, 12017])).
% 2.54/2.77 tff(12019,plain,
% 2.54/2.77 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2464, 97, 12007, 12018, 12014])).
% 2.54/2.77 tff(12020,plain,
% 2.54/2.77 ((s(s(s(elem!1))) = s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2469, 53, 12019])).
% 2.54/2.77 tff(12021,plain,
% 2.54/2.77 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12020, 12016])).
% 2.54/2.77 tff(12022,plain,
% 2.54/2.77 (((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(12023,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[12022])).
% 2.54/2.77 tff(12024,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[12023, 2483])).
% 2.54/2.77 tff(12025,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(12026,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[12025, 12024])).
% 2.54/2.77 tff(12027,plain,
% 2.54/2.77 (~r(s(s(s(elem!1))), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12026, 155, 12010, 12012, 12021])).
% 2.54/2.77 tff(12028,plain,
% 2.54/2.77 (b(s(s(s(elem!1))), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[246, 12027])).
% 2.54/2.77 tff(12029,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(12030,plain,
% 2.54/2.77 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(12031,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[12030])).
% 2.54/2.77 tff(12032,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[12031, 12029])).
% 2.54/2.77 tff(12033,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(12034,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[12033, 12032])).
% 2.54/2.77 tff(12035,plain,
% 2.54/2.77 (~r(z, s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12034, 155, 4300, 12010, 3009, 12021])).
% 2.54/2.77 tff(12036,plain,
% 2.54/2.77 (b(z, s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[590, 12035])).
% 2.54/2.77 tff(12037,plain,
% 2.54/2.77 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[4987, 12036, 12028, 5671])).
% 2.54/2.77 tff(12038,plain,
% 2.54/2.77 (r(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[143, 12037])).
% 2.54/2.77 tff(12039,plain,
% 2.54/2.77 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[4567, 12028, 5671, 5669])).
% 2.54/2.77 tff(12040,plain,
% 2.54/2.77 (r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[58, 12039])).
% 2.54/2.77 tff(12041,plain,
% 2.54/2.77 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(12042,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[12041])).
% 2.54/2.77 tff(12043,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[12042, 156])).
% 2.54/2.77 tff(12044,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(12045,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[12044, 12043])).
% 2.54/2.77 tff(12046,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12045, 155, 3, 3009, 12040, 12038])).
% 2.54/2.77 tff(12047,plain,((~b(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | b(s(z), s(s(s(elem!1)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(12048,plain,
% 2.54/2.77 (~b(s(s(s(z))), s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12047, 176, 3, 81])).
% 2.54/2.77 tff(12049,plain,
% 2.54/2.77 (r(s(s(s(z))), s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[421, 12048])).
% 2.54/2.77 tff(12050,plain,
% 2.54/2.77 (~r(s(s(s(z))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1656, 155, 5667, 3, 12049])).
% 2.54/2.77 tff(12051,plain,
% 2.54/2.77 (b(s(s(s(z))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1358, 12050])).
% 2.54/2.77 tff(12052,plain,
% 2.54/2.77 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2682, 2508])).
% 2.54/2.77 tff(12053,plain,
% 2.54/2.77 (~b(s(z), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[6628, 12052, 176])).
% 2.54/2.77 tff(12054,plain,
% 2.54/2.77 (r(s(z), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[253, 12053])).
% 2.54/2.77 tff(12055,plain,
% 2.54/2.77 (~r(s(s(z)), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2641, 12054, 3, 1960])).
% 2.54/2.77 tff(12056,plain,
% 2.54/2.77 (b(s(s(z)), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[437, 12055])).
% 2.54/2.77 tff(12057,plain,
% 2.54/2.77 (~b(z, s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1369, 12056, 1139, 3008, 83, 1360])).
% 2.54/2.77 tff(12058,plain,
% 2.54/2.77 (r(z, s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1318, 12057])).
% 2.54/2.77 tff(12059,plain,
% 2.54/2.77 (r(z, s(s(s(elem!1))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[12058, 6370])).
% 2.54/2.77 tff(12060,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[585, 12059])).
% 2.54/2.77 tff(12061,plain,((~(s(s(s(elem!1))) = s(s(s(z))))) | r(z, s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(12062,plain,
% 2.54/2.77 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12061, 585, 12007, 5671, 12051, 3, 12049, 176])).
% 2.54/2.77 tff(12063,plain,
% 2.54/2.77 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5875, 3009, 3, 12005])).
% 2.54/2.77 tff(12064,plain,
% 2.54/2.77 (b(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[143, 12063])).
% 2.54/2.77 tff(12065,plain,
% 2.54/2.77 (~b(s(s(s(elem!1))), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[4987, 3008, 12064, 5671])).
% 2.54/2.77 tff(12066,plain,
% 2.54/2.77 (r(s(s(s(elem!1))), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[246, 12065])).
% 2.54/2.77 tff(12067,plain,
% 2.54/2.77 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[11697, 12066, 12005, 12049, 12007, 3008, 5671, 12051])).
% 2.54/2.77 tff(12068,plain,
% 2.54/2.77 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2687, 12067, 12062])).
% 2.54/2.77 tff(12069,plain,
% 2.54/2.77 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[11989, 12068, 12051, 12007])).
% 2.54/2.77 tff(12070,plain,
% 2.54/2.77 (r(s(z), s(s(s(s(elem!1)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[280, 12069])).
% 2.54/2.77 tff(12071,plain,
% 2.54/2.77 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12003, 225, 81, 5669, 5671])).
% 2.54/2.77 tff(12072,plain,
% 2.54/2.77 (r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[58, 12071])).
% 2.54/2.77 tff(12073,plain,
% 2.54/2.77 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[317, 287, 225, 12072, 3])).
% 2.54/2.77 tff(12074,plain,
% 2.54/2.77 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[336, 12073])).
% 2.54/2.77 tff(12075,plain,
% 2.54/2.77 (~b(z, s(s(s(s(elem!1)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[10421, 287, 225, 2718, 12007, 5671, 12074])).
% 2.54/2.77 tff(12076,plain,
% 2.54/2.77 (r(z, s(s(s(s(elem!1)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1093, 12075])).
% 2.54/2.77 tff(12077,plain,
% 2.54/2.77 (~r(s(s(s(elem!1))), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[4930, 12076, 81, 225, 287])).
% 2.54/2.77 tff(12078,plain,
% 2.54/2.77 (b(s(s(s(elem!1))), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[246, 12077])).
% 2.54/2.77 tff(12079,plain,
% 2.54/2.77 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[4987, 12078, 3008, 5671])).
% 2.54/2.77 tff(12080,plain,
% 2.54/2.77 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[3021, 12076, 585])).
% 2.54/2.77 tff(12081,plain,
% 2.54/2.77 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[486, 12080, 2718])).
% 2.54/2.77 tff(12082,plain,
% 2.54/2.77 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2103, 12081, 3, 225, 287])).
% 2.54/2.77 tff(12083,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[143, 12082, 12079])).
% 2.54/2.77 tff(12084,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(z, s(s(s(elem!1)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(12085,plain,
% 2.54/2.77 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12084, 12070, 3009, 3, 585, 81])).
% 2.54/2.77 tff(12086,plain,
% 2.54/2.77 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[317, 12070, 3009, 12005, 3])).
% 2.54/2.77 tff(12087,plain,
% 2.54/2.77 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[336, 12086])).
% 2.54/2.77 tff(12088,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5546, 12087, 12085, 5671, 81, 4300, 12007, 5669])).
% 2.54/2.77 tff(12089,plain,(r(z, s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(12090,plain,
% 2.54/2.77 (r(z, s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12089, 176, 3, 81])).
% 2.54/2.77 tff(12091,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(12092,plain,
% 2.54/2.77 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(12093,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[12092])).
% 2.54/2.77 tff(12094,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 2.54/2.77 inference(transitivity,[status(thm)],[12093, 12091])).
% 2.54/2.77 tff(12095,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(12096,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[12095, 12094])).
% 2.54/2.77 tff(12097,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12096, 155, 12090, 81, 3, 3009, 12005])).
% 2.54/2.77 tff(12098,plain,(b(s(z), s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(12099,plain,
% 2.54/2.77 (b(s(z), s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12098, 81, 3])).
% 2.54/2.77 tff(12100,plain,
% 2.54/2.77 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1248, 12099, 1245])).
% 2.54/2.77 tff(12101,plain,
% 2.54/2.77 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[523, 12100])).
% 2.54/2.77 tff(12102,plain,
% 2.54/2.77 (~b(s(s(z)), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5665, 81, 3])).
% 2.54/2.77 tff(12103,plain,
% 2.54/2.77 (r(s(s(z)), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[122, 12102])).
% 2.54/2.77 tff(12104,plain,
% 2.54/2.77 (~r(z, s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[871, 155, 11995, 12103, 3])).
% 2.54/2.77 tff(12105,plain,
% 2.54/2.77 (b(z, s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[222, 12104])).
% 2.54/2.77 tff(12106,plain,
% 2.54/2.77 (~r(s(s(z)), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[966, 155, 11995, 81, 12103])).
% 2.54/2.77 tff(12107,plain,
% 2.54/2.77 (b(s(s(z)), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[625, 12106])).
% 2.54/2.77 tff(12108,plain,
% 2.54/2.77 (~r(s(s(s(z))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1656, 155, 12103, 3, 2591])).
% 2.54/2.77 tff(12109,plain,
% 2.54/2.77 (b(s(s(s(z))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1358, 12108])).
% 2.54/2.77 tff(12110,plain,
% 2.54/2.77 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(12111,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[12110])).
% 2.54/2.77 tff(12112,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[12111, 10306])).
% 2.54/2.77 tff(12113,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(12114,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[12113, 12112])).
% 2.54/2.77 tff(12115,plain,
% 2.54/2.77 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12114, 155, 1170, 12103, 3])).
% 2.54/2.77 tff(12116,plain,
% 2.54/2.77 (b(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[511, 12115])).
% 2.54/2.77 tff(12117,plain,
% 2.54/2.77 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[669, 12116, 12107, 4937])).
% 2.54/2.77 tff(12118,plain,
% 2.54/2.77 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[336, 12117])).
% 2.54/2.77 tff(12119,plain,
% 2.54/2.77 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[4141, 4138, 570])).
% 2.54/2.77 tff(12120,plain,
% 2.54/2.77 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[10998, 12116, 12109, 255])).
% 2.54/2.77 tff(12121,plain,
% 2.54/2.77 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1804, 12116, 11997, 12099])).
% 2.54/2.77 tff(12122,plain,
% 2.54/2.77 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[821, 12121, 3701])).
% 2.54/2.77 tff(12123,plain,
% 2.54/2.77 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[11989, 255, 11997, 12109])).
% 2.54/2.77 tff(12124,plain,
% 2.54/2.77 (~r(s(s(s(z))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1656, 155, 12103, 3, 1960])).
% 2.54/2.77 tff(12125,plain,
% 2.54/2.77 (b(s(s(s(z))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1358, 12124])).
% 2.54/2.77 tff(12126,plain,
% 2.54/2.77 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[11980, 255, 11997, 12125])).
% 2.54/2.77 tff(12127,plain,
% 2.54/2.77 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[11989, 255, 11997, 12125])).
% 2.54/2.77 tff(12128,plain,
% 2.54/2.77 (~r(s(s(z)), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5794, 5842, 1960, 145])).
% 2.54/2.77 tff(12129,plain,
% 2.54/2.77 (b(s(s(z)), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[437, 12128])).
% 2.54/2.77 tff(12130,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[11968, 97, 204, 12129, 1360, 7216])).
% 2.54/2.77 tff(12131,plain,((s(s(s(z))) = s(s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | b(s(s(s(z))), s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(12132,plain,
% 2.54/2.77 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[12131, 145, 12125, 1960, 12105, 12127, 12126, 570])).
% 2.54/2.77 tff(12133,plain,
% 2.54/2.77 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[12132])).
% 2.54/2.77 tff(12134,plain,
% 2.54/2.77 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.54/2.77 inference(symmetry,[status(thm)],[12133])).
% 2.54/2.77 tff(12135,plain,
% 2.54/2.77 (s(s(elem!1)) = s(s(z))),
% 2.54/2.77 inference(transitivity,[status(thm)],[167, 12134, 72])).
% 2.54/2.77 tff(12136,plain,
% 2.54/2.77 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[12135])).
% 2.54/2.77 tff(12137,plain,
% 2.54/2.77 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.54/2.77 inference(symmetry,[status(thm)],[12136])).
% 2.54/2.77 tff(12138,plain,
% 2.54/2.77 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[145, 12137])).
% 2.54/2.77 tff(12139,plain,
% 2.54/2.77 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1822, 12132, 1170])).
% 2.54/2.77 tff(12140,plain,
% 2.54/2.77 (s(s(z)) = s(s(elem!1))),
% 2.54/2.77 inference(transitivity,[status(thm)],[73, 12133, 19])).
% 2.54/2.77 tff(12141,plain,
% 2.54/2.77 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[12140])).
% 2.54/2.77 tff(12142,plain,
% 2.54/2.77 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(z)))),
% 2.54/2.78 inference(symmetry,[status(thm)],[12141])).
% 2.54/2.78 tff(12143,plain,
% 2.54/2.78 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[12140])).
% 2.54/2.78 tff(12144,plain,
% 2.54/2.78 (s(z) = s(elem!1)),
% 2.54/2.78 inference(transitivity,[status(thm)],[24, 12143, 29])).
% 2.54/2.78 tff(12145,plain,
% 2.54/2.78 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[12144, 12140])).
% 2.54/2.78 tff(12146,plain,
% 2.54/2.78 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 2.54/2.78 inference(transitivity,[status(thm)],[12145, 12142])).
% 2.54/2.78 tff(12147,plain,
% 2.54/2.78 (r(s(elem!1), s(s(z)))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[3, 12146])).
% 2.54/2.78 tff(12148,plain,
% 2.54/2.78 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[12140, 12144])).
% 2.54/2.78 tff(12149,plain,
% 2.54/2.78 (r(s(s(elem!1)), s(elem!1))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[12103, 12148])).
% 2.54/2.78 tff(12150,plain,
% 2.54/2.78 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1816, 495, 1812, 1393, 1520])).
% 2.54/2.78 tff(12151,plain,
% 2.54/2.78 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1822, 12150, 1393])).
% 2.54/2.78 tff(12152,plain,
% 2.54/2.78 (~r(s(s(s(s(elem!1)))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4414, 495, 81, 729])).
% 2.54/2.78 tff(12153,plain,
% 2.54/2.78 (b(s(s(s(s(elem!1)))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[842, 12152])).
% 2.54/2.78 tff(12154,plain,
% 2.54/2.78 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[884, 12153, 204, 83])).
% 2.54/2.78 tff(12155,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[452, 12154, 12151])).
% 2.54/2.78 tff(12156,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(12157,plain,
% 2.54/2.78 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12156, 12149, 11995, 12107, 12132, 12147, 81, 12105])).
% 2.54/2.78 tff(12158,plain,
% 2.54/2.78 (b(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[511, 12157])).
% 2.54/2.78 tff(12159,plain,
% 2.54/2.78 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1804, 12158, 11997, 12099])).
% 2.54/2.78 tff(12160,plain,
% 2.54/2.78 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[821, 12159, 3701])).
% 2.54/2.78 tff(12161,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(12162,plain,
% 2.54/2.78 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(12163,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[12162])).
% 2.54/2.78 tff(12164,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.54/2.78 inference(transitivity,[status(thm)],[12163, 12161])).
% 2.54/2.78 tff(12165,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(12166,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[12165, 12164])).
% 2.54/2.78 tff(12167,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12166, 155, 570, 1813, 4497, 824, 823])).
% 2.54/2.78 tff(12168,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(12169,plain,
% 2.54/2.78 (~r(s(s(s(s(elem!1)))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12168, 12160, 570, 12139, 12138])).
% 2.54/2.78 tff(12170,plain,
% 2.54/2.78 (b(s(s(s(s(elem!1)))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[842, 12169])).
% 2.54/2.78 tff(12171,plain,
% 2.54/2.78 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[669, 12158, 12107, 372])).
% 2.54/2.78 tff(12172,plain,
% 2.54/2.78 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[336, 12171])).
% 2.54/2.78 tff(12173,plain,
% 2.54/2.78 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[5279, 12172, 1170, 145])).
% 2.54/2.78 tff(12174,plain,
% 2.54/2.78 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[486, 12173, 472])).
% 2.54/2.78 tff(12175,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[5308, 12174, 12170, 11997, 255])).
% 2.54/2.78 tff(12176,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(12177,plain,
% 2.54/2.78 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12176, 255, 472, 1170, 570, 372, 81, 3, 2591])).
% 2.54/2.78 tff(12178,plain,
% 2.54/2.78 (b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[58, 12177])).
% 2.54/2.78 tff(12179,plain,
% 2.54/2.78 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2677, 12178, 2590])).
% 2.54/2.78 tff(12180,plain,
% 2.54/2.78 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2682, 12179])).
% 2.54/2.78 tff(12181,plain,
% 2.54/2.78 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2687, 12180, 12123])).
% 2.54/2.78 tff(12182,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(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))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(12183,plain,
% 2.54/2.78 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), 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(elem!1)))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(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))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(12184,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), 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(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(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)))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[12183])).
% 2.54/2.78 tff(12185,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), 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(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(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))))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[12184, 12182])).
% 2.54/2.78 tff(12186,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), 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(elem!1))))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(12187,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[12186, 12185])).
% 2.54/2.78 tff(12188,plain,
% 2.54/2.78 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12187, 155, 1170, 2591, 12181])).
% 2.54/2.78 tff(12189,plain,
% 2.54/2.78 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12188, 12122])).
% 2.54/2.78 tff(12190,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[384, 53, 12189, 12120, 286])).
% 2.54/2.78 tff(12191,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | b(s(s(s(z))), s(s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(12192,plain,
% 2.54/2.78 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12191, 12119, 3, 2590, 1170, 570, 4937, 81])).
% 2.54/2.78 tff(12193,plain,
% 2.54/2.78 (r(s(z), s(s(s(s(elem!1)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[280, 12192])).
% 2.54/2.78 tff(12194,plain,
% 2.54/2.78 (((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(12195,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[12194])).
% 2.54/2.78 tff(12196,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[12195, 889])).
% 2.54/2.78 tff(12197,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(12198,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[12197, 12196])).
% 2.54/2.78 tff(12199,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12198, 155, 12193, 12118, 1170, 3])).
% 2.54/2.78 tff(12200,plain,(r(z, s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | b(s(s(s(z))), s(s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(12201,plain,
% 2.54/2.78 (r(z, s(s(s(s(elem!1)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12200, 1170, 3, 2590, 570, 81])).
% 2.54/2.78 tff(12202,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(12203,plain,
% 2.54/2.78 (((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(12204,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[12203])).
% 2.54/2.78 tff(12205,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[12204, 12202])).
% 2.54/2.78 tff(12206,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z)))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(12207,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[12206, 12205])).
% 2.54/2.78 tff(12208,plain,
% 2.54/2.78 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12207, 155, 12201, 81, 1170, 3])).
% 2.54/2.78 tff(12209,plain,
% 2.54/2.78 (b(s(z), s(s(s(s(elem!1)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[280, 12208])).
% 2.54/2.78 tff(12210,plain,
% 2.54/2.78 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(12211,plain,
% 2.54/2.78 (((~![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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[12210])).
% 2.54/2.78 tff(12212,plain,
% 2.54/2.78 (((~![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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[12211, 5192])).
% 2.54/2.78 tff(12213,plain,
% 2.54/2.78 ((~![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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(12214,plain,
% 2.54/2.78 ((~![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(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[12213, 12212])).
% 2.54/2.78 tff(12215,plain,
% 2.54/2.78 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12214, 97, 12209, 12116, 12109])).
% 2.54/2.78 tff(12216,plain,
% 2.54/2.78 ((s(s(s(z))) = s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4836, 53, 12215])).
% 2.54/2.78 tff(12217,plain,
% 2.54/2.78 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12216, 4298])).
% 2.54/2.78 tff(12218,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(12219,plain,
% 2.54/2.78 (((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(12220,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[12219])).
% 2.54/2.78 tff(12221,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[12220, 12218])).
% 2.54/2.78 tff(12222,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(12223,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[12222, 12221])).
% 2.54/2.78 tff(12224,plain,
% 2.54/2.78 ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12223, 155, 12201, 1170, 2591])).
% 2.54/2.78 tff(12225,plain,
% 2.54/2.78 (~r(s(s(s(z))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12224, 12217])).
% 2.54/2.78 tff(12226,plain,
% 2.54/2.78 (b(s(s(s(z))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[402, 12225])).
% 2.54/2.78 tff(12227,plain,
% 2.54/2.78 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[10998, 12209, 12109, 12116])).
% 2.54/2.78 tff(12228,plain,
% 2.54/2.78 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[384, 53, 12227, 286])).
% 2.54/2.78 tff(12229,plain,
% 2.54/2.78 (~r(z, s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2449, 12217, 12201, 12228])).
% 2.54/2.78 tff(12230,plain,
% 2.54/2.78 (b(z, s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1318, 12229])).
% 2.54/2.78 tff(12231,plain,
% 2.54/2.78 (~b(s(s(z)), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[9409, 97, 12107, 12230, 12226])).
% 2.54/2.78 tff(12232,plain,
% 2.54/2.78 (r(s(s(z)), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[437, 12231])).
% 2.54/2.78 tff(12233,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[11560, 155, 1170, 12228, 12232, 2591])).
% 2.54/2.79 tff(12234,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | b(s(s(s(z))), s(s(z))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(12235,plain,
% 2.54/2.79 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[12234, 570, 2590, 3, 81])).
% 2.54/2.79 tff(12236,plain,
% 2.54/2.79 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[452, 12235])).
% 2.54/2.79 tff(12237,plain,
% 2.54/2.79 (~b(s(s(s(s(elem!1)))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[884, 12236, 12105, 12107])).
% 2.54/2.79 tff(12238,plain,
% 2.54/2.79 (r(s(s(s(s(elem!1)))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[842, 12237])).
% 2.54/2.79 tff(12239,plain,
% 2.54/2.79 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[4414, 12238, 81, 11995])).
% 2.54/2.79 tff(12240,plain,
% 2.54/2.79 (b(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[511, 12239])).
% 2.54/2.79 tff(12241,plain,
% 2.54/2.79 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1804, 12240, 11997, 12099])).
% 2.54/2.79 tff(12242,plain,
% 2.54/2.79 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[821, 12241, 802])).
% 2.54/2.79 tff(12243,plain,
% 2.54/2.79 (~r(s(s(s(elem!1))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[832, 12242, 570, 12238])).
% 2.54/2.79 tff(12244,plain,
% 2.54/2.79 (b(s(s(s(elem!1))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[246, 12243])).
% 2.54/2.79 tff(12245,plain,
% 2.54/2.79 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5648, 12244, 12099, 11995, 3, 12105, 11997, 2591])).
% 2.54/2.79 tff(12246,plain,
% 2.54/2.79 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[4567, 12244, 12107, 12105])).
% 2.54/2.79 tff(12247,plain,
% 2.54/2.79 (r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[58, 12246])).
% 2.54/2.79 tff(12248,plain,
% 2.54/2.79 (~r(z, s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[4887, 12238, 287, 81])).
% 2.54/2.79 tff(12249,plain,
% 2.54/2.79 (b(z, s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1093, 12248])).
% 2.54/2.79 tff(12250,plain,
% 2.54/2.79 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[669, 12249, 12107, 12240])).
% 2.54/2.79 tff(12251,plain,
% 2.54/2.79 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[336, 12250])).
% 2.54/2.79 tff(12252,plain,
% 2.54/2.79 (~r(s(z), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2171, 12251, 3, 287, 2591])).
% 2.54/2.79 tff(12253,plain,
% 2.54/2.79 (b(s(z), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[253, 12252])).
% 2.54/2.79 tff(12254,plain,
% 2.54/2.79 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2464, 97, 11997, 12109, 12253])).
% 2.54/2.79 tff(12255,plain,
% 2.54/2.79 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[12131, 12254, 12109, 2591, 12105, 12247, 12245, 570])).
% 2.54/2.79 tff(12256,plain,
% 2.54/2.79 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12255])).
% 2.54/2.79 tff(12257,plain,
% 2.54/2.79 (s(s(z)) = s(s(elem!1))),
% 2.54/2.79 inference(transitivity,[status(thm)],[73, 12256, 19])).
% 2.54/2.79 tff(12258,plain,
% 2.54/2.79 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12257])).
% 2.54/2.79 tff(12259,plain,
% 2.54/2.79 (s(z) = s(elem!1)),
% 2.54/2.79 inference(transitivity,[status(thm)],[24, 12258, 29])).
% 2.54/2.79 tff(12260,plain,
% 2.54/2.79 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12259, 12257])).
% 2.54/2.79 tff(12261,plain,
% 2.54/2.79 (r(s(elem!1), s(s(elem!1)))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[3, 12260])).
% 2.54/2.79 tff(12262,plain,
% 2.54/2.79 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1909, 12255, 287])).
% 2.54/2.79 tff(12263,plain,
% 2.54/2.79 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12259])).
% 2.54/2.79 tff(12264,plain,
% 2.54/2.79 (z = elem!1),
% 2.54/2.79 inference(transitivity,[status(thm)],[1443, 12263, 85])).
% 2.54/2.79 tff(12265,plain,
% 2.54/2.79 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12264])).
% 2.54/2.79 tff(12266,plain,
% 2.54/2.79 (r(s(z), z) <=> r(s(elem!1), z)),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12259])).
% 2.54/2.79 tff(12267,plain,
% 2.54/2.79 (r(s(elem!1), z)),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[81, 12266])).
% 2.54/2.79 tff(12268,plain,
% 2.54/2.79 (r(s(elem!1), elem!1)),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[12267, 12265])).
% 2.54/2.79 tff(12269,plain,
% 2.54/2.79 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[3107, 12255, 12238])).
% 2.54/2.79 tff(12270,plain,
% 2.54/2.79 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12257])).
% 2.54/2.79 tff(12271,plain,
% 2.54/2.79 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[12251, 12270])).
% 2.54/2.79 tff(12272,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(12273,plain,
% 2.54/2.79 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(12274,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12273])).
% 2.54/2.79 tff(12275,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[12274, 12272])).
% 2.54/2.79 tff(12276,plain,
% 2.54/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(12277,plain,
% 2.54/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[12276, 12275])).
% 2.54/2.79 tff(12278,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[12277, 155, 12271, 12269, 12268, 12262, 12261])).
% 2.54/2.79 tff(12279,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(12280,plain,
% 2.54/2.79 (~r(z, s(s(s(elem!1))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[12279, 81, 3, 8703, 12101, 2590])).
% 2.54/2.79 tff(12281,plain,
% 2.54/2.79 (b(z, s(s(s(elem!1))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[590, 12280])).
% 2.54/2.79 tff(12282,plain,
% 2.54/2.79 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5438, 12281, 3, 12099, 11997, 2591, 11995])).
% 2.54/2.79 tff(12283,plain,
% 2.54/2.79 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[306, 12281, 12105, 12107])).
% 2.54/2.79 tff(12284,plain,
% 2.54/2.79 (r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[58, 12283])).
% 2.54/2.79 tff(12285,plain,
% 2.54/2.79 (~b(z, s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1369, 5224, 11997, 124, 12107, 12125])).
% 2.54/2.79 tff(12286,plain,
% 2.54/2.79 (r(z, s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1318, 12285])).
% 2.54/2.79 tff(12287,plain,
% 2.54/2.79 (~r(s(s(s(z))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1308, 12286, 81, 338])).
% 2.54/2.79 tff(12288,plain,
% 2.54/2.79 (b(s(s(s(z))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[402, 12287])).
% 2.54/2.79 tff(12289,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5406, 97, 124, 12107, 5224, 12288])).
% 2.54/2.79 tff(12290,plain,((~r(s(z), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(12291,plain,
% 2.54/2.79 (~r(s(z), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[12290, 12281, 81, 3, 2591])).
% 2.54/2.79 tff(12292,plain,
% 2.54/2.79 (b(s(z), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[253, 12291])).
% 2.54/2.79 tff(12293,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2464, 97, 1139, 1360, 86, 5941])).
% 2.54/2.79 tff(12294,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(12295,plain,
% 2.54/2.79 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[12294, 12292, 12109, 11997])).
% 2.54/2.79 tff(12296,plain,
% 2.54/2.79 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[11703, 12295, 2591, 12107, 12281, 12109, 11997, 12284, 12282])).
% 2.54/2.79 tff(12297,plain,
% 2.54/2.79 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12296])).
% 2.54/2.79 tff(12298,plain,
% 2.54/2.79 (s(s(z)) = s(s(elem!1))),
% 2.54/2.79 inference(transitivity,[status(thm)],[73, 12297, 19])).
% 2.54/2.79 tff(12299,plain,
% 2.54/2.79 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12298])).
% 2.54/2.79 tff(12300,plain,
% 2.54/2.79 (s(z) = s(elem!1)),
% 2.54/2.79 inference(transitivity,[status(thm)],[24, 12299, 29])).
% 2.54/2.79 tff(12301,plain,
% 2.54/2.79 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12300, 12298])).
% 2.54/2.79 tff(12302,plain,
% 2.54/2.79 (r(s(elem!1), s(s(elem!1)))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[3, 12301])).
% 2.54/2.79 tff(12303,plain,
% 2.54/2.79 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1909, 12296, 8703])).
% 2.54/2.79 tff(12304,plain,
% 2.54/2.79 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12300])).
% 2.54/2.79 tff(12305,plain,
% 2.54/2.79 (z = elem!1),
% 2.54/2.79 inference(transitivity,[status(thm)],[1443, 12304, 85])).
% 2.54/2.79 tff(12306,plain,
% 2.54/2.79 (r(z, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12305])).
% 2.54/2.79 tff(12307,plain,
% 2.54/2.79 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5438, 124, 3, 12099, 11997, 1960, 11995])).
% 2.54/2.79 tff(12308,plain,
% 2.54/2.79 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[306, 124, 12105, 12107])).
% 2.54/2.79 tff(12309,plain,
% 2.54/2.79 (r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[58, 12308])).
% 2.54/2.79 tff(12310,plain,
% 2.54/2.79 (~r(s(z), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5241, 372, 11997, 12107, 81, 3, 1960, 124])).
% 2.54/2.79 tff(12311,plain,
% 2.54/2.79 (b(s(z), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[253, 12310])).
% 2.54/2.79 tff(12312,plain,
% 2.54/2.79 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2464, 97, 11997, 12125, 12311])).
% 2.54/2.79 tff(12313,plain,
% 2.54/2.79 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[11703, 12312, 1960, 12107, 124, 12125, 11997, 12309, 12307])).
% 2.54/2.79 tff(12314,plain,
% 2.54/2.79 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12313])).
% 2.54/2.79 tff(12315,plain,
% 2.54/2.79 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.54/2.79 inference(symmetry,[status(thm)],[12314])).
% 2.54/2.79 tff(12316,plain,
% 2.54/2.79 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[701, 513, 124, 372])).
% 2.54/2.79 tff(12317,plain,
% 2.54/2.79 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[486, 12316, 472])).
% 2.54/2.79 tff(12318,plain,
% 2.54/2.79 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[306, 124, 204, 83])).
% 2.54/2.79 tff(12319,plain,
% 2.54/2.79 (r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[58, 12318])).
% 2.54/2.79 tff(12320,plain,
% 2.54/2.79 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[669, 513, 83, 372])).
% 2.54/2.79 tff(12321,plain,
% 2.54/2.79 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[336, 12320])).
% 2.54/2.79 tff(12322,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(12323,plain,
% 2.54/2.79 (((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~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(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(12324,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12323])).
% 2.54/2.79 tff(12325,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[12324, 12322])).
% 2.54/2.79 tff(12326,plain,
% 2.54/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~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))))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(12327,plain,
% 2.54/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[12326, 12325])).
% 2.54/2.79 tff(12328,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[12327, 155, 488, 309, 145, 1960, 2630])).
% 2.54/2.79 tff(12329,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(12330,plain,
% 2.54/2.79 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[12329, 12321, 12319, 1960, 12317])).
% 2.54/2.79 tff(12331,plain,
% 2.54/2.79 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2687, 12330, 2684])).
% 2.54/2.79 tff(12332,plain,
% 2.54/2.79 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12331])).
% 2.54/2.79 tff(12333,plain,
% 2.54/2.79 (s(s(elem!1)) = s(s(z))),
% 2.54/2.79 inference(transitivity,[status(thm)],[167, 12332, 72])).
% 2.54/2.79 tff(12334,plain,
% 2.54/2.79 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12333])).
% 2.54/2.79 tff(12335,plain,
% 2.54/2.79 (s(elem!1) = s(z)),
% 2.54/2.79 inference(transitivity,[status(thm)],[30, 12334, 23])).
% 2.54/2.79 tff(12336,plain,
% 2.54/2.79 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12335])).
% 2.54/2.79 tff(12337,plain,
% 2.54/2.79 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 2.54/2.79 inference(symmetry,[status(thm)],[12336])).
% 2.54/2.79 tff(12338,plain,
% 2.54/2.79 (inj_0(s(elem!1)) = inj_0(s(z))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12335])).
% 2.54/2.79 tff(12339,plain,
% 2.54/2.79 (elem!1 = z),
% 2.54/2.79 inference(transitivity,[status(thm)],[1450, 12338, 17])).
% 2.54/2.79 tff(12340,plain,
% 2.54/2.79 (r(s(z), elem!1) <=> r(s(z), z)),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12339])).
% 2.54/2.79 tff(12341,plain,
% 2.54/2.79 (r(s(z), z) <=> r(s(z), elem!1)),
% 2.54/2.79 inference(symmetry,[status(thm)],[12340])).
% 2.54/2.79 tff(12342,plain,
% 2.54/2.79 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 2.54/2.79 inference(transitivity,[status(thm)],[12341, 12337])).
% 2.54/2.79 tff(12343,plain,
% 2.54/2.79 (r(s(elem!1), elem!1)),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[81, 12342])).
% 2.54/2.79 tff(12344,plain,
% 2.54/2.79 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12333])).
% 2.54/2.79 tff(12345,plain,
% 2.54/2.79 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.54/2.79 inference(symmetry,[status(thm)],[12344])).
% 2.54/2.79 tff(12346,plain,
% 2.54/2.79 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5279, 12317, 12319, 12321])).
% 2.54/2.79 tff(12347,plain,
% 2.54/2.79 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[452, 12346])).
% 2.54/2.79 tff(12348,plain,
% 2.54/2.79 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[12347, 12345])).
% 2.54/2.79 tff(12349,plain,
% 2.54/2.79 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 2.54/2.79 inference(commutativity,[status(thm)],[])).
% 2.54/2.79 tff(12350,plain,
% 2.54/2.79 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12331])).
% 2.54/2.79 tff(12351,plain,
% 2.54/2.79 ((s(s(s(s(elem!1)))) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12350])).
% 2.54/2.79 tff(12352,plain,
% 2.54/2.79 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[12351, 12349])).
% 2.54/2.79 tff(12353,plain,
% 2.54/2.79 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.54/2.79 inference(symmetry,[status(thm)],[12352])).
% 2.54/2.79 tff(12354,plain,
% 2.54/2.79 ((elem!1 = s(s(s(s(z))))) <=> (z = s(s(s(s(z)))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12339])).
% 2.54/2.79 tff(12355,plain,
% 2.54/2.79 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 2.54/2.79 inference(transitivity,[status(thm)],[12354, 7408])).
% 2.54/2.79 tff(12356,plain,
% 2.54/2.79 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 2.54/2.79 inference(symmetry,[status(thm)],[12355])).
% 2.54/2.79 tff(12357,plain,
% 2.54/2.79 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[12356, 12353, 1901])).
% 2.54/2.79 tff(12358,plain,
% 2.54/2.79 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12357])).
% 2.54/2.79 tff(12359,plain,
% 2.54/2.79 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[2856, 12358])).
% 2.54/2.79 tff(12360,plain,
% 2.54/2.79 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.54/2.79 inference(transitivity,[status(thm)],[12356, 12353])).
% 2.54/2.79 tff(12361,plain,
% 2.54/2.79 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12360])).
% 2.54/2.79 tff(12362,plain,
% 2.54/2.79 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[2856, 12361])).
% 2.54/2.79 tff(12363,plain,
% 2.54/2.79 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2682, 12331])).
% 2.54/2.79 tff(12364,plain,
% 2.54/2.79 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1909, 12363, 287])).
% 2.54/2.79 tff(12365,plain,
% 2.54/2.79 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12333])).
% 2.54/2.79 tff(12366,plain,
% 2.54/2.79 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.54/2.79 inference(symmetry,[status(thm)],[12365])).
% 2.54/2.79 tff(12367,plain,
% 2.54/2.79 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12339])).
% 2.54/2.79 tff(12368,plain,
% 2.54/2.79 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 2.54/2.79 inference(symmetry,[status(thm)],[12367])).
% 2.54/2.79 tff(12369,plain,
% 2.54/2.79 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.54/2.79 inference(transitivity,[status(thm)],[12368, 12366])).
% 2.54/2.79 tff(12370,plain,
% 2.54/2.79 (b(s(s(elem!1)), elem!1)),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[83, 12369])).
% 2.54/2.79 tff(12371,plain,
% 2.54/2.79 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12333])).
% 2.54/2.79 tff(12372,plain,
% 2.54/2.79 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 2.54/2.79 inference(symmetry,[status(thm)],[12371])).
% 2.54/2.79 tff(12373,plain,
% 2.54/2.79 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12339])).
% 2.54/2.79 tff(12374,plain,
% 2.54/2.79 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.54/2.79 inference(symmetry,[status(thm)],[12373])).
% 2.54/2.79 tff(12375,plain,
% 2.54/2.79 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 2.54/2.79 inference(transitivity,[status(thm)],[12374, 12372])).
% 2.54/2.79 tff(12376,plain,
% 2.54/2.79 (b(elem!1, s(s(elem!1)))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[204, 12375])).
% 2.54/2.79 tff(12377,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1949, 12376, 12370, 12364, 12362, 12359, 12348, 12343])).
% 2.54/2.79 tff(12378,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~r(s(z), z)) | (~b(s(s(z)), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(12379,plain,
% 2.54/2.79 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[12378, 12312, 81, 12107, 287, 12105, 1960, 472, 372, 124])).
% 2.54/2.79 tff(12380,plain,
% 2.54/2.79 (r(s(s(s(s(elem!1)))), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[511, 12379])).
% 2.54/2.79 tff(12381,plain,
% 2.54/2.79 (~r(s(s(s(s(elem!1)))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[4414, 12380, 81, 11995])).
% 2.54/2.79 tff(12382,plain,
% 2.54/2.79 (b(s(s(s(s(elem!1)))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[842, 12381])).
% 2.54/2.79 tff(12383,plain,
% 2.54/2.79 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[884, 12382, 12105, 12107])).
% 2.54/2.79 tff(12384,plain,
% 2.54/2.79 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[452, 12383])).
% 2.54/2.79 tff(12385,plain,
% 2.54/2.79 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[3793, 12382, 124, 372])).
% 2.54/2.79 tff(12386,plain,
% 2.54/2.79 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[486, 12385, 472])).
% 2.54/2.79 tff(12387,plain,
% 2.54/2.79 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5279, 12386, 12309, 12384])).
% 2.54/2.79 tff(12388,plain,
% 2.54/2.79 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[336, 12387])).
% 2.54/2.79 tff(12389,plain,
% 2.54/2.79 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1822, 12313, 12384])).
% 2.54/2.79 tff(12390,plain,
% 2.54/2.79 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5391, 12389, 12099, 11995, 3, 12107, 1960, 11997, 12388, 12309, 3701, 372])).
% 2.54/2.79 tff(12391,plain,
% 2.54/2.79 (b(s(s(z)), s(s(s(elem!1))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[143, 12390])).
% 2.54/2.79 tff(12392,plain,
% 2.54/2.79 (b(s(s(z)), s(s(s(z))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[12391, 12315])).
% 2.54/2.79 tff(12393,plain,
% 2.54/2.79 (b(z, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12313])).
% 2.54/2.79 tff(12394,plain,
% 2.54/2.79 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 2.54/2.79 inference(symmetry,[status(thm)],[12393])).
% 2.54/2.79 tff(12395,plain,
% 2.54/2.79 (b(z, s(s(s(z))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[124, 12394])).
% 2.54/2.79 tff(12396,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1369, 12395, 12392, 11997, 124, 12107, 12125])).
% 2.54/2.79 tff(12397,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(12398,plain,
% 2.54/2.79 (~b(z, s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[12397, 12281, 3, 2591, 12100, 81, 8703])).
% 2.54/2.79 tff(12399,plain,
% 2.54/2.79 (r(z, s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1093, 12398])).
% 2.54/2.79 tff(12400,plain,
% 2.54/2.79 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[12399, 12306])).
% 2.54/2.79 tff(12401,plain,
% 2.54/2.79 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12305])).
% 2.54/2.79 tff(12402,plain,
% 2.54/2.79 (r(s(z), z) <=> r(s(elem!1), z)),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12300])).
% 2.54/2.79 tff(12403,plain,
% 2.54/2.79 (r(s(elem!1), z)),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[81, 12402])).
% 2.54/2.79 tff(12404,plain,
% 2.54/2.79 (r(s(elem!1), elem!1)),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[12403, 12401])).
% 2.54/2.79 tff(12405,plain,
% 2.54/2.79 (~r(s(s(s(s(elem!1)))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[4887, 12399, 8703, 81])).
% 2.54/2.79 tff(12406,plain,
% 2.54/2.79 (b(s(s(s(s(elem!1)))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[842, 12405])).
% 2.54/2.79 tff(12407,plain,
% 2.54/2.79 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[884, 12406, 12105, 12107])).
% 2.54/2.79 tff(12408,plain,
% 2.54/2.79 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[452, 12407])).
% 2.54/2.79 tff(12409,plain,
% 2.54/2.79 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1822, 12296, 12408])).
% 2.54/2.79 tff(12410,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(12411,plain,
% 2.54/2.79 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(12412,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12411])).
% 2.54/2.79 tff(12413,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[12412, 12410])).
% 2.54/2.79 tff(12414,plain,
% 2.54/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(12415,plain,
% 2.54/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[12414, 12413])).
% 2.54/2.79 tff(12416,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[12415, 155, 12409, 12404, 12400, 12303, 12302])).
% 2.54/2.79 tff(12417,plain,((~r(s(z), z)) | (~r(s(z), s(s(z)))) | b(s(s(s(z))), s(s(z))) | b(s(z), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(12418,plain,
% 2.54/2.79 (~r(s(z), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[12417, 11993, 2590, 3])).
% 2.54/2.79 tff(12419,plain,
% 2.54/2.79 (b(s(z), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[568, 12418])).
% 2.54/2.79 tff(12420,plain,
% 2.54/2.79 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[10125, 97, 1139, 12419, 1360])).
% 2.54/2.79 tff(12421,plain,
% 2.54/2.79 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[10132, 97, 1139, 12419, 1360])).
% 2.54/2.79 tff(12422,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5852, 12421, 12420, 1300, 1, 570])).
% 2.54/2.79 tff(12423,plain,((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | b(s(s(s(z))), s(s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(12424,plain,
% 2.54/2.79 (~r(z, s(s(s(elem!1))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[12423, 11972, 1, 1139, 1360, 2590, 3])).
% 2.54/2.79 tff(12425,plain,
% 2.54/2.79 (b(z, s(s(s(elem!1))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[590, 12424])).
% 2.54/2.79 tff(12426,plain,
% 2.54/2.79 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[6479, 12425, 11962, 1361])).
% 2.54/2.79 tff(12427,plain,
% 2.54/2.79 (r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[58, 12426])).
% 2.54/2.79 tff(12428,plain,
% 2.54/2.79 (~b(s(s(s(elem!1))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[10212, 550, 1139, 204])).
% 2.54/2.79 tff(12429,plain,
% 2.54/2.79 (r(s(s(s(elem!1))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[246, 12428])).
% 2.54/2.79 tff(12430,plain,
% 2.54/2.79 ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[11695, 155, 1300, 145, 1960])).
% 2.54/2.80 tff(12431,plain,
% 2.54/2.80 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[12430, 12429])).
% 2.54/2.80 tff(12432,plain,
% 2.54/2.80 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[2687, 12431, 2466])).
% 2.54/2.80 tff(12433,plain,
% 2.54/2.80 ($false),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[10132, 97, 1139, 550, 1360, 12432])).
% 2.54/2.80 tff(12434,plain,((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.80 tff(12435,plain,
% 2.54/2.80 (~b(s(z), z)),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[12434, 11972, 1360, 4228, 1139, 12427, 2591, 11962])).
% 2.54/2.80 tff(12436,plain,
% 2.54/2.80 (r(s(z), z)),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[568, 12435])).
% 2.54/2.80 tff(12437,plain,
% 2.54/2.80 (b(s(z), s(s(s(elem!1))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[12098, 12436, 3])).
% 2.54/2.80 tff(12438,plain,
% 2.54/2.80 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[5438, 12437, 3, 12425, 1139, 2591, 729])).
% 2.54/2.80 tff(12439,plain,
% 2.54/2.80 (b(s(z), s(s(s(s(elem!1)))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[12417, 12436, 2590, 3])).
% 2.54/2.80 tff(12440,plain,
% 2.54/2.80 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[11989, 12439, 1139, 1360])).
% 2.54/2.80 tff(12441,plain,
% 2.54/2.80 (~b(s(s(z)), z)),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[11703, 12440, 2591, 1, 12425, 1360, 1139, 12427, 12438])).
% 2.54/2.80 tff(12442,plain,
% 2.54/2.80 (r(s(s(z)), z)),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[625, 12441])).
% 2.54/2.80 tff(12443,plain,
% 2.54/2.80 ($false),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[966, 155, 729, 12436, 12442, 11960])).
% 2.54/2.80 tff(12444,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(z, s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.80 tff(12445,plain,
% 2.54/2.80 ((~b(s(s(z)), s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | b(s(s(s(z))), s(s(z)))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[12444, 11419])).
% 2.54/2.80 tff(12446,plain,
% 2.54/2.80 (~b(s(s(s(z))), s(z))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[12445, 2590, 3, 1139, 1361, 1])).
% 2.54/2.80 tff(12447,plain,
% 2.54/2.80 (~r(s(s(s(z))), s(z))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[2930, 2591, 2, 3])).
% 2.54/2.80 tff(12448,plain,
% 2.54/2.80 ($false),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[1358, 12447, 12446])).
% 2.54/2.80 tff(12449,plain,(b(s(s(s(z))), s(s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.80 tff(12450,plain,
% 2.54/2.80 (b(s(s(s(z))), s(s(z)))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[12449, 1, 3, 11948, 1361, 2])).
% 2.54/2.80 tff(12451,plain,
% 2.54/2.80 (~b(s(s(s(z))), z)),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[2205, 12450, 204, 1361])).
% 2.54/2.80 tff(12452,plain,
% 2.54/2.80 (r(s(s(s(z))), z)),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[402, 12451])).
% 2.54/2.80 tff(12453,plain,
% 2.54/2.80 (~b(z, s(z))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[10600, 204, 1331, 1, 1139, 645, 3])).
% 2.54/2.80 tff(12454,plain,
% 2.54/2.80 (r(z, s(z))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[723, 12453])).
% 2.54/2.80 tff(12455,plain,
% 2.54/2.80 (~r(s(z), z)),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[11824, 12454, 645, 3])).
% 2.54/2.80 tff(12456,plain,
% 2.54/2.80 (b(s(z), z)),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[568, 12455])).
% 2.54/2.80 tff(12457,plain,
% 2.54/2.80 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[10132, 97, 1139, 12456, 1360])).
% 2.54/2.80 tff(12458,plain,
% 2.54/2.80 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[2687, 12457, 4228])).
% 2.54/2.80 tff(12459,plain,
% 2.54/2.80 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[10125, 97, 1139, 12456, 1360])).
% 2.54/2.80 tff(12460,plain,
% 2.54/2.80 (~b(s(s(s(elem!1))), z)),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[10212, 12456, 1139, 204])).
% 2.54/2.80 tff(12461,plain,
% 2.54/2.80 (r(s(s(s(elem!1))), z)),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[246, 12460])).
% 2.54/2.80 tff(12462,plain,
% 2.54/2.80 (~b(z, s(s(s(z))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[11970, 1361, 204, 1360])).
% 2.54/2.80 tff(12463,plain,
% 2.54/2.80 (r(z, s(s(s(z))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[1318, 12462])).
% 2.54/2.80 tff(12464,plain,
% 2.54/2.80 (~r(z, s(s(s(elem!1))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[5852, 12463, 2684, 1, 3087])).
% 2.54/2.80 tff(12465,plain,
% 2.54/2.80 (b(z, s(s(s(elem!1))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[590, 12464])).
% 2.54/2.80 tff(12466,plain,
% 2.54/2.80 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[6479, 12465, 204, 1361])).
% 2.54/2.80 tff(12467,plain,
% 2.54/2.80 (r(s(s(s(elem!1))), s(s(z)))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[58, 12466])).
% 2.54/2.80 tff(12468,plain,
% 2.54/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(12469,plain,
% 2.64/2.80 (((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(12470,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[12469])).
% 2.64/2.80 tff(12471,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.64/2.80 inference(transitivity,[status(thm)],[12470, 12468])).
% 2.64/2.80 tff(12472,plain,
% 2.64/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(12473,plain,
% 2.64/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[12472, 12471])).
% 2.64/2.80 tff(12474,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12473, 155, 288, 645, 12463, 12467, 4229])).
% 2.64/2.80 tff(12475,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~b(z, s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(12476,plain,
% 2.64/2.80 (~b(s(s(z)), s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12475, 12461, 645, 204, 12457, 1, 12459, 1360])).
% 2.64/2.80 tff(12477,plain,
% 2.64/2.80 (r(s(s(z)), s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[437, 12476])).
% 2.64/2.80 tff(12478,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(12479,plain,
% 2.64/2.80 (((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(12480,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[12479])).
% 2.64/2.80 tff(12481,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.64/2.80 inference(transitivity,[status(thm)],[12480, 12478])).
% 2.64/2.80 tff(12482,plain,
% 2.64/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(12483,plain,
% 2.64/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[12482, 12481])).
% 2.64/2.80 tff(12484,plain,
% 2.64/2.80 ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12483, 155, 645, 386, 2630])).
% 2.64/2.80 tff(12485,plain,
% 2.64/2.80 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12484, 1961])).
% 2.64/2.80 tff(12486,plain,
% 2.64/2.80 (b(s(s(z)), s(s(s(elem!1))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[143, 12485])).
% 2.64/2.80 tff(12487,plain,
% 2.64/2.80 (~r(s(s(z)), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[3595, 1961, 645, 729, 386])).
% 2.64/2.80 tff(12488,plain,
% 2.64/2.80 (b(s(s(z)), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[122, 12487])).
% 2.64/2.80 tff(12489,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[6908, 97, 1139, 550, 12488, 12486])).
% 2.64/2.80 tff(12490,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(12491,plain,
% 2.64/2.80 (~r(s(s(s(z))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12490, 12477, 12456, 645, 1139, 12458, 12454])).
% 2.64/2.80 tff(12492,plain,
% 2.64/2.80 (b(s(s(s(z))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[402, 12491])).
% 2.64/2.80 tff(12493,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[11909, 97, 12456, 204, 1360, 12492])).
% 2.64/2.80 tff(12494,plain,((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(12495,plain,
% 2.64/2.80 (~b(z, s(s(z)))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12494, 3, 645, 1139, 1, 1360, 1331])).
% 2.64/2.80 tff(12496,plain,
% 2.64/2.80 (r(z, s(s(z)))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[222, 12495])).
% 2.64/2.80 tff(12497,plain,
% 2.64/2.80 (~r(s(z), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[2054, 12496, 645, 3])).
% 2.64/2.80 tff(12498,plain,
% 2.64/2.80 (b(s(z), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[568, 12497])).
% 2.64/2.80 tff(12499,plain,
% 2.64/2.80 (~b(z, s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[10139, 12498, 1360, 1, 1139])).
% 2.64/2.80 tff(12500,plain,
% 2.64/2.80 (r(z, s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[723, 12499])).
% 2.64/2.80 tff(12501,plain,
% 2.64/2.80 (~r(s(s(z)), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[11426, 12500, 3, 12496])).
% 2.64/2.80 tff(12502,plain,
% 2.64/2.80 (b(s(s(z)), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[122, 12501])).
% 2.64/2.80 tff(12503,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[3623, 97, 12498, 12502, 1360, 1331])).
% 2.64/2.80 tff(12504,plain,((~r(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(12505,plain,
% 2.64/2.80 (~b(s(s(s(z))), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12504, 12450, 3, 11948, 1, 645])).
% 2.64/2.80 tff(12506,plain,
% 2.64/2.80 (r(s(s(s(z))), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1358, 12505])).
% 2.64/2.80 tff(12507,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(12508,plain,
% 2.64/2.80 (((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(12509,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[12508])).
% 2.64/2.80 tff(12510,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.64/2.80 inference(transitivity,[status(thm)],[12509, 12507])).
% 2.64/2.80 tff(12511,plain,
% 2.64/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(12512,plain,
% 2.64/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[12511, 12510])).
% 2.64/2.80 tff(12513,plain,
% 2.64/2.80 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12512, 155, 11419, 288, 12506, 12452])).
% 2.64/2.80 tff(12514,plain,
% 2.64/2.80 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[3089, 12513, 1])).
% 2.64/2.80 tff(12515,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[10598, 97, 11948, 12450, 11439, 12514])).
% 2.64/2.80 tff(12516,plain,((s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(12517,plain,
% 2.64/2.80 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12516, 11830, 204, 288, 3, 645, 2])).
% 2.64/2.80 tff(12518,plain,
% 2.64/2.80 (b(s(s(s(z))), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1846, 12517, 11948])).
% 2.64/2.80 tff(12519,plain,
% 2.64/2.80 (~r(z, s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[6652, 12517, 585])).
% 2.64/2.80 tff(12520,plain,
% 2.64/2.80 (b(z, s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1318, 12519])).
% 2.64/2.80 tff(12521,plain,
% 2.64/2.80 (((~![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(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(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(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(12522,plain,
% 2.64/2.80 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(12523,plain,
% 2.64/2.80 (((~![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(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~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(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[12522])).
% 2.64/2.80 tff(12524,plain,
% 2.64/2.80 (((~![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(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~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(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.64/2.80 inference(transitivity,[status(thm)],[12523, 12521])).
% 2.64/2.80 tff(12525,plain,
% 2.64/2.80 ((~![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(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(12526,plain,
% 2.64/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[12525, 12524])).
% 2.64/2.80 tff(12527,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12526, 97, 1139, 204, 1361, 1360, 127, 1330])).
% 2.64/2.80 tff(12528,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(12529,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12528, 12520, 12518, 204, 11948, 11830, 11439])).
% 2.64/2.80 tff(12530,plain,((~r(s(s(z)), z)) | (~b(z, s(s(z)))) | r(z, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(12531,plain,
% 2.64/2.81 (~r(s(s(z)), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12530, 585, 204, 288, 3, 2])).
% 2.64/2.81 tff(12532,plain,
% 2.64/2.81 (b(s(s(z)), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[625, 12531])).
% 2.64/2.81 tff(12533,plain,
% 2.64/2.81 (~r(s(s(s(z))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2930, 2597, 2, 3])).
% 2.64/2.81 tff(12534,plain,
% 2.64/2.81 (b(s(s(s(z))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[421, 12533])).
% 2.64/2.81 tff(12535,plain,
% 2.64/2.81 (~b(s(s(s(z))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[10183, 97, 204, 12532, 12534])).
% 2.64/2.81 tff(12536,plain,
% 2.64/2.81 (r(s(s(s(z))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[402, 12535])).
% 2.64/2.81 tff(12537,plain,
% 2.64/2.81 ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12512, 155, 11419, 288, 2597])).
% 2.64/2.81 tff(12538,plain,
% 2.64/2.81 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12537, 12536])).
% 2.64/2.81 tff(12539,plain,
% 2.64/2.81 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[3089, 12538, 1])).
% 2.64/2.81 tff(12540,plain,
% 2.64/2.81 (~b(z, s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1339, 12534, 204, 12532])).
% 2.64/2.81 tff(12541,plain,
% 2.64/2.81 (r(z, s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1318, 12540])).
% 2.64/2.81 tff(12542,plain,
% 2.64/2.81 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2488, 155, 288, 12541, 12536])).
% 2.64/2.81 tff(12543,plain,
% 2.64/2.81 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2687, 12542, 4228])).
% 2.64/2.81 tff(12544,plain,
% 2.64/2.81 (~b(s(z), s(s(s(elem!1))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1710, 86, 1139, 1702])).
% 2.64/2.81 tff(12545,plain,
% 2.64/2.81 (~r(s(z), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12089, 12544, 3, 585])).
% 2.64/2.81 tff(12546,plain,
% 2.64/2.81 (b(s(z), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[568, 12545])).
% 2.64/2.81 tff(12547,plain,
% 2.64/2.81 (((~![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(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(12548,plain,
% 2.64/2.81 (((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(12549,plain,
% 2.64/2.81 (((~![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))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12548])).
% 2.64/2.81 tff(12550,plain,
% 2.64/2.81 (((~![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))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[12549, 12547])).
% 2.64/2.81 tff(12551,plain,
% 2.64/2.81 ((~![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))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(12552,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[12551, 12550])).
% 2.64/2.81 tff(12553,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12552, 97, 1139, 12546, 204, 1331, 86, 5941])).
% 2.64/2.81 tff(12554,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(z)))) | r(z, s(s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(12555,plain,
% 2.64/2.81 (~b(s(z), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12554, 12534, 204, 11948, 12543, 3, 585, 12539])).
% 2.64/2.81 tff(12556,plain,
% 2.64/2.81 (r(s(z), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[253, 12555])).
% 2.64/2.81 tff(12557,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5909, 155, 11419, 12541, 12556, 2597])).
% 2.64/2.81 tff(12558,plain,((~r(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~r(s(z), s(s(z)))) | r(z, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(12559,plain,
% 2.64/2.81 (~r(s(s(s(z))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12558, 1, 3, 585, 288, 204, 2])).
% 2.64/2.81 tff(12560,plain,
% 2.64/2.81 (b(s(s(s(z))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1358, 12559])).
% 2.64/2.81 tff(12561,plain,
% 2.64/2.81 (~b(s(s(z)), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12449, 2590, 3, 1139, 1, 2])).
% 2.64/2.81 tff(12562,plain,
% 2.64/2.81 (r(s(s(z)), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[437, 12561])).
% 2.64/2.81 tff(12563,plain,
% 2.64/2.81 (~r(s(z), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2641, 12562, 3, 2591])).
% 2.64/2.81 tff(12564,plain,
% 2.64/2.81 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[11697, 2591, 1139, 124, 83, 1360, 145, 288])).
% 2.64/2.81 tff(12565,plain,
% 2.64/2.81 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2687, 12564, 4228])).
% 2.64/2.81 tff(12566,plain,
% 2.64/2.81 (~b(s(z), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12294, 12565, 1139, 1360])).
% 2.64/2.81 tff(12567,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[253, 12566, 12563])).
% 2.64/2.81 tff(12568,plain,(b(s(s(s(z))), s(s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(12569,plain,
% 2.64/2.81 (b(s(s(s(z))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12568, 12560, 11948, 3, 3008, 12532, 145, 288, 1, 2])).
% 2.64/2.81 tff(12570,plain,
% 2.64/2.81 (~b(s(s(s(z))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[10183, 97, 204, 12532, 12569])).
% 2.64/2.81 tff(12571,plain,
% 2.64/2.81 (r(s(s(s(z))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[402, 12570])).
% 2.64/2.81 tff(12572,plain,
% 2.64/2.81 (~b(z, s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1339, 12569, 204, 12532])).
% 2.64/2.81 tff(12573,plain,
% 2.64/2.81 (r(z, s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1318, 12572])).
% 2.64/2.81 tff(12574,plain,
% 2.64/2.81 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2488, 155, 288, 12573, 12571])).
% 2.64/2.81 tff(12575,plain,
% 2.64/2.81 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2687, 12574, 4228])).
% 2.64/2.81 tff(12576,plain,
% 2.64/2.81 (~b(s(z), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12294, 12575, 11948, 12560])).
% 2.64/2.81 tff(12577,plain,
% 2.64/2.81 (r(s(z), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[253, 12576])).
% 2.64/2.81 tff(12578,plain,
% 2.64/2.81 (~r(s(z), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1308, 12577, 12573, 12571])).
% 2.64/2.81 tff(12579,plain,
% 2.64/2.81 (b(s(z), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[568, 12578])).
% 2.64/2.81 tff(12580,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[10132, 97, 11948, 12579, 12560, 12575])).
% 2.64/2.81 tff(12581,plain,((s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(z))) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(12582,plain,
% 2.64/2.81 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12581, 585, 204, 3, 11820, 2, 288])).
% 2.64/2.81 tff(12583,plain,
% 2.64/2.81 (~b(s(s(s(z))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1995, 12582, 5])).
% 2.64/2.81 tff(12584,plain,
% 2.64/2.81 (b(s(s(s(z))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1846, 12582, 11948])).
% 2.64/2.81 tff(12585,plain,
% 2.64/2.81 (~r(z, s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[6652, 12582, 585])).
% 2.64/2.81 tff(12586,plain,
% 2.64/2.81 (b(z, s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1318, 12585])).
% 2.64/2.81 tff(12587,plain,
% 2.64/2.81 (r(s(s(s(z))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[8734, 12582, 11820])).
% 2.64/2.81 tff(12588,plain,
% 2.64/2.81 (~b(s(s(z)), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[11970, 12586, 204, 12584])).
% 2.64/2.81 tff(12589,plain,
% 2.64/2.81 (r(s(s(z)), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[437, 12588])).
% 2.64/2.81 tff(12590,plain,
% 2.64/2.81 (~r(s(z), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2641, 12589, 3, 12587])).
% 2.64/2.81 tff(12591,plain,
% 2.64/2.81 (b(s(z), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[253, 12590])).
% 2.64/2.81 tff(12592,plain,
% 2.64/2.81 (((~![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(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(12593,plain,
% 2.64/2.81 (((~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(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(12594,plain,
% 2.64/2.81 (((~![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))), 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(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12593])).
% 2.64/2.81 tff(12595,plain,
% 2.64/2.81 (((~![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))), 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(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[12594, 12592])).
% 2.64/2.81 tff(12596,plain,
% 2.64/2.81 ((~![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))), 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)))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(12597,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[12596, 12595])).
% 2.64/2.81 tff(12598,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12597, 97, 550, 1360, 86, 1330])).
% 2.64/2.81 tff(12599,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(12600,plain,
% 2.64/2.81 (~b(s(z), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12599, 12591, 12586, 12584])).
% 2.64/2.81 tff(12601,plain,
% 2.64/2.81 (r(s(z), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[568, 12600])).
% 2.64/2.81 tff(12602,plain,
% 2.64/2.81 (b(s(z), s(s(s(s(elem!1)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12417, 12601, 3, 12583])).
% 2.64/2.81 tff(12603,plain,
% 2.64/2.81 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[11529, 12582])).
% 2.64/2.81 tff(12604,plain,
% 2.64/2.81 (b(s(z), s(s(s(elem!1))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12061, 12603, 3, 11948, 585, 12532, 12587, 12584])).
% 2.64/2.81 tff(12605,plain,
% 2.64/2.81 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12582])).
% 2.64/2.81 tff(12606,plain,
% 2.64/2.81 (s(s(z)) = s(s(elem!1))),
% 2.64/2.81 inference(transitivity,[status(thm)],[73, 12605, 19])).
% 2.64/2.81 tff(12607,plain,
% 2.64/2.81 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12606])).
% 2.64/2.81 tff(12608,plain,
% 2.64/2.81 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.64/2.81 inference(transitivity,[status(thm)],[12607, 1428])).
% 2.64/2.81 tff(12609,plain,
% 2.64/2.81 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12608])).
% 2.64/2.81 tff(12610,plain,
% 2.64/2.81 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[331, 12609])).
% 2.64/2.81 tff(12611,plain,
% 2.64/2.81 (r(s(s(z)), s(s(s(elem!1))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[10091, 12589, 12582])).
% 2.64/2.81 tff(12612,plain,
% 2.64/2.81 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12582])).
% 2.64/2.81 tff(12613,plain,
% 2.64/2.81 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[12612, 1414])).
% 2.64/2.81 tff(12614,plain,
% 2.64/2.81 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[12613, 2507])).
% 2.64/2.81 tff(12615,plain,
% 2.64/2.81 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12614])).
% 2.64/2.81 tff(12616,plain,
% 2.64/2.81 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[286, 12615])).
% 2.64/2.81 tff(12617,plain,
% 2.64/2.81 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12606])).
% 2.64/2.81 tff(12618,plain,
% 2.64/2.81 (s(z) = s(elem!1)),
% 2.64/2.81 inference(transitivity,[status(thm)],[24, 12617, 29])).
% 2.64/2.81 tff(12619,plain,
% 2.64/2.81 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12606, 12618])).
% 2.64/2.81 tff(12620,plain,
% 2.64/2.81 (r(s(s(elem!1)), s(elem!1))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[2, 12619])).
% 2.64/2.81 tff(12621,plain,
% 2.64/2.81 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12606])).
% 2.64/2.81 tff(12622,plain,
% 2.64/2.81 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(z)))),
% 2.64/2.81 inference(symmetry,[status(thm)],[12621])).
% 2.64/2.81 tff(12623,plain,
% 2.64/2.81 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12618, 12606])).
% 2.64/2.81 tff(12624,plain,
% 2.64/2.81 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 2.64/2.81 inference(transitivity,[status(thm)],[12623, 12622])).
% 2.64/2.81 tff(12625,plain,
% 2.64/2.81 (r(s(elem!1), s(s(z)))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[3, 12624])).
% 2.64/2.81 tff(12626,plain,
% 2.64/2.81 ((~r(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(z), z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12156, 11419])).
% 2.64/2.81 tff(12627,plain,
% 2.64/2.81 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12626, 12625, 12532, 12620, 12582, 12601, 204])).
% 2.64/2.81 tff(12628,plain,
% 2.64/2.81 (b(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[511, 12627])).
% 2.64/2.81 tff(12629,plain,
% 2.64/2.81 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1804, 12628, 11948, 12604])).
% 2.64/2.81 tff(12630,plain,
% 2.64/2.81 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[821, 12629, 12616])).
% 2.64/2.81 tff(12631,plain,
% 2.64/2.81 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5371, 12630, 11820, 12582, 12611])).
% 2.64/2.81 tff(12632,plain,
% 2.64/2.81 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1484, 12631, 12610])).
% 2.64/2.81 tff(12633,plain,
% 2.64/2.81 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5417, 12632, 12604, 12602])).
% 2.64/2.81 tff(12634,plain,
% 2.64/2.81 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1822, 12631, 12582])).
% 2.64/2.81 tff(12635,plain,
% 2.64/2.81 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[452, 12634])).
% 2.64/2.81 tff(12636,plain,
% 2.64/2.81 (~b(s(s(s(s(elem!1)))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[884, 12635, 204, 12532])).
% 2.64/2.81 tff(12637,plain,
% 2.64/2.81 (r(s(s(s(s(elem!1)))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[842, 12636])).
% 2.64/2.81 tff(12638,plain,
% 2.64/2.81 (~r(z, s(s(s(s(elem!1)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[3464, 12637, 288, 585, 12633])).
% 2.64/2.81 tff(12639,plain,
% 2.64/2.81 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12613])).
% 2.64/2.81 tff(12640,plain,
% 2.64/2.81 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[286, 12639])).
% 2.64/2.81 tff(12641,plain,
% 2.64/2.81 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[486, 12633, 12640])).
% 2.64/2.81 tff(12642,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[940, 155, 488, 309, 823, 224])).
% 2.64/2.81 tff(12643,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(12644,plain,
% 2.64/2.81 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12643, 12641, 12611, 12630])).
% 2.64/2.81 tff(12645,plain,
% 2.64/2.81 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[336, 12644])).
% 2.64/2.81 tff(12646,plain,
% 2.64/2.81 (~b(z, s(s(s(s(elem!1)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[669, 12645, 12532, 12628])).
% 2.64/2.81 tff(12647,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1093, 12646, 12638])).
% 2.64/2.81 tff(12648,plain,(r(z, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | b(s(s(s(elem!1))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(12649,plain,
% 2.64/2.81 (r(z, s(s(s(elem!1))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12648, 5, 11818, 3, 2, 2596])).
% 2.64/2.81 tff(12650,plain,
% 2.64/2.81 (b(s(s(s(elem!1))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[11947, 3, 2, 11818, 2596])).
% 2.64/2.81 tff(12651,plain,
% 2.64/2.81 (b(s(s(s(z))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1358, 12447])).
% 2.64/2.81 tff(12652,plain,
% 2.64/2.81 (~b(s(s(z)), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12449, 1, 3, 1139, 2590, 2])).
% 2.64/2.81 tff(12653,plain,
% 2.64/2.81 (r(s(s(z)), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[437, 12652])).
% 2.64/2.81 tff(12654,plain,
% 2.64/2.81 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5794, 12653, 145, 2591])).
% 2.64/2.81 tff(12655,plain,
% 2.64/2.81 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2687, 12654, 4228])).
% 2.64/2.81 tff(12656,plain,
% 2.64/2.81 (~r(s(z), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2641, 12653, 3, 2591])).
% 2.64/2.81 tff(12657,plain,
% 2.64/2.81 (b(s(z), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[253, 12656])).
% 2.64/2.81 tff(12658,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12294, 12657, 12655, 1139, 12651])).
% 2.64/2.81 tff(12659,plain,((s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | b(s(s(s(z))), s(s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(12660,plain,
% 2.64/2.81 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12659, 2590, 3, 145, 12650, 2])).
% 2.64/2.81 tff(12661,plain,
% 2.64/2.81 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[11529, 12660])).
% 2.64/2.81 tff(12662,plain,
% 2.64/2.81 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12661])).
% 2.64/2.81 tff(12663,plain,
% 2.64/2.81 (s(s(elem!1)) = s(s(z))),
% 2.64/2.81 inference(transitivity,[status(thm)],[167, 12662, 72])).
% 2.64/2.81 tff(12664,plain,
% 2.64/2.81 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(elem!1))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12663])).
% 2.64/2.81 tff(12665,plain,
% 2.64/2.81 (r(s(s(z)), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.64/2.81 inference(symmetry,[status(thm)],[12664])).
% 2.64/2.81 tff(12666,plain,
% 2.64/2.81 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12663])).
% 2.64/2.81 tff(12667,plain,
% 2.64/2.81 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.64/2.81 inference(symmetry,[status(thm)],[12666])).
% 2.64/2.81 tff(12668,plain,
% 2.64/2.81 (s(z) = s(elem!1)),
% 2.64/2.81 inference(transitivity,[status(thm)],[24, 12667, 29])).
% 2.64/2.81 tff(12669,plain,
% 2.64/2.81 (r(s(s(z)), s(z)) <=> r(s(s(z)), s(elem!1))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12668])).
% 2.64/2.81 tff(12670,plain,
% 2.64/2.81 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.64/2.81 inference(transitivity,[status(thm)],[12669, 12665])).
% 2.64/2.81 tff(12671,plain,
% 2.64/2.81 (r(s(s(elem!1)), s(elem!1))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[2, 12670])).
% 2.64/2.81 tff(12672,plain,
% 2.64/2.81 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12668])).
% 2.64/2.81 tff(12673,plain,
% 2.64/2.81 (r(s(elem!1), s(s(z)))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[3, 12672])).
% 2.64/2.81 tff(12674,plain,
% 2.64/2.81 (s(elem!1) = s(z)),
% 2.64/2.81 inference(transitivity,[status(thm)],[30, 12666, 23])).
% 2.64/2.81 tff(12675,plain,
% 2.64/2.81 (inj_0(s(elem!1)) = inj_0(s(z))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12674])).
% 2.64/2.81 tff(12676,plain,
% 2.64/2.81 (elem!1 = z),
% 2.64/2.81 inference(transitivity,[status(thm)],[1450, 12675, 17])).
% 2.64/2.81 tff(12677,plain,
% 2.64/2.81 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12676])).
% 2.64/2.81 tff(12678,plain,
% 2.64/2.81 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.64/2.81 inference(symmetry,[status(thm)],[12677])).
% 2.64/2.81 tff(12679,plain,
% 2.64/2.81 (b(elem!1, s(s(z)))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[11818, 12678])).
% 2.64/2.81 tff(12680,plain,
% 2.64/2.81 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12663, 12661])).
% 2.64/2.81 tff(12681,plain,
% 2.64/2.81 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.64/2.81 inference(symmetry,[status(thm)],[12680])).
% 2.64/2.81 tff(12682,plain,
% 2.64/2.81 (~b(s(s(s(z))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9913, 12660, 239])).
% 2.64/2.81 tff(12683,plain,
% 2.64/2.81 (r(s(s(s(z))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[402, 12682])).
% 2.64/2.81 tff(12684,plain,
% 2.64/2.81 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[11529, 1393])).
% 2.64/2.81 tff(12685,plain,
% 2.64/2.81 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12684])).
% 2.64/2.81 tff(12686,plain,
% 2.64/2.81 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(z)))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12685])).
% 2.64/2.81 tff(12687,plain,
% 2.64/2.81 (r(s(s(z)), s(s(s(elem!1))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[10091, 1961, 1393])).
% 2.64/2.81 tff(12688,plain,
% 2.64/2.81 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12684])).
% 2.64/2.81 tff(12689,plain,
% 2.64/2.81 (s(s(elem!1)) = s(s(z))),
% 2.64/2.81 inference(transitivity,[status(thm)],[167, 12688, 72])).
% 2.64/2.81 tff(12690,plain,
% 2.64/2.81 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(elem!1))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12689])).
% 2.64/2.81 tff(12691,plain,
% 2.64/2.81 (r(s(s(z)), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.64/2.81 inference(symmetry,[status(thm)],[12690])).
% 2.64/2.81 tff(12692,plain,
% 2.64/2.81 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12689])).
% 2.64/2.81 tff(12693,plain,
% 2.64/2.81 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.64/2.81 inference(symmetry,[status(thm)],[12692])).
% 2.64/2.81 tff(12694,plain,
% 2.64/2.81 (s(z) = s(elem!1)),
% 2.64/2.81 inference(transitivity,[status(thm)],[24, 12693, 29])).
% 2.64/2.81 tff(12695,plain,
% 2.64/2.81 (r(s(s(z)), s(z)) <=> r(s(s(z)), s(elem!1))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12694])).
% 2.64/2.81 tff(12696,plain,
% 2.64/2.81 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.64/2.81 inference(transitivity,[status(thm)],[12695, 12691])).
% 2.64/2.81 tff(12697,plain,
% 2.64/2.81 (r(s(s(elem!1)), s(elem!1))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[2, 12696])).
% 2.64/2.81 tff(12698,plain,
% 2.64/2.81 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12694])).
% 2.64/2.81 tff(12699,plain,
% 2.64/2.81 (r(s(elem!1), s(s(z)))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[3, 12698])).
% 2.64/2.81 tff(12700,plain,
% 2.64/2.81 (~r(s(z), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2641, 1961, 3, 1960])).
% 2.64/2.81 tff(12701,plain,
% 2.64/2.81 (b(s(z), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[253, 12700])).
% 2.64/2.81 tff(12702,plain,
% 2.64/2.81 (b(s(z), s(s(s(elem!1))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[6628, 12701, 1393])).
% 2.64/2.81 tff(12703,plain,
% 2.64/2.81 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12684])).
% 2.64/2.81 tff(12704,plain,
% 2.64/2.81 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[12703, 4295])).
% 2.64/2.81 tff(12705,plain,
% 2.64/2.81 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.64/2.81 inference(symmetry,[status(thm)],[12704])).
% 2.64/2.81 tff(12706,plain,
% 2.64/2.81 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[12705, 2507])).
% 2.64/2.81 tff(12707,plain,
% 2.64/2.81 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12706])).
% 2.64/2.81 tff(12708,plain,
% 2.64/2.81 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[286, 12707])).
% 2.64/2.81 tff(12709,plain,
% 2.64/2.81 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5371, 1813, 145, 1393, 224])).
% 2.64/2.81 tff(12710,plain,
% 2.64/2.81 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[821, 12709, 12708])).
% 2.64/2.81 tff(12711,plain,
% 2.64/2.81 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1816, 1813, 1393, 1520, 1812])).
% 2.64/2.81 tff(12712,plain,
% 2.64/2.81 (b(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[511, 12711])).
% 2.64/2.81 tff(12713,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1804, 12712, 12710, 1139, 193])).
% 2.64/2.81 tff(12714,plain,((~r(s(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))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(12715,plain,
% 2.64/2.81 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12714, 12702, 11948, 1393, 12699, 12697, 145, 12687])).
% 2.64/2.81 tff(12716,plain,
% 2.64/2.81 ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[3595, 11419])).
% 2.64/2.81 tff(12717,plain,
% 2.64/2.81 (~r(s(s(z)), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[12716, 1961, 2, 386])).
% 2.64/2.81 tff(12718,plain,
% 2.64/2.81 (b(s(s(z)), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[625, 12717])).
% 2.64/2.81 tff(12719,plain,
% 2.64/2.81 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1822, 12715, 1393])).
% 2.64/2.81 tff(12720,plain,
% 2.64/2.81 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[452, 12719])).
% 2.64/2.81 tff(12721,plain,
% 2.64/2.81 (~b(s(s(s(s(elem!1)))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[884, 12720, 204, 12718])).
% 2.64/2.81 tff(12722,plain,
% 2.64/2.81 (r(s(s(s(s(elem!1)))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[842, 12721])).
% 2.64/2.81 tff(12723,plain,
% 2.64/2.81 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[832, 12722, 570, 288])).
% 2.64/2.81 tff(12724,plain,
% 2.64/2.81 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[821, 12723, 12708])).
% 2.64/2.81 tff(12725,plain,
% 2.64/2.81 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1804, 12724, 11948, 12702])).
% 2.64/2.81 tff(12726,plain,
% 2.64/2.81 (r(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[511, 506])).
% 2.64/2.81 tff(12727,plain,
% 2.64/2.81 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1154, 506, 1139])).
% 2.64/2.81 tff(12728,plain,
% 2.64/2.81 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5048, 495, 463, 729])).
% 2.64/2.81 tff(12729,plain,
% 2.64/2.81 (b(s(z), s(s(s(s(elem!1)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[280, 12728])).
% 2.64/2.81 tff(12730,plain,
% 2.64/2.81 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[4856, 97, 1139, 12729, 87])).
% 2.64/2.81 tff(12731,plain,
% 2.64/2.81 (r(s(s(z)), s(s(s(elem!1))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[141, 53, 42, 12730])).
% 2.64/2.81 tff(12732,plain,
% 2.64/2.81 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[4864, 97, 1139, 12729, 87])).
% 2.64/2.81 tff(12733,plain,
% 2.64/2.81 (r(s(s(s(elem!1))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[58, 12732])).
% 2.64/2.81 tff(12734,plain,
% 2.64/2.81 (~r(s(z), s(s(s(elem!1))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[161, 155, 3, 12733, 12731])).
% 2.64/2.81 tff(12735,plain,
% 2.64/2.81 (b(s(z), s(s(s(elem!1))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[179, 53, 12734, 174])).
% 2.64/2.81 tff(12736,plain,
% 2.64/2.81 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1860, 473, 255, 1139])).
% 2.64/2.81 tff(12737,plain,
% 2.64/2.81 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1484, 12736, 1820])).
% 2.64/2.81 tff(12738,plain,
% 2.64/2.81 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.64/2.81 inference(symmetry,[status(thm)],[12737])).
% 2.64/2.81 tff(12739,plain,
% 2.64/2.81 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12738])).
% 2.64/2.81 tff(12740,plain,
% 2.64/2.81 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.64/2.81 inference(symmetry,[status(thm)],[12739])).
% 2.64/2.81 tff(12741,plain,
% 2.64/2.81 (r(s(s(elem!1)), s(z))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[495, 12740])).
% 2.64/2.81 tff(12742,plain,
% 2.64/2.81 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12738])).
% 2.64/2.81 tff(12743,plain,
% 2.64/2.81 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 2.64/2.81 inference(symmetry,[status(thm)],[12742])).
% 2.64/2.81 tff(12744,plain,
% 2.64/2.81 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5456, 12737, 473])).
% 2.64/2.81 tff(12745,plain,
% 2.64/2.81 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12737])).
% 2.64/2.81 tff(12746,plain,
% 2.64/2.81 (s(s(s(elem!1))) = s(elem!1)),
% 2.64/2.81 inference(transitivity,[status(thm)],[271, 12745, 29])).
% 2.64/2.81 tff(12747,plain,
% 2.64/2.81 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[12746])).
% 2.64/2.81 tff(12748,plain,
% 2.64/2.81 (b(s(z), s(elem!1))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[193, 12747])).
% 2.64/2.81 tff(12749,plain,
% 2.64/2.81 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5477, 12748, 12737, 255, 12744])).
% 2.64/2.81 tff(12750,plain,
% 2.64/2.81 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[452, 12749])).
% 2.64/2.81 tff(12751,plain,
% 2.64/2.81 (r(s(s(elem!1)), s(s(z)))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[12750, 12743])).
% 2.64/2.81 tff(12752,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 2.64/2.81 tff(12753,plain,
% 2.64/2.81 (((~![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)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(12754,plain,
% 2.64/2.82 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(12755,plain,
% 2.64/2.82 (((~![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)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[12754])).
% 2.64/2.82 tff(12756,plain,
% 2.64/2.82 (((~![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)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[12755, 12753])).
% 2.64/2.82 tff(12757,plain,
% 2.64/2.82 ((~![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)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(12758,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[12757, 12756])).
% 2.64/2.82 tff(12759,plain,
% 2.64/2.82 ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12758, 97, 12752, 5468])).
% 2.64/2.82 tff(12760,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12759, 5467, 5464])).
% 2.64/2.82 tff(12761,plain,((~b(s(s(elem!1)), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(12762,plain,
% 2.64/2.82 (~b(s(s(elem!1)), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12761, 12748, 255, 12737, 12744])).
% 2.64/2.82 tff(12763,plain,
% 2.64/2.82 (((~![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))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(12764,plain,
% 2.64/2.82 ((~![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))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(12765,plain,
% 2.64/2.82 ((~![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)),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[12764, 12763])).
% 2.64/2.82 tff(12766,plain,
% 2.64/2.82 (r(s(s(elem!1)), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12765, 53, 170, 12762])).
% 2.64/2.82 tff(12767,plain,
% 2.64/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(12768,plain,
% 2.64/2.82 (((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(12769,plain,
% 2.64/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[12768])).
% 2.64/2.82 tff(12770,plain,
% 2.64/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[12769, 12767])).
% 2.64/2.82 tff(12771,plain,
% 2.64/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(12772,plain,
% 2.64/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[12771, 12770])).
% 2.64/2.82 tff(12773,plain,
% 2.64/2.82 (~r(s(s(elem!1)), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12772, 155, 729, 3, 12766, 12751])).
% 2.64/2.82 tff(12774,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12773, 12741])).
% 2.64/2.82 tff(12775,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | r(s(s(s(s(elem!1)))), s(s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(12776,plain,
% 2.64/2.82 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12775, 12735, 729, 3, 12729, 495, 1820, 1139])).
% 2.64/2.82 tff(12777,plain,
% 2.64/2.82 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[486, 12776, 472])).
% 2.64/2.82 tff(12778,plain,
% 2.64/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(12779,plain,
% 2.64/2.82 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(12780,plain,
% 2.64/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[12779])).
% 2.64/2.82 tff(12781,plain,
% 2.64/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[12780, 12778])).
% 2.64/2.82 tff(12782,plain,
% 2.64/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(12783,plain,
% 2.64/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[12782, 12781])).
% 2.64/2.82 tff(12784,plain,
% 2.64/2.82 (~r(z, s(s(s(elem!1))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12783, 155, 729, 463, 12777, 495])).
% 2.64/2.82 tff(12785,plain,
% 2.64/2.82 (b(z, s(s(s(elem!1))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[590, 12784])).
% 2.64/2.82 tff(12786,plain,
% 2.64/2.82 (((~![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(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(12787,plain,
% 2.64/2.82 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(12788,plain,
% 2.64/2.82 (((~![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(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[12787])).
% 2.64/2.82 tff(12789,plain,
% 2.64/2.82 (((~![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(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[12788, 12786])).
% 2.64/2.82 tff(12790,plain,
% 2.64/2.82 ((~![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(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(12791,plain,
% 2.64/2.82 ((~![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(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[12790, 12789])).
% 2.64/2.82 tff(12792,plain,
% 2.64/2.82 (~b(s(z), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12791, 97, 1139, 12735, 12785])).
% 2.64/2.82 tff(12793,plain,
% 2.64/2.82 (r(s(z), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[568, 12792])).
% 2.64/2.82 tff(12794,plain,
% 2.64/2.82 (~r(s(s(s(s(elem!1)))), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[4412, 155, 729, 12793, 495])).
% 2.64/2.82 tff(12795,plain,
% 2.64/2.82 (b(s(s(s(s(elem!1)))), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[842, 12794])).
% 2.64/2.82 tff(12796,plain,
% 2.64/2.82 (((~![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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(12797,plain,
% 2.64/2.82 (((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(12798,plain,
% 2.64/2.82 (((~![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(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[12797])).
% 2.64/2.82 tff(12799,plain,
% 2.64/2.82 (((~![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(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.64/2.82 inference(transitivity,[status(thm)],[12798, 12796])).
% 2.64/2.82 tff(12800,plain,
% 2.64/2.82 ((~![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(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(12801,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[12800, 12799])).
% 2.64/2.82 tff(12802,plain,
% 2.64/2.82 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12801, 97, 1139, 12735, 126, 12785, 12795])).
% 2.64/2.82 tff(12803,plain,
% 2.64/2.82 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[821, 12802, 3701])).
% 2.64/2.82 tff(12804,plain,
% 2.64/2.82 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[4824, 12735, 126, 12729, 12795, 87])).
% 2.64/2.82 tff(12805,plain,
% 2.64/2.82 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[336, 12804])).
% 2.64/2.82 tff(12806,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[940, 155, 12777, 12805, 12803, 12731])).
% 2.64/2.82 tff(12807,plain,((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(12808,plain,
% 2.64/2.82 (~b(s(s(z)), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12807, 3, 126, 729, 495, 463, 472, 1139, 1820])).
% 2.64/2.82 tff(12809,plain,
% 2.64/2.82 (r(s(s(z)), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[122, 12808])).
% 2.64/2.82 tff(12810,plain,
% 2.64/2.82 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[10311, 155, 12809, 3, 495])).
% 2.64/2.82 tff(12811,plain,
% 2.64/2.82 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[452, 12810])).
% 2.64/2.82 tff(12812,plain,
% 2.64/2.82 (~r(z, s(s(z)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[871, 155, 729, 12809, 3])).
% 2.64/2.82 tff(12813,plain,
% 2.64/2.82 (b(z, s(s(z)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[222, 12812])).
% 2.64/2.82 tff(12814,plain,
% 2.64/2.82 (~b(s(z), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[10212, 12813, 126, 1139])).
% 2.64/2.82 tff(12815,plain,
% 2.64/2.82 (r(s(z), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[568, 12814])).
% 2.64/2.82 tff(12816,plain,
% 2.64/2.82 (~r(s(s(s(s(elem!1)))), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[4414, 12815, 729, 495])).
% 2.64/2.82 tff(12817,plain,
% 2.64/2.82 (b(s(s(s(s(elem!1)))), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[842, 12816])).
% 2.64/2.82 tff(12818,plain,
% 2.64/2.82 (~r(s(s(z)), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[966, 155, 729, 12815, 12809])).
% 2.64/2.82 tff(12819,plain,
% 2.64/2.82 (b(s(s(z)), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[625, 12818])).
% 2.64/2.82 tff(12820,plain,
% 2.64/2.82 (((~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(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(12821,plain,
% 2.64/2.82 (((~![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(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(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[12820])).
% 2.64/2.82 tff(12822,plain,
% 2.64/2.82 (((~![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(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(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[12821, 877])).
% 2.64/2.82 tff(12823,plain,
% 2.64/2.82 ((~![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(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)))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(12824,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[12823, 12822])).
% 2.64/2.82 tff(12825,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12824, 97, 12813, 12819, 12817, 12811])).
% 2.64/2.82 tff(12826,plain,((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(12827,plain,
% 2.64/2.82 (~r(s(z), s(s(z)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12826, 126, 495, 729, 1139, 463, 472, 1820])).
% 2.64/2.82 tff(12828,plain,
% 2.64/2.82 (b(s(z), s(s(z)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[548, 12827])).
% 2.64/2.82 tff(12829,plain,
% 2.64/2.82 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[3812, 876, 12729, 535])).
% 2.64/2.82 tff(12830,plain,
% 2.64/2.82 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[336, 12829])).
% 2.64/2.82 tff(12831,plain,
% 2.64/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(12832,plain,
% 2.64/2.83 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(12833,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[12832])).
% 2.64/2.83 tff(12834,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 2.64/2.83 inference(transitivity,[status(thm)],[12833, 12831])).
% 2.64/2.83 tff(12835,plain,
% 2.64/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(12836,plain,
% 2.64/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[12835, 12834])).
% 2.64/2.83 tff(12837,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12836, 155, 729, 463, 309, 226, 495])).
% 2.64/2.83 tff(12838,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(12839,plain,
% 2.64/2.83 (~r(z, s(s(z)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12838, 12830, 463, 729, 495])).
% 2.64/2.83 tff(12840,plain,
% 2.64/2.83 (b(z, s(s(z)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[222, 12839])).
% 2.64/2.83 tff(12841,plain,
% 2.64/2.83 (((~![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(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(12842,plain,
% 2.64/2.83 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(12843,plain,
% 2.64/2.83 (((~![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(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z))))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[12842])).
% 2.64/2.83 tff(12844,plain,
% 2.64/2.83 (((~![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(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))))),
% 2.64/2.83 inference(transitivity,[status(thm)],[12843, 12841])).
% 2.64/2.83 tff(12845,plain,
% 2.64/2.83 ((~![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(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(12846,plain,
% 2.64/2.83 ((~![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(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z))))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[12845, 12844])).
% 2.64/2.83 tff(12847,plain,
% 2.64/2.83 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12846, 97, 126, 12840, 876])).
% 2.64/2.83 tff(12848,plain,
% 2.64/2.83 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[821, 12847, 3701])).
% 2.64/2.83 tff(12849,plain,
% 2.64/2.83 (((~![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(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(12850,plain,
% 2.64/2.83 (((~b(z, s(s(z)))) | (~b(z, s(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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(12851,plain,
% 2.64/2.83 (((~![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(z)))) | (~b(z, s(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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z))))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[12850])).
% 2.64/2.83 tff(12852,plain,
% 2.64/2.83 (((~![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(z)))) | (~b(z, s(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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))))),
% 2.64/2.83 inference(transitivity,[status(thm)],[12851, 12849])).
% 2.64/2.83 tff(12853,plain,
% 2.64/2.83 ((~![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(z)))) | (~b(z, s(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)))))))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(12854,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z))))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[12853, 12852])).
% 2.64/2.83 tff(12855,plain,
% 2.64/2.83 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12854, 97, 126, 12840, 876])).
% 2.64/2.83 tff(12856,plain,
% 2.64/2.83 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[486, 12855, 472])).
% 2.64/2.83 tff(12857,plain,
% 2.64/2.83 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[940, 155, 12856, 12830, 12848])).
% 2.64/2.83 tff(12858,plain,
% 2.64/2.83 (~r(z, s(s(s(elem!1))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12783, 155, 729, 463, 12856, 495])).
% 2.64/2.83 tff(12859,plain,
% 2.64/2.83 (b(z, s(s(s(elem!1))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[590, 12858])).
% 2.64/2.83 tff(12860,plain,
% 2.64/2.83 (~r(s(s(z)), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[3045, 12859, 126, 12830, 12856, 495, 463])).
% 2.64/2.83 tff(12861,plain,
% 2.64/2.83 (b(s(s(z)), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[122, 12860])).
% 2.64/2.83 tff(12862,plain,
% 2.64/2.83 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[4856, 97, 1139, 12729, 12861])).
% 2.64/2.83 tff(12863,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[141, 53, 42, 12862, 12857])).
% 2.64/2.83 tff(12864,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(12865,plain,
% 2.64/2.83 (~b(s(s(s(s(elem!1)))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12864, 126, 1139, 495, 463, 729, 472, 12828])).
% 2.64/2.83 tff(12866,plain,
% 2.64/2.83 (r(s(s(s(s(elem!1)))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[842, 12865])).
% 2.64/2.83 tff(12867,plain,
% 2.64/2.83 (~r(s(z), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[4414, 12866, 729, 495])).
% 2.64/2.83 tff(12868,plain,
% 2.64/2.83 (b(s(z), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[568, 12867])).
% 2.64/2.83 tff(12869,plain,
% 2.64/2.83 (~b(z, s(s(z)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[10212, 12868, 126, 1139])).
% 2.64/2.83 tff(12870,plain,
% 2.64/2.83 (r(z, s(s(z)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[222, 12869])).
% 2.64/2.83 tff(12871,plain,
% 2.64/2.83 (((~![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(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(12872,plain,
% 2.64/2.83 (((~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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(12873,plain,
% 2.64/2.83 (((~![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(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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[12872])).
% 2.64/2.83 tff(12874,plain,
% 2.64/2.83 (((~![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(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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.64/2.83 inference(transitivity,[status(thm)],[12873, 12871])).
% 2.64/2.83 tff(12875,plain,
% 2.64/2.83 ((~![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(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))))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(12876,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[12875, 12874])).
% 2.64/2.83 tff(12877,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12876, 97, 1139, 550, 126, 124])).
% 2.64/2.83 tff(12878,plain,((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(12879,plain,
% 2.64/2.83 (~b(z, s(s(s(elem!1))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12878, 12868, 126, 1139])).
% 2.64/2.83 tff(12880,plain,
% 2.64/2.83 (r(z, s(s(s(elem!1))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[590, 12879])).
% 2.64/2.83 tff(12881,plain,
% 2.64/2.83 (~b(s(s(z)), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[5184, 12880, 12870, 1139, 12729])).
% 2.64/2.83 tff(12882,plain,
% 2.64/2.83 (r(s(s(z)), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[122, 12881])).
% 2.64/2.83 tff(12883,plain,
% 2.64/2.83 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[3278, 12882, 12866, 12870, 495])).
% 2.64/2.83 tff(12884,plain,
% 2.64/2.83 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[452, 12883])).
% 2.64/2.83 tff(12885,plain,
% 2.64/2.83 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12838, 12870, 463, 729, 495])).
% 2.64/2.83 tff(12886,plain,
% 2.64/2.83 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[336, 12885])).
% 2.64/2.83 tff(12887,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[3265, 97, 12729, 12886, 12884, 12828])).
% 2.64/2.83 tff(12888,plain,((~b(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(12889,plain,
% 2.64/2.83 (~b(s(s(s(elem!1))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12888, 495, 463, 729, 1139, 472, 1820])).
% 2.64/2.83 tff(12890,plain,
% 2.64/2.83 (r(s(s(s(elem!1))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[246, 12889])).
% 2.64/2.83 tff(12891,plain,
% 2.64/2.83 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[1872, 824, 463, 12890])).
% 2.64/2.83 tff(12892,plain,
% 2.64/2.83 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[486, 12891, 472])).
% 2.64/2.83 tff(12893,plain,
% 2.64/2.83 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[1860, 12892, 12729, 1139])).
% 2.64/2.83 tff(12894,plain,
% 2.64/2.83 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[1484, 12893, 1820])).
% 2.64/2.83 tff(12895,plain,
% 2.64/2.83 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[12894])).
% 2.64/2.83 tff(12896,plain,
% 2.64/2.83 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 2.64/2.83 inference(symmetry,[status(thm)],[12895])).
% 2.64/2.83 tff(12897,plain,
% 2.64/2.83 (s(elem!1) = s(s(s(elem!1)))),
% 2.64/2.83 inference(transitivity,[status(thm)],[30, 12896, 270])).
% 2.64/2.83 tff(12898,plain,
% 2.64/2.83 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[12897])).
% 2.64/2.83 tff(12899,plain,
% 2.64/2.83 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 2.64/2.83 inference(symmetry,[status(thm)],[12898])).
% 2.64/2.83 tff(12900,plain,
% 2.64/2.83 (b(s(elem!1), s(z))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[1139, 12899])).
% 2.64/2.83 tff(12901,plain,
% 2.64/2.83 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.64/2.83 inference(symmetry,[status(thm)],[12894])).
% 2.64/2.83 tff(12902,plain,
% 2.64/2.83 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[12901])).
% 2.64/2.83 tff(12903,plain,
% 2.64/2.83 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(elem!1)))),
% 2.64/2.83 inference(symmetry,[status(thm)],[12902])).
% 2.64/2.83 tff(12904,plain,
% 2.64/2.83 (b(s(z), s(s(elem!1)))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[12729, 12903])).
% 2.64/2.83 tff(12905,plain,
% 2.64/2.83 (s(s(s(s(elem!1)))) = elem!1),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[1734, 12894])).
% 2.64/2.83 tff(12906,plain,
% 2.64/2.83 (s(s(elem!1)) = elem!1),
% 2.64/2.83 inference(transitivity,[status(thm)],[12901, 12905])).
% 2.64/2.83 tff(12907,plain,
% 2.64/2.83 (b(s(s(elem!1)), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[12906])).
% 2.64/2.83 tff(12908,plain,
% 2.64/2.83 (b(elem!1, s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.64/2.83 inference(symmetry,[status(thm)],[12907])).
% 2.64/2.83 tff(12909,plain,
% 2.64/2.83 (elem!1 = s(s(s(s(elem!1))))),
% 2.64/2.83 inference(symmetry,[status(thm)],[12905])).
% 2.64/2.83 tff(12910,plain,
% 2.64/2.83 (elem!1 = s(s(elem!1))),
% 2.64/2.83 inference(transitivity,[status(thm)],[12909, 12894])).
% 2.64/2.83 tff(12911,plain,
% 2.64/2.83 (b(elem!1, s(elem!1)) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[12910, 12897])).
% 2.64/2.83 tff(12912,plain,
% 2.64/2.83 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 2.64/2.83 inference(symmetry,[status(thm)],[12911])).
% 2.64/2.83 tff(12913,plain,
% 2.64/2.83 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[12894])).
% 2.64/2.83 tff(12914,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(12915,plain,
% 2.64/2.83 (((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(12916,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[12915])).
% 2.64/2.83 tff(12917,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.64/2.83 inference(transitivity,[status(thm)],[12916, 12914])).
% 2.64/2.83 tff(12918,plain,
% 2.64/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(12919,plain,
% 2.64/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[12918, 12917])).
% 2.64/2.83 tff(12920,plain,
% 2.64/2.83 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12919, 155, 729, 12890, 495])).
% 2.64/2.83 tff(12921,plain,
% 2.64/2.83 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12920, 824])).
% 2.64/2.83 tff(12922,plain,
% 2.64/2.83 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[821, 12921, 3701])).
% 2.64/2.83 tff(12923,plain,
% 2.64/2.83 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[12922, 12913])).
% 2.64/2.83 tff(12924,plain,
% 2.64/2.83 (b(elem!1, s(elem!1))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[12923, 12912])).
% 2.64/2.83 tff(12925,plain,
% 2.64/2.83 (b(s(s(elem!1)), s(elem!1))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[12924, 12908])).
% 2.64/2.83 tff(12926,plain,
% 2.64/2.83 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[12897])).
% 2.64/2.83 tff(12927,plain,
% 2.64/2.83 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.64/2.83 inference(symmetry,[status(thm)],[12926])).
% 2.64/2.83 tff(12928,plain,
% 2.64/2.83 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[5456, 12894, 12892])).
% 2.64/2.83 tff(12929,plain,
% 2.64/2.83 (b(s(elem!1), s(s(elem!1)))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[12928, 12927])).
% 2.64/2.83 tff(12930,plain,
% 2.64/2.83 (((~![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)), 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(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(12931,plain,
% 2.64/2.83 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(12932,plain,
% 2.64/2.83 (((~![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)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(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(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[12931])).
% 2.64/2.83 tff(12933,plain,
% 2.64/2.83 (((~![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)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(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(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.64/2.83 inference(transitivity,[status(thm)],[12932, 12930])).
% 2.64/2.83 tff(12934,plain,
% 2.64/2.83 ((~![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)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(12935,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[12934, 12933])).
% 2.64/2.83 tff(12936,plain,
% 2.64/2.83 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12935, 97])).
% 2.64/2.83 tff(12937,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12936, 12929, 12925, 12904, 12900])).
% 2.64/2.83 tff(12938,plain,((~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(z))) | r(s(s(s(s(elem!1)))), s(s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(12939,plain,
% 2.64/2.83 (~r(s(s(s(s(elem!1)))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12938, 12727, 1820, 1139, 729, 12726, 463])).
% 2.64/2.84 tff(12940,plain,
% 2.64/2.84 (b(s(s(s(s(elem!1)))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[842, 12939])).
% 2.64/2.84 tff(12941,plain,
% 2.64/2.84 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[5048, 12726, 463, 729])).
% 2.64/2.84 tff(12942,plain,
% 2.64/2.84 (b(s(z), s(s(s(s(elem!1)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[280, 12941])).
% 2.64/2.84 tff(12943,plain,
% 2.64/2.84 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12838, 226, 463, 729, 495])).
% 2.64/2.84 tff(12944,plain,
% 2.64/2.84 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[336, 12943])).
% 2.64/2.84 tff(12945,plain,
% 2.64/2.84 (~r(s(z), s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[5351, 226, 463, 729, 495])).
% 2.64/2.84 tff(12946,plain,
% 2.64/2.84 (b(s(z), s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[548, 12945])).
% 2.64/2.84 tff(12947,plain,
% 2.64/2.84 (~b(s(s(s(s(elem!1)))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[3812, 12946, 12729, 12944])).
% 2.64/2.84 tff(12948,plain,
% 2.64/2.84 (r(s(s(s(s(elem!1)))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[842, 12947])).
% 2.64/2.84 tff(12949,plain,
% 2.64/2.84 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1872, 12948, 463, 12890])).
% 2.64/2.84 tff(12950,plain,
% 2.64/2.84 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[486, 12949, 472])).
% 2.64/2.84 tff(12951,plain,
% 2.64/2.84 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1860, 12950, 12729, 1139])).
% 2.64/2.84 tff(12952,plain,
% 2.64/2.84 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1484, 12951, 1820])).
% 2.64/2.84 tff(12953,plain,
% 2.64/2.84 (s(s(s(s(elem!1)))) = elem!1),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1734, 12952])).
% 2.64/2.84 tff(12954,plain,
% 2.64/2.84 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.64/2.84 inference(symmetry,[status(thm)],[12952])).
% 2.64/2.84 tff(12955,plain,
% 2.64/2.84 (s(s(elem!1)) = elem!1),
% 2.64/2.84 inference(transitivity,[status(thm)],[12954, 12953])).
% 2.64/2.84 tff(12956,plain,
% 2.64/2.84 (b(s(s(elem!1)), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[12955])).
% 2.64/2.84 tff(12957,plain,
% 2.64/2.84 (b(elem!1, s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.64/2.84 inference(symmetry,[status(thm)],[12956])).
% 2.64/2.84 tff(12958,plain,
% 2.64/2.84 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[12952])).
% 2.64/2.84 tff(12959,plain,
% 2.64/2.84 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 2.64/2.84 inference(symmetry,[status(thm)],[12958])).
% 2.64/2.84 tff(12960,plain,
% 2.64/2.84 (s(elem!1) = s(s(s(elem!1)))),
% 2.64/2.84 inference(transitivity,[status(thm)],[30, 12959, 270])).
% 2.64/2.84 tff(12961,plain,
% 2.64/2.84 (elem!1 = s(s(s(s(elem!1))))),
% 2.64/2.84 inference(symmetry,[status(thm)],[12953])).
% 2.64/2.84 tff(12962,plain,
% 2.64/2.84 (elem!1 = s(s(elem!1))),
% 2.64/2.84 inference(transitivity,[status(thm)],[12961, 12952])).
% 2.64/2.84 tff(12963,plain,
% 2.64/2.84 (b(elem!1, s(elem!1)) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[12962, 12960])).
% 2.64/2.84 tff(12964,plain,
% 2.64/2.84 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 2.64/2.84 inference(symmetry,[status(thm)],[12963])).
% 2.64/2.84 tff(12965,plain,
% 2.64/2.84 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[12952])).
% 2.64/2.84 tff(12966,plain,
% 2.64/2.84 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12920, 12948])).
% 2.64/2.84 tff(12967,plain,
% 2.64/2.84 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[821, 12966, 3701])).
% 2.64/2.84 tff(12968,plain,
% 2.64/2.84 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[12967, 12965])).
% 2.64/2.84 tff(12969,plain,
% 2.64/2.84 (b(elem!1, s(elem!1))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[12968, 12964])).
% 2.64/2.84 tff(12970,plain,
% 2.64/2.84 (b(s(s(elem!1)), s(elem!1))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[12969, 12957])).
% 2.64/2.84 tff(12971,plain,
% 2.64/2.84 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[12954])).
% 2.64/2.84 tff(12972,plain,
% 2.64/2.84 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(elem!1)))),
% 2.64/2.84 inference(symmetry,[status(thm)],[12971])).
% 2.64/2.84 tff(12973,plain,
% 2.64/2.84 (b(s(z), s(s(elem!1)))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[12729, 12972])).
% 2.64/2.84 tff(12974,plain,
% 2.64/2.84 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[12954])).
% 2.64/2.84 tff(12975,plain,
% 2.64/2.84 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(elem!1)))),
% 2.64/2.84 inference(symmetry,[status(thm)],[12974])).
% 2.64/2.84 tff(12976,plain,
% 2.64/2.84 (b(s(s(z)), s(s(elem!1)))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[12944, 12975])).
% 2.64/2.84 tff(12977,plain,
% 2.64/2.84 (((~![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(z), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(12978,plain,
% 2.64/2.84 (((~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(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(12979,plain,
% 2.64/2.84 (((~![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(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(z), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[12978])).
% 2.64/2.84 tff(12980,plain,
% 2.64/2.84 (((~![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(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(z), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[12979, 12977])).
% 2.64/2.84 tff(12981,plain,
% 2.64/2.84 ((~![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(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)))))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(12982,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[12981, 12980])).
% 2.64/2.84 tff(12983,plain,
% 2.64/2.84 (~b(s(s(elem!1)), s(elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12982, 97, 12946, 12976, 12973])).
% 2.64/2.84 tff(12984,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12983, 12970])).
% 2.64/2.84 tff(12985,plain,((~r(z, s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(12986,plain,
% 2.64/2.84 (~r(z, s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12985, 472, 1139, 1820, 729, 495, 463])).
% 2.64/2.84 tff(12987,plain,
% 2.64/2.84 (b(z, s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[222, 12986])).
% 2.64/2.84 tff(12988,plain,
% 2.64/2.84 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 2.64/2.84 inference(symmetry,[status(thm)],[12745])).
% 2.64/2.84 tff(12989,plain,
% 2.64/2.84 (s(elem!1) = s(s(s(elem!1)))),
% 2.64/2.84 inference(transitivity,[status(thm)],[30, 12988, 270])).
% 2.64/2.84 tff(12990,plain,
% 2.64/2.84 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[12989])).
% 2.64/2.84 tff(12991,plain,
% 2.64/2.84 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 2.64/2.84 inference(symmetry,[status(thm)],[12990])).
% 2.64/2.84 tff(12992,plain,
% 2.64/2.84 (b(s(elem!1), s(z))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[1139, 12991])).
% 2.64/2.84 tff(12993,plain,
% 2.64/2.84 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[12989])).
% 2.64/2.84 tff(12994,plain,
% 2.64/2.84 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.64/2.84 inference(symmetry,[status(thm)],[12993])).
% 2.64/2.84 tff(12995,plain,
% 2.64/2.84 (b(s(elem!1), s(s(elem!1)))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[12744, 12994])).
% 2.64/2.84 tff(12996,plain,
% 2.64/2.84 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[12738])).
% 2.64/2.84 tff(12997,plain,
% 2.64/2.84 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(elem!1)))),
% 2.64/2.84 inference(symmetry,[status(thm)],[12996])).
% 2.64/2.84 tff(12998,plain,
% 2.64/2.84 (b(s(z), s(s(elem!1)))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[255, 12997])).
% 2.64/2.84 tff(12999,plain,
% 2.64/2.84 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(elem!1)), z)),
% 2.64/2.84 inference(monotonicity,[status(thm)],[12737])).
% 2.64/2.84 tff(13000,plain,
% 2.64/2.84 (b(s(s(elem!1)), z)),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[876, 12999])).
% 2.64/2.84 tff(13001,plain,
% 2.64/2.84 (((~![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(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(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(13002,plain,
% 2.64/2.84 (((~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(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(13003,plain,
% 2.64/2.84 (((~![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(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(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13002])).
% 2.64/2.84 tff(13004,plain,
% 2.64/2.84 (((~![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(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(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[13003, 13001])).
% 2.64/2.84 tff(13005,plain,
% 2.64/2.84 ((~![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(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))))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(13006,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[13005, 13004])).
% 2.64/2.84 tff(13007,plain,
% 2.64/2.84 ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13006, 97, 13000])).
% 2.64/2.84 tff(13008,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13007, 12998, 12995, 12992])).
% 2.64/2.84 tff(13009,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | r(s(s(s(s(elem!1)))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(13010,plain,
% 2.64/2.84 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13009, 876, 12729, 1139, 1820])).
% 2.64/2.84 tff(13011,plain,
% 2.64/2.84 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[486, 13010, 472])).
% 2.64/2.84 tff(13012,plain,
% 2.64/2.84 (~r(z, s(s(s(elem!1))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12783, 155, 729, 463, 13011, 495])).
% 2.64/2.84 tff(13013,plain,
% 2.64/2.84 (b(z, s(s(s(elem!1))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[590, 13012])).
% 2.64/2.84 tff(13014,plain,
% 2.64/2.84 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[212, 87, 124, 204])).
% 2.64/2.84 tff(13015,plain,
% 2.64/2.84 (r(s(s(s(elem!1))), s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[58, 13014])).
% 2.64/2.84 tff(13016,plain,
% 2.64/2.84 ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9162, 155, 463, 309, 288])).
% 2.64/2.84 tff(13017,plain,
% 2.64/2.84 (~r(s(s(z)), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13016, 5176])).
% 2.64/2.84 tff(13018,plain,
% 2.64/2.84 (b(s(s(z)), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[625, 13017])).
% 2.64/2.84 tff(13019,plain,
% 2.64/2.84 (((~![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(s(elem!1))))) | (~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(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(13020,plain,
% 2.64/2.84 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~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(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(13021,plain,
% 2.64/2.84 (((~![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(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~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(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13020])).
% 2.64/2.84 tff(13022,plain,
% 2.64/2.84 (((~![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(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~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(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[13021, 13019])).
% 2.64/2.84 tff(13023,plain,
% 2.64/2.84 ((~![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(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~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)))))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(13024,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[13023, 13022])).
% 2.64/2.84 tff(13025,plain,
% 2.64/2.84 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13024, 97, 124, 13018, 876])).
% 2.64/2.84 tff(13026,plain,
% 2.64/2.84 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[452, 13025])).
% 2.64/2.84 tff(13027,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1044, 155, 488, 309, 13026, 13015])).
% 2.64/2.84 tff(13028,plain,((~b(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(13029,plain,
% 2.64/2.84 (~b(s(s(z)), s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13028, 13011, 309, 13013, 876, 463, 12890, 1139, 12729, 12987])).
% 2.64/2.84 tff(13030,plain,
% 2.64/2.84 (r(s(s(z)), s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[122, 13029])).
% 2.64/2.84 tff(13031,plain,
% 2.64/2.84 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[3031, 155, 13011, 309, 13030, 495])).
% 2.64/2.84 tff(13032,plain,
% 2.64/2.84 (b(s(s(z)), s(s(s(elem!1))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[141, 53, 42, 13031])).
% 2.64/2.84 tff(13033,plain,
% 2.64/2.84 (~r(s(s(z)), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[3040, 155, 463, 309, 13030, 495])).
% 2.64/2.84 tff(13034,plain,
% 2.64/2.84 (b(s(s(z)), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[625, 13033])).
% 2.64/2.84 tff(13035,plain,
% 2.64/2.84 (((~![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(s(elem!1))))) | (~b(s(s(s(elem!1))), 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(13036,plain,
% 2.64/2.84 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(13037,plain,
% 2.64/2.84 (((~![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(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13036])).
% 2.64/2.84 tff(13038,plain,
% 2.64/2.84 (((~![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(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[13037, 13035])).
% 2.64/2.84 tff(13039,plain,
% 2.64/2.84 ((~![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(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(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)))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(13040,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[13039, 13038])).
% 2.64/2.84 tff(13041,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13040, 97, 1139, 13013, 13034, 13032])).
% 2.64/2.84 tff(13042,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(13043,plain,
% 2.64/2.84 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13042, 12940, 1139, 12726, 463, 729, 12727, 1820])).
% 2.64/2.84 tff(13044,plain,
% 2.64/2.84 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[336, 13043])).
% 2.64/2.84 tff(13045,plain,
% 2.64/2.84 (~b(s(z), s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[3812, 13044, 12942, 12940])).
% 2.64/2.84 tff(13046,plain,
% 2.64/2.84 (r(s(z), s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[548, 13045])).
% 2.64/2.84 tff(13047,plain,
% 2.64/2.84 (((~![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(s(s(s(elem!1)))))) | (~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(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(13048,plain,
% 2.64/2.84 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(13049,plain,
% 2.64/2.84 (((~![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(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[13048])).
% 2.64/2.84 tff(13050,plain,
% 2.64/2.84 (((~![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(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[13049, 13047])).
% 2.64/2.85 tff(13051,plain,
% 2.64/2.85 ((~![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(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(13052,plain,
% 2.64/2.85 ((~![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)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[13051, 13050])).
% 2.64/2.85 tff(13053,plain,
% 2.64/2.85 (~b(s(s(z)), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13052, 97, 12942, 13044, 12940])).
% 2.64/2.85 tff(13054,plain,
% 2.64/2.85 (r(s(s(z)), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[122, 13053])).
% 2.64/2.85 tff(13055,plain,
% 2.64/2.85 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[10311, 155, 13054, 13046, 12726])).
% 2.64/2.85 tff(13056,plain,
% 2.64/2.85 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[452, 13055])).
% 2.64/2.85 tff(13057,plain,
% 2.64/2.85 (~r(z, s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[12985, 12727, 1139, 1820, 729, 12726, 463])).
% 2.64/2.85 tff(13058,plain,
% 2.64/2.85 (b(z, s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[222, 13057])).
% 2.64/2.85 tff(13059,plain,
% 2.64/2.85 (((~![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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, 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(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(13060,plain,
% 2.64/2.85 (((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(13061,plain,
% 2.64/2.85 (((~![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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, 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(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13060])).
% 2.64/2.85 tff(13062,plain,
% 2.64/2.85 (((~![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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, 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(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[13061, 13059])).
% 2.64/2.85 tff(13063,plain,
% 2.64/2.85 ((~![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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(13064,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[13063, 13062])).
% 2.64/2.85 tff(13065,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13064, 97, 13044, 13058, 12940, 13056])).
% 2.64/2.85 tff(13066,plain,(b(s(s(s(s(elem!1)))), s(z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(13067,plain,
% 2.64/2.85 (b(s(s(s(s(elem!1)))), s(z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13066, 11419])).
% 2.64/2.85 tff(13068,plain,
% 2.64/2.85 (~r(z, s(s(s(s(elem!1)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13067, 12725, 11948, 12715])).
% 2.64/2.85 tff(13069,plain,
% 2.64/2.85 (b(z, s(s(s(s(elem!1)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1093, 13068])).
% 2.64/2.85 tff(13070,plain,
% 2.64/2.85 (b(z, s(s(s(s(z)))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[13069, 12686])).
% 2.64/2.85 tff(13071,plain,
% 2.64/2.85 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.64/2.85 inference(symmetry,[status(thm)],[12685])).
% 2.64/2.85 tff(13072,plain,
% 2.64/2.85 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13071])).
% 2.64/2.85 tff(13073,plain,
% 2.64/2.85 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.85 inference(symmetry,[status(thm)],[13072])).
% 2.64/2.85 tff(13074,plain,
% 2.64/2.85 (b(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[12720, 13073])).
% 2.64/2.85 tff(13075,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[7406, 97, 204, 12718, 13074, 13070])).
% 2.64/2.85 tff(13076,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(13077,plain,
% 2.64/2.85 (~r(s(s(z)), s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13076, 12660, 570, 2596, 11818, 145, 2, 12683, 3, 2591])).
% 2.64/2.85 tff(13078,plain,
% 2.64/2.85 (b(s(s(z)), s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[437, 13077])).
% 2.64/2.85 tff(13079,plain,
% 2.64/2.85 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[13078, 12681])).
% 2.64/2.85 tff(13080,plain,
% 2.64/2.85 (s(elem!1) = s(z)),
% 2.64/2.85 inference(transitivity,[status(thm)],[30, 12692, 23])).
% 2.64/2.85 tff(13081,plain,
% 2.64/2.85 (inj_0(s(elem!1)) = inj_0(s(z))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13080])).
% 2.64/2.85 tff(13082,plain,
% 2.64/2.85 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.64/2.85 inference(symmetry,[status(thm)],[13081])).
% 2.64/2.85 tff(13083,plain,
% 2.64/2.85 (z = elem!1),
% 2.64/2.85 inference(transitivity,[status(thm)],[1443, 13082, 85])).
% 2.64/2.85 tff(13084,plain,
% 2.64/2.85 (elem!1 = z),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1888, 13083])).
% 2.64/2.85 tff(13085,plain,
% 2.64/2.85 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(elem!1)))) = s(s(z)))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[12689])).
% 2.64/2.85 tff(13086,plain,
% 2.64/2.85 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[13085, 319])).
% 2.64/2.85 tff(13087,plain,
% 2.64/2.85 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.64/2.85 inference(symmetry,[status(thm)],[13086])).
% 2.64/2.85 tff(13088,plain,
% 2.64/2.85 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13087])).
% 2.64/2.85 tff(13089,plain,
% 2.64/2.85 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[331, 13088])).
% 2.64/2.85 tff(13090,plain,
% 2.64/2.85 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1816, 12726, 1393, 1520, 1812])).
% 2.64/2.85 tff(13091,plain,
% 2.64/2.85 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1484, 13090, 13089])).
% 2.64/2.85 tff(13092,plain,
% 2.64/2.85 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2401, 13091, 2391, 2389, 13083])).
% 2.64/2.85 tff(13093,plain,
% 2.64/2.85 (~r(z, s(s(s(s(elem!1)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13067, 13090, 1139, 506])).
% 2.64/2.85 tff(13094,plain,
% 2.64/2.85 (b(z, s(s(s(s(elem!1)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1093, 13093])).
% 2.64/2.85 tff(13095,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2407, 13094, 13092, 13084])).
% 2.64/2.85 tff(13096,plain,(b(s(s(s(s(elem!1)))), s(z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(13097,plain,
% 2.64/2.85 (b(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13096, 13079, 12679, 12650, 12660, 12673, 12671])).
% 2.64/2.85 tff(13098,plain,
% 2.64/2.85 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[3214])).
% 2.64/2.85 tff(13099,plain,
% 2.64/2.85 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.85 inference(symmetry,[status(thm)],[13098])).
% 2.64/2.85 tff(13100,plain,
% 2.64/2.85 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13099])).
% 2.64/2.85 tff(13101,assumption,(~b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 2.64/2.85 tff(13102,plain,
% 2.64/2.85 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[13101, 13100])).
% 2.64/2.85 tff(13103,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[513, 13102])).
% 2.64/2.85 tff(13104,plain,(b(s(s(s(s(z)))), s(z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~(s(s(s(elem!1))) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(13105,plain,
% 2.64/2.85 (b(s(s(s(s(z)))), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13104, 13097, 12661])).
% 2.64/2.85 tff(13106,plain,
% 2.64/2.85 (r(z, s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[6374, 12661, 570])).
% 2.64/2.85 tff(13107,plain,
% 2.64/2.85 (((~![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), 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)))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(13108,plain,
% 2.64/2.85 (((~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)))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(13109,plain,
% 2.64/2.85 (((~![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), 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))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13108])).
% 2.64/2.85 tff(13110,plain,
% 2.64/2.85 (((~![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), 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)))))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[13109, 13107])).
% 2.64/2.85 tff(13111,plain,
% 2.64/2.85 ((~![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), 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)))))))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(13112,plain,
% 2.64/2.85 ((~![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), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[13111, 13110])).
% 2.64/2.85 tff(13113,plain,
% 2.64/2.85 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13112, 97, 11827, 1360, 10217])).
% 2.64/2.85 tff(13114,plain,
% 2.64/2.85 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2829, 13113])).
% 2.64/2.85 tff(13115,plain,
% 2.64/2.85 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13071])).
% 2.64/2.85 tff(13116,plain,
% 2.64/2.85 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.85 inference(symmetry,[status(thm)],[13115])).
% 2.64/2.85 tff(13117,plain,
% 2.64/2.85 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 2.64/2.85 inference(monotonicity,[status(thm)],[12689])).
% 2.64/2.85 tff(13118,plain,
% 2.64/2.85 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.64/2.85 inference(symmetry,[status(thm)],[13117])).
% 2.64/2.85 tff(13119,plain,
% 2.64/2.85 (elem!1 = z),
% 2.64/2.85 inference(transitivity,[status(thm)],[1450, 13081, 17])).
% 2.64/2.85 tff(13120,plain,
% 2.64/2.85 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13119])).
% 2.64/2.85 tff(13121,plain,
% 2.64/2.85 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 2.64/2.85 inference(symmetry,[status(thm)],[13120])).
% 2.64/2.85 tff(13122,plain,
% 2.64/2.85 (r(s(s(z)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.64/2.85 inference(transitivity,[status(thm)],[13121, 13118])).
% 2.64/2.85 tff(13123,plain,
% 2.64/2.85 (r(s(s(elem!1)), elem!1)),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[645, 13122])).
% 2.64/2.85 tff(13124,plain,
% 2.64/2.85 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(z)))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[12684, 12689])).
% 2.64/2.85 tff(13125,plain,
% 2.64/2.85 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(z))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[13124, 430])).
% 2.64/2.85 tff(13126,plain,
% 2.64/2.85 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.64/2.85 inference(symmetry,[status(thm)],[13125])).
% 2.64/2.85 tff(13127,plain,
% 2.64/2.85 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13126])).
% 2.64/2.85 tff(13128,plain,
% 2.64/2.85 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[432, 13127])).
% 2.64/2.85 tff(13129,plain,
% 2.64/2.85 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[12684])).
% 2.64/2.85 tff(13130,plain,
% 2.64/2.85 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.64/2.85 inference(symmetry,[status(thm)],[13129])).
% 2.64/2.85 tff(13131,plain,
% 2.64/2.85 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13119])).
% 2.64/2.85 tff(13132,plain,
% 2.64/2.85 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.64/2.85 inference(symmetry,[status(thm)],[13131])).
% 2.64/2.85 tff(13133,plain,
% 2.64/2.85 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[13132, 13130])).
% 2.64/2.85 tff(13134,plain,
% 2.64/2.85 (r(elem!1, s(s(s(elem!1))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[1300, 13133])).
% 2.64/2.85 tff(13135,plain,
% 2.64/2.85 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.64/2.85 inference(monotonicity,[status(thm)],[12684])).
% 2.64/2.85 tff(13136,plain,
% 2.64/2.85 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.64/2.85 inference(symmetry,[status(thm)],[13135])).
% 2.64/2.85 tff(13137,plain,
% 2.64/2.85 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13119])).
% 2.64/2.85 tff(13138,plain,
% 2.64/2.85 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 2.64/2.85 inference(symmetry,[status(thm)],[13137])).
% 2.64/2.85 tff(13139,plain,
% 2.64/2.85 (r(s(s(s(z))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 2.64/2.85 inference(transitivity,[status(thm)],[13138, 13136])).
% 2.64/2.85 tff(13140,plain,
% 2.64/2.85 (r(s(s(s(elem!1))), elem!1)),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[386, 13139])).
% 2.64/2.85 tff(13141,plain,
% 2.64/2.85 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[12684, 12689])).
% 2.64/2.85 tff(13142,plain,
% 2.64/2.85 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.85 inference(symmetry,[status(thm)],[13141])).
% 2.64/2.85 tff(13143,plain,
% 2.64/2.85 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[1960, 13142])).
% 2.64/2.85 tff(13144,plain,
% 2.64/2.85 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13071])).
% 2.64/2.85 tff(13145,plain,
% 2.64/2.85 (((~![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), 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), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(13146,plain,
% 2.64/2.85 (((~b(s(z), 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(z))) | (~b(s(s(s(s(z)))), 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(s(z)))), s(s(s(z))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(13147,plain,
% 2.64/2.85 (((~![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), 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(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), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13146])).
% 2.64/2.85 tff(13148,plain,
% 2.64/2.85 (((~![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), 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(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), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[13147, 13145])).
% 2.64/2.85 tff(13149,plain,
% 2.64/2.85 ((~![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), 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(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(13150,plain,
% 2.64/2.85 ((~![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), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[13149, 13148])).
% 2.64/2.85 tff(13151,plain,
% 2.64/2.85 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13150, 97, 11827, 1360, 10217])).
% 2.64/2.85 tff(13152,plain,
% 2.64/2.85 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4169, 13151])).
% 2.64/2.85 tff(13153,plain,
% 2.64/2.85 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[13152, 13144])).
% 2.64/2.85 tff(13154,plain,
% 2.64/2.85 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13071])).
% 2.64/2.85 tff(13155,plain,
% 2.64/2.85 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[13114, 13154])).
% 2.64/2.85 tff(13156,plain,
% 2.64/2.85 (~r(z, s(s(s(s(elem!1)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2449, 13155, 1300, 13153])).
% 2.64/2.85 tff(13157,plain,
% 2.64/2.85 (b(z, s(s(s(s(elem!1)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1093, 13156])).
% 2.64/2.85 tff(13158,plain,
% 2.64/2.85 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2407, 13157, 13084])).
% 2.64/2.85 tff(13159,plain,
% 2.64/2.85 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[11262, 13158, 13083, 13143, 13140, 13134, 13128, 13123])).
% 2.64/2.85 tff(13160,plain,
% 2.64/2.85 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1484, 13159, 13089])).
% 2.64/2.85 tff(13161,plain,
% 2.64/2.85 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[7352, 13160, 1393])).
% 2.64/2.85 tff(13162,plain,
% 2.64/2.85 (r(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[13161, 13116])).
% 2.64/2.85 tff(13163,plain,
% 2.64/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(13164,plain,
% 2.64/2.85 (((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~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))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(13165,plain,
% 2.64/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[13164])).
% 2.64/2.85 tff(13166,plain,
% 2.64/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[13165, 13163])).
% 2.64/2.85 tff(13167,plain,
% 2.64/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(13168,plain,
% 2.64/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[13167, 13166])).
% 2.64/2.85 tff(13169,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13168, 155, 645, 1960, 386, 13162, 13114])).
% 2.64/2.85 tff(13170,plain,((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(13171,plain,
% 2.64/2.85 (~r(s(s(z)), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13170, 2591, 12683, 12660, 13106, 12651, 13105, 3])).
% 2.64/2.85 tff(13172,plain,
% 2.64/2.85 (b(s(s(z)), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[625, 13171])).
% 2.64/2.85 tff(13173,plain,
% 2.64/2.85 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[12661])).
% 2.64/2.86 tff(13174,plain,
% 2.64/2.86 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.86 inference(symmetry,[status(thm)],[13173])).
% 2.64/2.86 tff(13175,plain,
% 2.64/2.86 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[12661])).
% 2.64/2.86 tff(13176,plain,
% 2.64/2.86 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.64/2.86 inference(symmetry,[status(thm)],[13175])).
% 2.64/2.86 tff(13177,plain,
% 2.64/2.86 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[13176])).
% 2.64/2.86 tff(13178,plain,
% 2.64/2.86 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[13177, 13174])).
% 2.64/2.86 tff(13179,plain,
% 2.64/2.86 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[12234, 81, 3, 570, 2590])).
% 2.64/2.86 tff(13180,plain,
% 2.64/2.86 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[452, 13179])).
% 2.64/2.86 tff(13181,plain,
% 2.64/2.86 (~b(s(s(s(s(elem!1)))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[884, 13180, 204, 83])).
% 2.64/2.86 tff(13182,plain,
% 2.64/2.86 (r(s(s(s(s(elem!1)))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[842, 13181])).
% 2.64/2.86 tff(13183,plain,
% 2.64/2.86 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[12626, 81, 12699, 1812, 1393, 83, 204])).
% 2.64/2.86 tff(13184,plain,
% 2.64/2.86 (b(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[511, 13183])).
% 2.64/2.86 tff(13185,plain,
% 2.64/2.86 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1804, 13184, 1139, 193])).
% 2.64/2.86 tff(13186,plain,
% 2.64/2.86 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[821, 13185, 12708])).
% 2.64/2.86 tff(13187,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[832, 13186, 13182, 570, 288])).
% 2.64/2.86 tff(13188,plain,((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(13189,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13188, 12099, 81, 288, 1139, 570, 204, 83, 1812, 1393, 3, 2590])).
% 2.64/2.86 tff(13190,plain,((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(13191,plain,
% 2.64/2.86 (~r(s(z), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13190, 13172, 12650, 570, 11818, 2596, 12671, 12660, 3, 2590])).
% 2.64/2.86 tff(13192,plain,
% 2.64/2.86 (b(s(z), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[568, 13191])).
% 2.64/2.86 tff(13193,plain,
% 2.64/2.86 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13150, 97, 13192, 12651, 13105])).
% 2.64/2.86 tff(13194,plain,
% 2.64/2.86 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[4169, 13193])).
% 2.64/2.86 tff(13195,plain,
% 2.64/2.86 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[13194, 13178])).
% 2.64/2.86 tff(13196,plain,
% 2.64/2.86 (~r(s(s(s(s(elem!1)))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[832, 13195, 570, 2596])).
% 2.64/2.86 tff(13197,plain,
% 2.64/2.86 (b(s(s(s(s(elem!1)))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[842, 13196])).
% 2.64/2.86 tff(13198,plain,
% 2.64/2.86 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[884, 13197, 11818, 13172])).
% 2.64/2.86 tff(13199,plain,
% 2.64/2.86 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[12661])).
% 2.64/2.86 tff(13200,plain,
% 2.64/2.86 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.86 inference(symmetry,[status(thm)],[13199])).
% 2.64/2.86 tff(13201,plain,
% 2.64/2.86 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[13176])).
% 2.64/2.86 tff(13202,plain,
% 2.64/2.86 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[13201, 13200])).
% 2.64/2.86 tff(13203,plain,
% 2.64/2.86 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13112, 97, 13192, 12651, 13105])).
% 2.64/2.86 tff(13204,plain,
% 2.64/2.86 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2829, 13203])).
% 2.64/2.86 tff(13205,plain,
% 2.64/2.86 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[13204, 13202])).
% 2.64/2.86 tff(13206,plain,
% 2.64/2.86 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[13204, 13201])).
% 2.64/2.86 tff(13207,plain,
% 2.64/2.86 (~r(s(s(s(s(elem!1)))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[832, 823, 570, 288])).
% 2.64/2.86 tff(13208,plain,
% 2.64/2.86 (b(s(s(s(s(elem!1)))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[842, 13207])).
% 2.64/2.86 tff(13209,plain,
% 2.64/2.86 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[884, 13208, 204, 83])).
% 2.64/2.86 tff(13210,plain,
% 2.64/2.86 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[452, 13209])).
% 2.64/2.86 tff(13211,plain,
% 2.64/2.86 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1822, 13210, 1393])).
% 2.64/2.86 tff(13212,plain,
% 2.64/2.86 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2439, 823, 1889])).
% 2.64/2.86 tff(13213,plain,
% 2.64/2.86 (~r(z, s(s(s(s(elem!1)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2449, 13212, 1300, 2441])).
% 2.64/2.86 tff(13214,plain,
% 2.64/2.86 (b(z, s(s(s(s(elem!1)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1093, 13213])).
% 2.64/2.86 tff(13215,plain,
% 2.64/2.86 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[669, 13214, 339, 83])).
% 2.64/2.86 tff(13216,plain,
% 2.64/2.86 (r(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[511, 13215])).
% 2.64/2.86 tff(13217,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1816, 13216, 13211, 1812, 1393, 1520])).
% 2.64/2.86 tff(13218,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(13219,plain,
% 2.64/2.86 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13218, 13195, 13106, 12660, 13172, 12673, 11818, 2596, 13206, 570, 12671])).
% 2.64/2.86 tff(13220,plain,
% 2.64/2.86 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[336, 13219])).
% 2.64/2.86 tff(13221,plain,
% 2.64/2.86 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[5279, 13220, 145, 13205])).
% 2.64/2.86 tff(13222,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[452, 13221, 13198])).
% 2.64/2.86 tff(13223,plain,(b(s(s(s(z))), s(s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(13224,plain,
% 2.64/2.86 (b(s(s(s(z))), s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13223, 11820, 12649, 3, 2, 239])).
% 2.64/2.86 tff(13225,plain,
% 2.64/2.86 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1995, 13224, 5])).
% 2.64/2.86 tff(13226,plain,
% 2.64/2.86 (~b(s(s(s(z))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[12494, 645, 204, 3, 11948, 1331, 1])).
% 2.64/2.86 tff(13227,plain,
% 2.64/2.86 (r(s(s(s(z))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1358, 13226])).
% 2.64/2.86 tff(13228,plain,
% 2.64/2.86 (~b(s(s(z)), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[12516, 645, 204, 288, 3, 1, 2])).
% 2.64/2.86 tff(13229,plain,
% 2.64/2.86 (r(s(s(z)), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[437, 13228])).
% 2.64/2.86 tff(13230,plain,
% 2.64/2.86 ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[3605, 11419])).
% 2.64/2.86 tff(13231,plain,
% 2.64/2.86 (~r(s(z), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13230, 13229, 2, 645])).
% 2.64/2.86 tff(13232,plain,
% 2.64/2.86 (b(s(z), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[253, 13231])).
% 2.64/2.86 tff(13233,plain,
% 2.64/2.86 (~r(s(s(s(z))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[12716, 13229, 2, 645])).
% 2.64/2.86 tff(13234,plain,
% 2.64/2.86 (b(s(s(s(z))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[402, 13233])).
% 2.64/2.86 tff(13235,plain,
% 2.64/2.86 (((~![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), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(13236,plain,
% 2.64/2.86 (((~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(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(13237,plain,
% 2.64/2.86 (((~![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))), 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(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[13236])).
% 2.64/2.86 tff(13238,plain,
% 2.64/2.86 (((~![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))), 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(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.64/2.86 inference(transitivity,[status(thm)],[13237, 13235])).
% 2.64/2.86 tff(13239,plain,
% 2.64/2.86 ((~![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))), 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)))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(13240,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[13239, 13238])).
% 2.64/2.86 tff(13241,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13240, 97, 550, 86, 1330, 1216])).
% 2.64/2.86 tff(13242,plain,((~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(13243,plain,
% 2.64/2.86 (~b(z, s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13242, 13234, 11827, 13232])).
% 2.64/2.86 tff(13244,plain,
% 2.64/2.86 (r(z, s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1318, 13243])).
% 2.64/2.86 tff(13245,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[9265, 155, 645, 2, 13244, 13229, 13227])).
% 2.64/2.86 tff(13246,plain,((~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(13247,plain,
% 2.64/2.86 (~r(s(s(z)), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13246, 13224, 11818, 3, 2, 13225, 2596])).
% 2.64/2.86 tff(13248,plain,
% 2.64/2.86 (b(s(s(z)), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[625, 13247])).
% 2.64/2.86 tff(13249,plain,
% 2.64/2.86 (~b(s(s(s(z))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[10183, 97, 11818, 13248, 13224])).
% 2.64/2.86 tff(13250,plain,
% 2.64/2.86 (r(s(s(s(z))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[402, 13249])).
% 2.64/2.86 tff(13251,plain,
% 2.64/2.86 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1674, 155, 12649, 2596, 13250])).
% 2.64/2.86 tff(13252,plain,
% 2.64/2.86 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[3089, 13251, 13225])).
% 2.64/2.86 tff(13253,plain,
% 2.64/2.86 (~b(z, s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1339, 13248, 11818, 13224])).
% 2.64/2.86 tff(13254,plain,
% 2.64/2.86 (r(z, s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1318, 13253])).
% 2.64/2.86 tff(13255,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(13256,plain,
% 2.64/2.86 (((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(13257,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[13256])).
% 2.64/2.86 tff(13258,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[13257, 13255])).
% 2.64/2.86 tff(13259,plain,
% 2.64/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(13260,plain,
% 2.64/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[13259, 13258])).
% 2.64/2.86 tff(13261,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13260, 155, 11419, 570, 1300, 225, 2597])).
% 2.64/2.86 tff(13262,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(13263,plain,
% 2.64/2.86 (~r(s(z), s(s(s(elem!1))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13262, 2597, 1300, 570])).
% 2.64/2.86 tff(13264,plain,
% 2.64/2.86 (b(s(z), s(s(s(elem!1))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[181, 13263])).
% 2.64/2.86 tff(13265,plain,
% 2.64/2.86 (~b(s(z), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1710, 13264, 1139, 1702])).
% 2.64/2.86 tff(13266,plain,
% 2.64/2.86 (r(s(z), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[253, 13265])).
% 2.64/2.86 tff(13267,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[5909, 155, 11419, 1300, 13266, 2597])).
% 2.64/2.86 tff(13268,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(13269,plain,
% 2.64/2.86 (~r(s(s(s(z))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13268, 13254, 12650, 13252, 12649])).
% 2.64/2.86 tff(13270,plain,
% 2.64/2.86 (b(s(s(s(z))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1358, 13269])).
% 2.64/2.86 tff(13271,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[11541, 12099, 81, 1139, 570, 1, 288, 386])).
% 2.64/2.86 tff(13272,plain,((~r(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(13273,plain,
% 2.64/2.86 (~r(s(z), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13272, 12649, 12650, 13225, 2596, 13250, 3])).
% 2.64/2.86 tff(13274,plain,
% 2.64/2.86 (b(s(z), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[568, 13273])).
% 2.64/2.86 tff(13275,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[10125, 97, 12650, 13274, 13270, 13252])).
% 2.64/2.86 tff(13276,plain,(b(s(s(s(elem!1))), s(s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(13277,plain,
% 2.64/2.86 (b(s(s(s(elem!1))), s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13276, 3, 2, 239])).
% 2.64/2.86 tff(13278,plain,
% 2.64/2.86 (~b(z, s(s(s(elem!1))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[11838, 60, 288, 204, 2])).
% 2.64/2.86 tff(13279,plain,
% 2.64/2.86 (r(z, s(s(s(elem!1))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[590, 13278])).
% 2.64/2.86 tff(13280,plain,
% 2.64/2.86 (~r(z, s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[12423, 12651, 11948, 570, 1, 2590, 3])).
% 2.64/2.86 tff(13281,plain,
% 2.64/2.86 (b(z, s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1318, 13280])).
% 2.64/2.86 tff(13282,plain,
% 2.64/2.86 (~b(s(s(z)), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[12449, 2590, 3, 11948, 1, 2])).
% 2.64/2.86 tff(13283,plain,
% 2.64/2.86 (r(s(s(z)), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[437, 13282])).
% 2.64/2.86 tff(13284,plain,
% 2.64/2.86 (~r(s(z), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2641, 13283, 3, 2591])).
% 2.64/2.86 tff(13285,plain,
% 2.64/2.86 (b(s(z), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[253, 13284])).
% 2.64/2.86 tff(13286,plain,
% 2.64/2.86 (~b(s(z), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[12599, 13281, 13285, 12651])).
% 2.64/2.86 tff(13287,plain,
% 2.64/2.86 (r(s(z), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[568, 13286])).
% 2.64/2.86 tff(13288,plain,
% 2.64/2.86 (~r(s(s(z)), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[11825, 13287, 3])).
% 2.64/2.86 tff(13289,plain,
% 2.64/2.86 (b(s(s(z)), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[625, 13288])).
% 2.64/2.86 tff(13290,plain,
% 2.64/2.86 (~r(s(s(s(z))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13272, 13287, 11948, 570, 288, 1, 3])).
% 2.64/2.86 tff(13291,plain,
% 2.64/2.86 (b(s(s(s(z))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[402, 13290])).
% 2.64/2.86 tff(13292,plain,
% 2.64/2.86 (~b(s(s(s(s(elem!1)))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[11562, 13291, 13289, 2591, 13281])).
% 2.64/2.86 tff(13293,plain,
% 2.64/2.86 (r(s(s(s(s(elem!1)))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[842, 13292])).
% 2.64/2.86 tff(13294,plain,
% 2.64/2.86 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[832, 13293, 570, 288])).
% 2.64/2.86 tff(13295,plain,
% 2.64/2.86 (b(s(z), s(s(s(elem!1))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[12098, 13287, 3])).
% 2.64/2.86 tff(13296,plain,
% 2.64/2.86 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[11568, 13293, 13287])).
% 2.64/2.86 tff(13297,plain,
% 2.64/2.86 (b(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[511, 13296])).
% 2.64/2.86 tff(13298,plain,
% 2.64/2.86 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1804, 13297, 11948, 13295])).
% 2.64/2.86 tff(13299,plain,
% 2.64/2.86 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[821, 13298, 13294])).
% 2.64/2.86 tff(13300,plain,
% 2.64/2.86 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[523, 13299])).
% 2.64/2.86 tff(13301,plain,
% 2.64/2.86 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[349, 13300])).
% 2.64/2.86 tff(13302,plain,
% 2.64/2.86 (s(s(s(s(elem!1)))) = elem!1),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1734, 13301])).
% 2.64/2.86 tff(13303,plain,
% 2.64/2.86 (r(s(s(s(s(z)))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(z)))), elem!1)),
% 2.64/2.86 inference(monotonicity,[status(thm)],[13302])).
% 2.64/2.86 tff(13304,plain,
% 2.64/2.86 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.64/2.86 inference(symmetry,[status(thm)],[13303])).
% 2.64/2.86 tff(13305,plain,
% 2.64/2.86 (~(s(s(s(s(z)))) = elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2786, 13300])).
% 2.64/2.86 tff(13306,plain,
% 2.64/2.86 (b(s(s(s(s(z)))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(z)))), elem!1)),
% 2.64/2.86 inference(monotonicity,[status(thm)],[13302])).
% 2.64/2.86 tff(13307,plain,
% 2.64/2.86 ((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[13306])).
% 2.64/2.86 tff(13308,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 2.64/2.86 tff(13309,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(13310,plain,
% 2.64/2.86 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(13311,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[13310])).
% 2.64/2.86 tff(13312,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 2.64/2.86 inference(transitivity,[status(thm)],[13311, 13309])).
% 2.64/2.86 tff(13313,plain,
% 2.64/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(13314,plain,
% 2.64/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[13313, 13312])).
% 2.64/2.86 tff(13315,plain,
% 2.64/2.86 (~r(s(s(s(s(z)))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13314, 155, 11419, 81, 13308])).
% 2.64/2.86 tff(13316,plain,
% 2.64/2.86 (b(s(s(s(s(z)))), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2860, 13315])).
% 2.64/2.86 tff(13317,plain,
% 2.64/2.86 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(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)))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(13318,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[13317])).
% 2.64/2.86 tff(13319,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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)))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[13318, 10190])).
% 2.64/2.86 tff(13320,plain,
% 2.64/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(13321,plain,
% 2.64/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[13320, 13319])).
% 2.64/2.86 tff(13322,plain,
% 2.64/2.86 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13321, 155, 2, 3, 13308])).
% 2.64/2.86 tff(13323,plain,
% 2.64/2.86 (b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2886, 80])).
% 2.64/2.86 tff(13324,plain,
% 2.64/2.86 (b(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13323, 13322])).
% 2.64/2.86 tff(13325,plain,
% 2.64/2.86 (~r(s(s(z)), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[11825, 81, 3])).
% 2.64/2.86 tff(13326,plain,
% 2.64/2.86 (b(s(s(z)), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[625, 13325])).
% 2.64/2.86 tff(13327,plain,
% 2.64/2.86 (((~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(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(13328,plain,
% 2.64/2.86 (((~![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(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(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[13327])).
% 2.64/2.86 tff(13329,plain,
% 2.64/2.86 (((~![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(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(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.64/2.86 inference(transitivity,[status(thm)],[13328, 7393])).
% 2.64/2.86 tff(13330,plain,
% 2.64/2.86 ((~![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(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)))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(13331,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[13330, 13329])).
% 2.64/2.86 tff(13332,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[13331, 97, 204, 13326, 13324, 13316])).
% 2.64/2.86 tff(13333,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(13334,plain,
% 2.64/2.87 (~r(s(s(s(s(z)))), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[13333, 13287, 2, 3, 204])).
% 2.64/2.87 tff(13335,plain,
% 2.64/2.87 (b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[2807, 2795])).
% 2.64/2.87 tff(13336,plain,
% 2.64/2.87 (b(s(s(s(s(z)))), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[13335, 13334])).
% 2.64/2.87 tff(13337,plain,
% 2.64/2.87 (b(s(z), s(s(s(s(elem!1)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[12417, 13287, 3, 2590])).
% 2.64/2.87 tff(13338,plain,
% 2.64/2.87 (((~![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(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(13339,plain,
% 2.64/2.87 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(13340,plain,
% 2.64/2.87 (((~![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(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13339])).
% 2.64/2.87 tff(13341,plain,
% 2.64/2.87 (((~![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(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[13340, 13338])).
% 2.64/2.87 tff(13342,plain,
% 2.64/2.87 ((~![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(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(13343,plain,
% 2.64/2.87 ((~![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(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[13342, 13341])).
% 2.64/2.87 tff(13344,plain,
% 2.64/2.87 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[13343, 97, 13337, 13297, 13336])).
% 2.64/2.87 tff(13345,plain,
% 2.64/2.87 (~b(s(s(s(s(z)))), elem!1)),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[13344, 13307])).
% 2.64/2.87 tff(13346,plain,
% 2.64/2.87 (r(s(s(s(s(z)))), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[2873, 13345, 13305])).
% 2.64/2.87 tff(13347,plain,
% 2.64/2.87 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[13346, 13304])).
% 2.64/2.87 tff(13348,plain,
% 2.64/2.87 (((~![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(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(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))))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(13349,plain,
% 2.64/2.87 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(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(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))))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(13350,plain,
% 2.64/2.87 (((~![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(s(s(elem!1)))))) | (~b(s(z), s(s(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(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)))))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13349])).
% 2.64/2.87 tff(13351,plain,
% 2.64/2.87 (((~![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(s(s(elem!1)))))) | (~b(s(z), s(s(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(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))))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[13350, 13348])).
% 2.64/2.87 tff(13352,plain,
% 2.64/2.87 ((~![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(s(s(elem!1)))))) | (~b(s(z), s(s(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))))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(13353,plain,
% 2.64/2.87 ((~![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(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)))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[13352, 13351])).
% 2.64/2.87 tff(13354,plain,
% 2.64/2.87 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[13353, 97, 13337, 12651, 13336])).
% 2.64/2.87 tff(13355,plain,
% 2.64/2.87 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[4169, 13354])).
% 2.64/2.87 tff(13356,plain,
% 2.64/2.87 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13300])).
% 2.64/2.87 tff(13357,plain,
% 2.64/2.87 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[1710, 13295, 11948, 13285])).
% 2.64/2.87 tff(13358,plain,
% 2.64/2.87 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[3089, 13357, 1])).
% 2.64/2.87 tff(13359,plain,
% 2.64/2.87 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[13358, 13356])).
% 2.64/2.87 tff(13360,plain,
% 2.64/2.87 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[10998, 13297, 12651, 13337])).
% 2.64/2.87 tff(13361,plain,
% 2.64/2.87 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[2747, 13360])).
% 2.64/2.87 tff(13362,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(13363,plain,
% 2.64/2.87 (((~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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(13364,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13363])).
% 2.64/2.87 tff(13365,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[13364, 13362])).
% 2.64/2.87 tff(13366,plain,
% 2.64/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(13367,plain,
% 2.64/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[13366, 13365])).
% 2.64/2.87 tff(13368,plain,
% 2.64/2.87 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[13367, 155, 13361, 13359, 13355])).
% 2.64/2.87 tff(13369,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[13368, 13347])).
% 2.64/2.87 tff(13370,plain,(b(s(s(s(z))), s(s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(13371,plain,
% 2.64/2.87 (b(s(s(s(z))), s(s(z)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[13370, 1, 3, 204, 13279, 288, 2])).
% 2.64/2.87 tff(13372,plain,
% 2.64/2.87 (~r(s(s(z)), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[13246, 13371, 204, 3, 2, 1, 288])).
% 2.64/2.87 tff(13373,plain,
% 2.64/2.87 (~b(s(s(z)), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[11937, 13371, 60, 13279, 1, 204])).
% 2.64/2.87 tff(13374,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[625, 13373, 13372])).
% 2.64/2.87 tff(13375,plain,((s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(13376,plain,
% 2.64/2.87 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[13375, 13277, 11818, 3, 2, 2596])).
% 2.64/2.87 tff(13377,plain,
% 2.64/2.87 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13376])).
% 2.64/2.87 tff(13378,plain,
% 2.64/2.87 (s(s(z)) = s(s(elem!1))),
% 2.64/2.87 inference(transitivity,[status(thm)],[73, 13377, 19])).
% 2.64/2.87 tff(13379,plain,
% 2.64/2.87 ((s(s(z)) = s(s(s(s(s(elem!1)))))) <=> (s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13378])).
% 2.64/2.87 tff(13380,plain,
% 2.64/2.87 ((s(s(z)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.64/2.87 inference(transitivity,[status(thm)],[13379, 11819])).
% 2.64/2.87 tff(13381,plain,
% 2.64/2.87 ((~(s(s(z)) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13380])).
% 2.64/2.87 tff(13382,assumption,(s(s(z)) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.64/2.87 tff(13383,plain,
% 2.64/2.87 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13382])).
% 2.64/2.87 tff(13384,plain,
% 2.64/2.87 (s(z) = s(s(s(s(elem!1))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[24, 13383, 6167])).
% 2.64/2.87 tff(13385,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[275, 13384])).
% 2.64/2.87 tff(13386,plain,(~(s(s(z)) = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(13387,plain,
% 2.64/2.87 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[13386, 13381])).
% 2.64/2.87 tff(13388,plain,
% 2.64/2.87 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13378])).
% 2.64/2.87 tff(13389,plain,
% 2.64/2.87 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.64/2.87 inference(symmetry,[status(thm)],[13388])).
% 2.64/2.87 tff(13390,plain,
% 2.64/2.87 (s(elem!1) = s(z)),
% 2.64/2.87 inference(transitivity,[status(thm)],[30, 13389, 23])).
% 2.64/2.87 tff(13391,plain,
% 2.64/2.87 (r(s(s(s(s(s(elem!1))))), s(elem!1)) <=> r(s(s(s(s(s(elem!1))))), s(z))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13390])).
% 2.64/2.87 tff(13392,plain,
% 2.64/2.87 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.64/2.87 inference(symmetry,[status(thm)],[13391])).
% 2.64/2.87 tff(13393,plain,
% 2.64/2.87 (~(s(s(s(s(s(elem!1))))) = s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[6222, 13376])).
% 2.64/2.87 tff(13394,plain,
% 2.64/2.87 (b(s(s(s(s(s(elem!1))))), s(elem!1)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13390])).
% 2.64/2.87 tff(13395,plain,
% 2.64/2.87 ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) <=> (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13394])).
% 2.64/2.87 tff(13396,plain,
% 2.64/2.87 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13390])).
% 2.64/2.87 tff(13397,plain,
% 2.64/2.87 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.64/2.87 inference(symmetry,[status(thm)],[13396])).
% 2.64/2.87 tff(13398,plain,
% 2.64/2.87 (b(s(s(s(elem!1))), s(elem!1))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[12650, 13397])).
% 2.64/2.87 tff(13399,plain,
% 2.64/2.87 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.64/2.87 inference(symmetry,[status(thm)],[13377])).
% 2.64/2.87 tff(13400,plain,
% 2.64/2.87 (s(s(elem!1)) = s(s(z))),
% 2.64/2.87 inference(transitivity,[status(thm)],[167, 13399, 72])).
% 2.64/2.87 tff(13401,plain,
% 2.64/2.87 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13400])).
% 2.64/2.87 tff(13402,plain,
% 2.64/2.87 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.64/2.87 inference(symmetry,[status(thm)],[13401])).
% 2.64/2.87 tff(13403,plain,
% 2.64/2.87 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13376])).
% 2.64/2.87 tff(13404,plain,
% 2.64/2.87 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[13403, 1414])).
% 2.64/2.87 tff(13405,plain,
% 2.64/2.87 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[13404, 2507])).
% 2.64/2.87 tff(13406,plain,
% 2.64/2.87 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13405])).
% 2.64/2.87 tff(13407,plain,
% 2.64/2.87 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[286, 13406])).
% 2.64/2.87 tff(13408,plain,
% 2.64/2.87 (s(z) = s(elem!1)),
% 2.64/2.87 inference(transitivity,[status(thm)],[24, 13388, 29])).
% 2.64/2.87 tff(13409,plain,
% 2.64/2.87 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13378, 13408])).
% 2.64/2.87 tff(13410,plain,
% 2.64/2.87 (r(s(s(elem!1)), s(elem!1))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[2, 13409])).
% 2.64/2.87 tff(13411,plain,
% 2.64/2.87 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13378])).
% 2.64/2.87 tff(13412,plain,
% 2.64/2.87 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(z)))),
% 2.64/2.87 inference(symmetry,[status(thm)],[13411])).
% 2.64/2.87 tff(13413,plain,
% 2.64/2.87 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13408, 13378])).
% 2.64/2.87 tff(13414,plain,
% 2.64/2.87 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 2.64/2.87 inference(transitivity,[status(thm)],[13413, 13412])).
% 2.64/2.87 tff(13415,plain,
% 2.64/2.87 (r(s(elem!1), s(s(z)))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[3, 13414])).
% 2.64/2.87 tff(13416,plain,
% 2.64/2.87 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13376])).
% 2.64/2.87 tff(13417,plain,
% 2.64/2.87 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13416, 13378])).
% 2.64/2.87 tff(13418,plain,
% 2.64/2.87 (~b(s(s(s(z))), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[9913, 13376, 239])).
% 2.64/2.87 tff(13419,plain,
% 2.64/2.87 (r(s(s(s(z))), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[402, 13418])).
% 2.64/2.87 tff(13420,plain,
% 2.64/2.87 (b(s(s(s(z))), s(s(z)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[2677, 13376, 13277])).
% 2.64/2.87 tff(13421,plain,
% 2.64/2.87 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13378])).
% 2.64/2.87 tff(13422,plain,
% 2.64/2.87 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 2.64/2.87 inference(symmetry,[status(thm)],[13421])).
% 2.64/2.87 tff(13423,plain,
% 2.64/2.87 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13408])).
% 2.64/2.87 tff(13424,plain,
% 2.64/2.87 (z = elem!1),
% 2.64/2.87 inference(transitivity,[status(thm)],[1443, 13423, 85])).
% 2.64/2.87 tff(13425,plain,
% 2.64/2.87 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13424])).
% 2.64/2.87 tff(13426,plain,
% 2.64/2.87 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 2.64/2.87 inference(transitivity,[status(thm)],[13425, 13422])).
% 2.64/2.87 tff(13427,plain,
% 2.64/2.87 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13378])).
% 2.64/2.87 tff(13428,plain,
% 2.64/2.87 (b(z, s(s(elem!1)))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[11818, 13427])).
% 2.64/2.87 tff(13429,plain,
% 2.64/2.87 (b(elem!1, s(s(z)))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[13428, 13426])).
% 2.64/2.87 tff(13430,plain,
% 2.64/2.87 (~b(z, s(s(s(elem!1))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[11838, 13277, 2596, 11818, 2])).
% 2.64/2.87 tff(13431,plain,
% 2.64/2.87 (r(z, s(s(s(elem!1))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[590, 13430])).
% 2.64/2.87 tff(13432,plain,
% 2.64/2.87 (b(elem!1, s(s(elem!1)))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[13428, 13425])).
% 2.64/2.87 tff(13433,plain,
% 2.64/2.87 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.64/2.87 inference(symmetry,[status(thm)],[7318])).
% 2.64/2.87 tff(13434,plain,
% 2.64/2.87 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[10818, 645, 288, 1889, 570])).
% 2.64/2.87 tff(13435,plain,
% 2.64/2.87 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[8079, 13434, 8063])).
% 2.64/2.87 tff(13436,plain,
% 2.64/2.87 (b(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[13096, 13435, 2389, 1139, 1393, 1520, 11855])).
% 2.64/2.87 tff(13437,plain,
% 2.64/2.87 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[13436, 13433])).
% 2.64/2.87 tff(13438,plain,
% 2.64/2.87 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 2.64/2.87 inference(monotonicity,[status(thm)],[1401])).
% 2.64/2.87 tff(13439,plain,
% 2.64/2.87 ((s(elem!1) = elem!1) <=> (elem!1 = s(elem!1))),
% 2.64/2.87 inference(commutativity,[status(thm)],[])).
% 2.64/2.87 tff(13440,plain,
% 2.64/2.87 ((s(z) = elem!1) <=> (s(elem!1) = elem!1)),
% 2.64/2.87 inference(monotonicity,[status(thm)],[1401])).
% 2.64/2.87 tff(13441,plain,
% 2.64/2.87 ((s(z) = elem!1) <=> (elem!1 = s(elem!1))),
% 2.64/2.87 inference(transitivity,[status(thm)],[13440, 13439])).
% 2.64/2.87 tff(13442,plain,
% 2.64/2.87 ((elem!1 = s(elem!1)) <=> (s(z) = elem!1)),
% 2.64/2.87 inference(symmetry,[status(thm)],[13441])).
% 2.64/2.87 tff(13443,plain,
% 2.64/2.87 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 2.64/2.87 inference(monotonicity,[status(thm)],[1444])).
% 2.64/2.87 tff(13444,plain,
% 2.64/2.87 ((s(elem!1) = z) <=> (elem!1 = s(elem!1))),
% 2.64/2.87 inference(transitivity,[status(thm)],[13443, 13439])).
% 2.64/2.87 tff(13445,plain,
% 2.64/2.87 ((s(elem!1) = z) <=> (s(z) = elem!1)),
% 2.64/2.87 inference(transitivity,[status(thm)],[13444, 13442])).
% 2.64/2.87 tff(13446,plain,
% 2.64/2.87 ((~(s(elem!1) = z)) <=> (~(s(z) = elem!1))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13445])).
% 2.64/2.87 tff(13447,plain,
% 2.64/2.87 (~(s(z) = elem!1)),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[40, 13446])).
% 2.64/2.87 tff(13448,plain,
% 2.64/2.87 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.64/2.87 inference(monotonicity,[status(thm)],[1399])).
% 2.64/2.87 tff(13449,plain,
% 2.64/2.87 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 2.64/2.87 inference(symmetry,[status(thm)],[13448])).
% 2.64/2.87 tff(13450,plain,
% 2.64/2.87 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 2.64/2.87 inference(transitivity,[status(thm)],[3319, 3318, 13449])).
% 2.64/2.87 tff(13451,plain,
% 2.64/2.87 (r(s(s(z)), elem!1)),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[645, 13450])).
% 2.64/2.87 tff(13452,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 2.64/2.87 tff(13453,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(13454,plain,
% 2.64/2.87 (((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(13455,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), z))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[13454])).
% 2.64/2.87 tff(13456,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 2.64/2.87 inference(transitivity,[status(thm)],[13455, 13453])).
% 2.64/2.87 tff(13457,plain,
% 2.64/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(13458,plain,
% 2.64/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), z))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[13457, 13456])).
% 2.64/2.87 tff(13459,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[13458, 155, 6845, 13452, 729, 645, 2])).
% 2.64/2.87 tff(13460,plain,((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(13461,plain,
% 2.64/2.87 ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13460, 11419])).
% 2.64/2.88 tff(13462,plain,
% 2.64/2.88 (~r(s(z), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13461, 13451, 2, 645])).
% 2.64/2.88 tff(13463,plain,
% 2.64/2.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(13464,plain,
% 2.64/2.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(13465,plain,
% 2.64/2.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[13464, 13463])).
% 2.64/2.88 tff(13466,plain,
% 2.64/2.88 ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13465, 53])).
% 2.64/2.88 tff(13467,plain,
% 2.64/2.88 (b(s(z), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13466, 13462, 13447])).
% 2.64/2.88 tff(13468,plain,
% 2.64/2.88 (b(s(elem!1), elem!1)),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[13467, 13438])).
% 2.64/2.88 tff(13469,plain,
% 2.64/2.88 (b(s(s(s(elem!1))), s(elem!1))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[1139, 10807])).
% 2.64/2.88 tff(13470,plain,
% 2.64/2.88 (((~![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(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), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(13471,plain,
% 2.64/2.88 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(13472,plain,
% 2.64/2.88 (((~![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(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))) | (~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(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), elem!1))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[13471])).
% 2.64/2.88 tff(13473,plain,
% 2.64/2.88 (((~![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(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))) | (~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(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), elem!1)))),
% 2.64/2.88 inference(transitivity,[status(thm)],[13472, 13470])).
% 2.64/2.88 tff(13474,plain,
% 2.64/2.88 ((~![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(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))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(13475,plain,
% 2.64/2.88 ((~![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(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), elem!1))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[13474, 13473])).
% 2.64/2.88 tff(13476,plain,
% 2.64/2.88 ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13475, 97, 13469, 13468])).
% 2.64/2.88 tff(13477,plain,
% 2.64/2.88 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13476, 13437])).
% 2.64/2.88 tff(13478,plain,
% 2.64/2.88 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[821, 13477, 4451])).
% 2.64/2.88 tff(13479,plain,
% 2.64/2.88 (~r(s(s(s(s(elem!1)))), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[832, 13478, 570, 288])).
% 2.64/2.88 tff(13480,plain,
% 2.64/2.88 (b(s(s(s(s(elem!1)))), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[842, 13479])).
% 2.64/2.88 tff(13481,plain,
% 2.64/2.88 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[4474, 13480, 1444])).
% 2.64/2.88 tff(13482,plain,
% 2.64/2.88 (((~![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(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(13483,plain,
% 2.64/2.88 (((~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(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(13484,plain,
% 2.64/2.88 (((~![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(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(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[13483])).
% 2.64/2.88 tff(13485,plain,
% 2.64/2.88 (((~![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(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(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.64/2.88 inference(transitivity,[status(thm)],[13484, 13482])).
% 2.64/2.88 tff(13486,plain,
% 2.64/2.88 ((~![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(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))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(13487,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[13486, 13485])).
% 2.64/2.88 tff(13488,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13487, 97, 13481, 1914, 13468, 13437])).
% 2.64/2.88 tff(13489,plain,((~r(s(s(z)), z)) | (~b(elem!1, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(13490,plain,
% 2.64/2.88 (~r(s(s(z)), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13489, 13432, 13431, 2596, 13376, 2, 13429, 12650, 13415])).
% 2.64/2.88 tff(13491,plain,
% 2.64/2.88 (b(s(s(z)), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[625, 13490])).
% 2.64/2.88 tff(13492,plain,
% 2.64/2.88 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[7433, 13491, 11818, 13420, 13419])).
% 2.64/2.88 tff(13493,plain,
% 2.64/2.88 (r(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13323, 13492])).
% 2.64/2.88 tff(13494,plain,
% 2.64/2.88 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[13493, 13417])).
% 2.64/2.88 tff(13495,plain,
% 2.64/2.88 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1816, 13494, 13376, 13415, 13410])).
% 2.64/2.88 tff(13496,plain,
% 2.64/2.88 (b(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[511, 13495])).
% 2.64/2.88 tff(13497,plain,
% 2.64/2.88 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.64/2.88 inference(monotonicity,[status(thm)],[13424])).
% 2.64/2.88 tff(13498,plain,
% 2.64/2.88 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 2.64/2.88 inference(monotonicity,[status(thm)],[13378])).
% 2.64/2.88 tff(13499,plain,
% 2.64/2.88 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.64/2.88 inference(transitivity,[status(thm)],[13498, 13497])).
% 2.64/2.88 tff(13500,plain,
% 2.64/2.88 (b(s(s(elem!1)), elem!1)),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[13491, 13499])).
% 2.64/2.88 tff(13501,plain,
% 2.64/2.88 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[13400])).
% 2.64/2.88 tff(13502,plain,
% 2.64/2.88 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.88 inference(symmetry,[status(thm)],[13501])).
% 2.64/2.88 tff(13503,plain,
% 2.64/2.88 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[13277, 13502])).
% 2.64/2.88 tff(13504,plain,
% 2.64/2.88 (r(s(s(z)), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[13378])).
% 2.64/2.88 tff(13505,plain,
% 2.64/2.88 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(elem!1))),
% 2.64/2.88 inference(symmetry,[status(thm)],[13504])).
% 2.64/2.88 tff(13506,plain,
% 2.64/2.88 (r(s(s(z)), s(z)) <=> r(s(s(z)), s(elem!1))),
% 2.64/2.88 inference(transitivity,[status(thm)],[13409, 13505])).
% 2.64/2.88 tff(13507,plain,
% 2.64/2.88 (r(s(s(z)), s(elem!1))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[2, 13506])).
% 2.64/2.88 tff(13508,plain,
% 2.64/2.88 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[513, 13433])).
% 2.64/2.88 tff(13509,plain,
% 2.64/2.88 ((elem!1 = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 2.64/2.88 inference(symmetry,[status(thm)],[13439])).
% 2.64/2.88 tff(13510,plain,
% 2.64/2.88 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 2.64/2.88 inference(transitivity,[status(thm)],[13444, 13509])).
% 2.64/2.88 tff(13511,plain,
% 2.64/2.88 ((~(s(elem!1) = z)) <=> (~(s(elem!1) = elem!1))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[13510])).
% 2.64/2.88 tff(13512,plain,
% 2.64/2.88 (~(s(elem!1) = elem!1)),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[40, 13511])).
% 2.64/2.88 tff(13513,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(13514,plain,
% 2.64/2.88 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(13515,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[13514])).
% 2.64/2.88 tff(13516,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.64/2.88 inference(transitivity,[status(thm)],[13515, 13513])).
% 2.64/2.88 tff(13517,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(13518,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[13517, 13516])).
% 2.64/2.88 tff(13519,plain,
% 2.64/2.88 ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13518, 155, 1512, 1510])).
% 2.64/2.88 tff(13520,plain,
% 2.64/2.88 (~r(s(elem!1), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13519, 9564])).
% 2.64/2.88 tff(13521,plain,
% 2.64/2.88 (((~![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))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(13522,plain,
% 2.64/2.88 ((~![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))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(13523,plain,
% 2.64/2.88 ((~![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)),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[13522, 13521])).
% 2.64/2.88 tff(13524,plain,
% 2.64/2.88 (b(s(elem!1), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13523, 53, 13520, 13512])).
% 2.64/2.88 tff(13525,plain,
% 2.64/2.88 ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13475, 97, 2423, 13524])).
% 2.64/2.88 tff(13526,plain,
% 2.64/2.88 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13525, 13508])).
% 2.64/2.88 tff(13527,plain,
% 2.64/2.88 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[821, 13526, 4451])).
% 2.64/2.88 tff(13528,plain,
% 2.64/2.88 (~r(s(s(s(s(elem!1)))), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[832, 13527, 570, 288])).
% 2.64/2.88 tff(13529,plain,
% 2.64/2.88 (b(s(s(s(s(elem!1)))), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[842, 13528])).
% 2.64/2.88 tff(13530,plain,
% 2.64/2.88 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[4474, 13529, 1444])).
% 2.64/2.88 tff(13531,plain,
% 2.64/2.88 (((~![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(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(13532,plain,
% 2.64/2.88 (((~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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(13533,plain,
% 2.64/2.88 (((~![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(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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[13532])).
% 2.64/2.88 tff(13534,plain,
% 2.64/2.88 (((~![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(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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)))),
% 2.64/2.88 inference(transitivity,[status(thm)],[13533, 13531])).
% 2.64/2.88 tff(13535,plain,
% 2.64/2.88 ((~![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(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)))))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(13536,plain,
% 2.64/2.88 ((~![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(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[13535, 13534])).
% 2.64/2.88 tff(13537,plain,
% 2.64/2.88 ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13536, 97, 2423, 13524])).
% 2.64/2.88 tff(13538,plain,
% 2.64/2.88 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13537, 13508])).
% 2.64/2.88 tff(13539,plain,
% 2.64/2.88 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[486, 13538, 1418])).
% 2.64/2.88 tff(13540,plain,
% 2.64/2.88 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[924, 13527, 225, 13539])).
% 2.64/2.88 tff(13541,plain,
% 2.64/2.88 (b(s(z), s(s(s(s(elem!1)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[280, 13540])).
% 2.64/2.88 tff(13542,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(13543,plain,
% 2.64/2.88 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(13544,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[13543])).
% 2.64/2.88 tff(13545,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.64/2.88 inference(transitivity,[status(thm)],[13544, 13542])).
% 2.64/2.88 tff(13546,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(13547,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[13546, 13545])).
% 2.64/2.88 tff(13548,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13547, 155, 729, 570, 463, 488, 225])).
% 2.64/2.88 tff(13549,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(13550,plain,
% 2.64/2.88 ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13549, 11419])).
% 2.64/2.88 tff(13551,plain,
% 2.64/2.88 (~r(z, s(s(s(s(elem!1)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13550, 13539, 570, 225])).
% 2.64/2.88 tff(13552,plain,
% 2.64/2.88 (b(z, s(s(s(s(elem!1)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1093, 13551])).
% 2.64/2.88 tff(13553,plain,
% 2.64/2.88 (((~![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), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(13554,plain,
% 2.64/2.88 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(13555,plain,
% 2.64/2.89 (((~![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(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13554])).
% 2.64/2.89 tff(13556,plain,
% 2.64/2.89 (((~![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(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[13555, 13553])).
% 2.64/2.89 tff(13557,plain,
% 2.64/2.89 ((~![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(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(13558,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[13557, 13556])).
% 2.64/2.89 tff(13559,plain,
% 2.64/2.89 ($false),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13558, 97, 550, 255, 372, 1458])).
% 2.64/2.89 tff(13560,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.89 tff(13561,plain,
% 2.64/2.89 ($false),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13560, 13552, 13541, 550, 13530])).
% 2.64/2.89 tff(13562,plain,((~r(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~(s(s(s(z))) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.89 tff(13563,plain,
% 2.64/2.89 (~r(s(z), s(s(s(elem!1))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13562, 550, 570, 288, 13469, 513, 1393])).
% 2.64/2.89 tff(13564,plain,
% 2.64/2.89 (b(s(z), s(s(s(elem!1))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[181, 13563])).
% 2.64/2.89 tff(13565,plain,
% 2.64/2.89 (b(s(elem!1), s(s(s(elem!1))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[13564, 1514])).
% 2.64/2.89 tff(13566,plain,
% 2.64/2.89 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1804, 13564, 1139, 513])).
% 2.64/2.89 tff(13567,plain,
% 2.64/2.89 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[821, 13566, 4451])).
% 2.64/2.89 tff(13568,plain,
% 2.64/2.89 (~r(s(s(s(s(elem!1)))), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[832, 13567, 570, 288])).
% 2.64/2.89 tff(13569,plain,
% 2.64/2.89 (b(s(s(s(s(elem!1)))), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[842, 13568])).
% 2.64/2.89 tff(13570,plain,
% 2.64/2.89 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[4474, 13569, 1444])).
% 2.64/2.89 tff(13571,plain,
% 2.64/2.89 (((~![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(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)))))) | (~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(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(13572,plain,
% 2.64/2.89 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(13573,plain,
% 2.64/2.89 (((~![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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(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)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13572])).
% 2.64/2.89 tff(13574,plain,
% 2.64/2.89 (((~![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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(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)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))),
% 2.64/2.89 inference(transitivity,[status(thm)],[13573, 13571])).
% 2.64/2.89 tff(13575,plain,
% 2.64/2.89 ((~![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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(13576,plain,
% 2.64/2.89 ((~![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(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)))))) | (~b(s(s(elem!1)), elem!1))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[13575, 13574])).
% 2.64/2.89 tff(13577,plain,
% 2.64/2.89 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13576, 97, 13570, 1915, 1914])).
% 2.64/2.89 tff(13578,plain,
% 2.64/2.89 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1631, 13577, 1508])).
% 2.64/2.89 tff(13579,plain,
% 2.64/2.89 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1626, 13578, 1433, 1510, 1529, 1520, 13565, 1512, 1393])).
% 2.64/2.89 tff(13580,plain,
% 2.64/2.89 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[486, 13579, 1418])).
% 2.64/2.89 tff(13581,plain,
% 2.64/2.89 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[13580, 8360])).
% 2.64/2.89 tff(13582,plain,
% 2.64/2.89 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[2439, 13567, 1889])).
% 2.64/2.89 tff(13583,plain,
% 2.64/2.89 (r(z, s(s(s(z))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[6374, 12684, 570])).
% 2.64/2.89 tff(13584,plain,
% 2.64/2.89 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[4669, 13578, 1393, 1520, 1813])).
% 2.64/2.89 tff(13585,plain,
% 2.64/2.89 (b(s(z), s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[280, 13584])).
% 2.64/2.89 tff(13586,plain,
% 2.64/2.89 (~b(z, s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13560, 13585, 550, 13570])).
% 2.64/2.89 tff(13587,plain,
% 2.64/2.89 (r(z, s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1093, 13586])).
% 2.64/2.89 tff(13588,plain,
% 2.64/2.89 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[2449, 13587, 13583, 13582])).
% 2.64/2.89 tff(13589,plain,
% 2.64/2.89 ($false),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13588, 13581])).
% 2.64/2.89 tff(13590,plain,((~b(s(z), z)) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.89 tff(13591,plain,
% 2.64/2.89 (~b(s(z), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13590, 13376, 13415, 13494, 13507, 13503, 13500, 13432, 13431, 2596, 12650, 13496])).
% 2.64/2.89 tff(13592,plain,
% 2.64/2.89 (r(s(z), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[568, 13591])).
% 2.64/2.89 tff(13593,plain,
% 2.64/2.89 (b(s(z), s(s(s(elem!1))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[12098, 13592, 3])).
% 2.64/2.89 tff(13594,plain,
% 2.64/2.89 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1804, 13593, 12650, 13496])).
% 2.64/2.89 tff(13595,plain,
% 2.64/2.89 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[821, 13594, 13407])).
% 2.64/2.89 tff(13596,plain,
% 2.64/2.89 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13404])).
% 2.64/2.89 tff(13597,plain,
% 2.64/2.89 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[286, 13596])).
% 2.64/2.89 tff(13598,plain,
% 2.64/2.89 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13424])).
% 2.64/2.89 tff(13599,plain,
% 2.64/2.89 (r(s(s(s(elem!1))), elem!1)),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[2596, 13598])).
% 2.64/2.89 tff(13600,plain,
% 2.64/2.89 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13390])).
% 2.64/2.89 tff(13601,plain,
% 2.64/2.89 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.64/2.89 inference(symmetry,[status(thm)],[13600])).
% 2.64/2.89 tff(13602,plain,
% 2.64/2.89 (b(s(elem!1), s(s(s(elem!1))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[13593, 13601])).
% 2.64/2.89 tff(13603,plain,
% 2.64/2.89 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13424])).
% 2.64/2.89 tff(13604,plain,
% 2.64/2.89 (r(elem!1, s(s(s(elem!1))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[13431, 13603])).
% 2.64/2.89 tff(13605,plain,
% 2.64/2.89 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13378])).
% 2.64/2.89 tff(13606,plain,
% 2.64/2.89 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.64/2.89 inference(transitivity,[status(thm)],[13605, 1428])).
% 2.64/2.89 tff(13607,plain,
% 2.64/2.89 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[13606, 1505])).
% 2.64/2.89 tff(13608,plain,
% 2.64/2.89 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13607])).
% 2.64/2.89 tff(13609,plain,
% 2.64/2.89 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[331, 13608])).
% 2.64/2.89 tff(13610,plain,
% 2.64/2.89 (~r(s(s(s(s(elem!1)))), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[832, 13595, 13431, 2596])).
% 2.64/2.89 tff(13611,plain,
% 2.64/2.89 (b(s(s(s(s(elem!1)))), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[842, 13610])).
% 2.64/2.89 tff(13612,plain,
% 2.64/2.89 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[4474, 13611, 13424])).
% 2.64/2.89 tff(13613,plain,
% 2.64/2.89 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13576, 97, 13612, 13500, 13432])).
% 2.64/2.89 tff(13614,plain,
% 2.64/2.89 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1631, 13613, 13609])).
% 2.64/2.89 tff(13615,plain,
% 2.64/2.89 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1626, 13614, 13507, 13604, 13503, 13415, 13602, 13599, 13376])).
% 2.64/2.89 tff(13616,plain,
% 2.64/2.89 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[486, 13615, 13597])).
% 2.64/2.89 tff(13617,plain,
% 2.64/2.89 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13378])).
% 2.64/2.89 tff(13618,plain,
% 2.64/2.89 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(symmetry,[status(thm)],[13617])).
% 2.64/2.89 tff(13619,plain,
% 2.64/2.89 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[13614, 13618])).
% 2.64/2.89 tff(13620,plain,
% 2.64/2.89 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[12643, 13619, 13616, 13595])).
% 2.64/2.89 tff(13621,plain,
% 2.64/2.89 (b(s(s(z)), s(s(s(elem!1))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[143, 13620])).
% 2.64/2.89 tff(13622,plain,
% 2.64/2.89 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[13621, 13402])).
% 2.64/2.89 tff(13623,plain,
% 2.64/2.89 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13390])).
% 2.64/2.89 tff(13624,plain,
% 2.64/2.89 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.64/2.89 inference(symmetry,[status(thm)],[13623])).
% 2.64/2.89 tff(13625,plain,
% 2.64/2.89 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[13496, 13624])).
% 2.64/2.89 tff(13626,plain,
% 2.64/2.89 (r(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[1393])).
% 2.64/2.89 tff(13627,plain,
% 2.64/2.89 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.64/2.89 inference(symmetry,[status(thm)],[13626])).
% 2.64/2.89 tff(13628,plain,
% 2.64/2.89 ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13627])).
% 2.64/2.89 tff(13629,assumption,(b(s(s(s(s(s(elem!1))))), s(elem!1))), introduced(assumption)).
% 2.64/2.89 tff(13630,assumption,(b(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 2.64/2.89 tff(13631,plain,
% 2.64/2.89 (((~![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(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(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(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(13632,plain,
% 2.64/2.89 (((~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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(13633,plain,
% 2.64/2.89 (((~![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(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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13632])).
% 2.64/2.89 tff(13634,plain,
% 2.64/2.89 (((~![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(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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[13633, 13631])).
% 2.64/2.89 tff(13635,plain,
% 2.64/2.89 ((~![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(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)))))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(13636,plain,
% 2.64/2.89 ((~![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(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[13635, 13634])).
% 2.64/2.89 tff(13637,plain,
% 2.64/2.89 ((~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))))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13636, 97, 1617, 13630])).
% 2.64/2.89 tff(13638,plain,
% 2.64/2.89 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13637, 13629])).
% 2.64/2.89 tff(13639,plain,
% 2.64/2.89 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[6254, 13638, 8167])).
% 2.64/2.89 tff(13640,plain,
% 2.64/2.89 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[8199, 155, 488, 823, 13639])).
% 2.64/2.89 tff(13641,plain,
% 2.64/2.89 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[13640, 13628])).
% 2.64/2.89 tff(13642,plain,
% 2.64/2.89 (((~![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(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(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(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(13643,plain,
% 2.64/2.89 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(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(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(13644,plain,
% 2.64/2.89 (((~![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(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(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(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13643])).
% 2.64/2.89 tff(13645,plain,
% 2.64/2.89 (((~![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(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(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(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[13644, 13642])).
% 2.64/2.89 tff(13646,plain,
% 2.64/2.89 ((~![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(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(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(s(elem!1))))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(13647,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[13646, 13645])).
% 2.64/2.89 tff(13648,plain,
% 2.64/2.89 ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13647, 97, 1529, 2391, 2423, 1617])).
% 2.64/2.89 tff(13649,plain,
% 2.64/2.89 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13648, 13629])).
% 2.64/2.89 tff(13650,plain,
% 2.64/2.89 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[13649, 7493])).
% 2.64/2.89 tff(13651,plain,
% 2.64/2.89 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[6289, 13650, 7492])).
% 2.64/2.89 tff(13652,plain,
% 2.64/2.89 ($false),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13651, 13641])).
% 2.64/2.89 tff(13653,plain,((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.89 tff(13654,plain,
% 2.64/2.89 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13653, 13376, 13616, 13595, 13602, 13625, 13503, 13622, 13398])).
% 2.64/2.89 tff(13655,plain,
% 2.64/2.89 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[13654, 13395])).
% 2.64/2.89 tff(13656,plain,
% 2.64/2.89 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[6239, 13655, 13393])).
% 2.64/2.89 tff(13657,plain,
% 2.64/2.89 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[13656, 13392])).
% 2.64/2.89 tff(13658,plain,
% 2.64/2.89 (r(s(elem!1), s(s(elem!1)))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[3, 13413])).
% 2.64/2.89 tff(13659,plain,
% 2.64/2.89 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(13660,plain,
% 2.64/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13659])).
% 2.64/2.89 tff(13661,plain,
% 2.64/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[13660, 7524])).
% 2.64/2.89 tff(13662,plain,
% 2.64/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(13663,plain,
% 2.64/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[13662, 13661])).
% 2.64/2.89 tff(13664,plain,
% 2.64/2.89 ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13663, 155, 13410, 13658])).
% 2.64/2.89 tff(13665,plain,
% 2.64/2.89 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[13664, 13657])).
% 2.64/2.89 tff(13666,plain,
% 2.64/2.89 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[6269, 13665, 13387])).
% 2.64/2.89 tff(13667,plain,
% 2.64/2.89 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13424])).
% 2.64/2.89 tff(13668,plain,
% 2.64/2.89 ((s(s(s(s(s(elem!1))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[13667, 6292])).
% 2.64/2.89 tff(13669,plain,
% 2.64/2.89 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.64/2.89 inference(transitivity,[status(thm)],[13668, 6293])).
% 2.64/2.89 tff(13670,plain,
% 2.64/2.89 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13669])).
% 2.64/2.89 tff(13671,plain,
% 2.64/2.89 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[6299, 13670])).
% 2.64/2.89 tff(13672,plain,
% 2.64/2.89 (r(z, s(z)) <=> r(elem!1, s(elem!1))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13424, 13408])).
% 2.64/2.89 tff(13673,plain,
% 2.64/2.89 (r(elem!1, s(elem!1))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[11419, 13672])).
% 2.64/2.89 tff(13674,plain,
% 2.64/2.89 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13408, 13424])).
% 2.64/2.89 tff(13675,plain,
% 2.64/2.89 ((~b(s(z), z)) <=> (~b(s(elem!1), elem!1))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13674])).
% 2.64/2.89 tff(13676,plain,
% 2.64/2.89 (~b(s(elem!1), elem!1)),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[13591, 13675])).
% 2.64/2.89 tff(13677,plain,
% 2.64/2.89 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 2.64/2.89 inference(monotonicity,[status(thm)],[13424])).
% 2.64/2.89 tff(13678,plain,
% 2.64/2.89 ((s(elem!1) = z) <=> (elem!1 = s(elem!1))),
% 2.64/2.89 inference(transitivity,[status(thm)],[13677, 13439])).
% 2.64/2.89 tff(13679,plain,
% 2.64/2.89 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 2.64/2.89 inference(transitivity,[status(thm)],[13678, 13509])).
% 2.64/2.90 tff(13680,plain,
% 2.64/2.90 ((~(s(elem!1) = z)) <=> (~(s(elem!1) = elem!1))),
% 2.64/2.90 inference(monotonicity,[status(thm)],[13679])).
% 2.64/2.90 tff(13681,plain,
% 2.64/2.90 (~(s(elem!1) = elem!1)),
% 2.64/2.90 inference(modus_ponens,[status(thm)],[40, 13680])).
% 2.64/2.90 tff(13682,plain,
% 2.64/2.90 (r(s(elem!1), elem!1)),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[13523, 53, 13681, 13676])).
% 2.64/2.90 tff(13683,plain,
% 2.64/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.64/2.90 inference(rewrite,[status(thm)],[])).
% 2.64/2.90 tff(13684,plain,
% 2.64/2.90 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.64/2.90 inference(rewrite,[status(thm)],[])).
% 2.64/2.90 tff(13685,plain,
% 2.64/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 2.64/2.90 inference(monotonicity,[status(thm)],[13684])).
% 2.64/2.90 tff(13686,plain,
% 2.64/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.64/2.90 inference(transitivity,[status(thm)],[13685, 13683])).
% 2.64/2.90 tff(13687,plain,
% 2.64/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.64/2.90 inference(quant_inst,[status(thm)],[])).
% 2.64/2.90 tff(13688,plain,
% 2.64/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.64/2.90 inference(modus_ponens,[status(thm)],[13687, 13686])).
% 2.64/2.90 tff(13689,plain,
% 2.64/2.90 ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[13688, 155, 13682, 13673])).
% 2.64/2.90 tff(13690,plain,
% 2.64/2.90 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[13689, 13657])).
% 2.64/2.90 tff(13691,plain,
% 2.64/2.90 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[6313, 13690, 13671])).
% 2.64/2.90 tff(13692,plain,
% 2.64/2.90 (elem!1 = z),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[1888, 13424])).
% 2.64/2.90 tff(13693,plain,
% 2.64/2.90 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[2439, 13595, 13692])).
% 2.64/2.90 tff(13694,plain,
% 2.64/2.90 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[11529, 13376])).
% 2.64/2.90 tff(13695,plain,
% 2.64/2.90 (r(z, s(s(s(z))))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[6374, 13694, 13431])).
% 2.74/2.90 tff(13696,plain,
% 2.74/2.90 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[13376])).
% 2.74/2.90 tff(13697,plain,
% 2.74/2.90 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.74/2.90 inference(symmetry,[status(thm)],[13696])).
% 2.74/2.90 tff(13698,plain,
% 2.74/2.90 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[13616, 13697])).
% 2.74/2.90 tff(13699,plain,
% 2.74/2.90 (~r(z, s(s(s(s(elem!1)))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[2449, 13698, 13695, 13693])).
% 2.74/2.90 tff(13700,plain,
% 2.74/2.90 (b(z, s(s(s(s(elem!1)))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1093, 13699])).
% 2.74/2.90 tff(13701,plain,
% 2.74/2.90 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[2407, 13700, 13692])).
% 2.74/2.90 tff(13702,plain,
% 2.74/2.90 (((~![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(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $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(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)))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(13703,plain,
% 2.74/2.90 (((~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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(13704,plain,
% 2.74/2.90 (((~![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(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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[13703])).
% 2.74/2.90 tff(13705,plain,
% 2.74/2.90 (((~![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(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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.74/2.90 inference(transitivity,[status(thm)],[13704, 13702])).
% 2.74/2.90 tff(13706,plain,
% 2.74/2.90 ((~![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(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)))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(13707,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[13706, 13705])).
% 2.74/2.90 tff(13708,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13707, 97, 13701, 13500, 13691, 13666])).
% 2.74/2.90 tff(13709,plain,((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(13710,plain,
% 2.74/2.90 (~r(s(z), s(s(z)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13709, 2, 239])).
% 2.74/2.90 tff(13711,plain,
% 2.74/2.90 (b(s(z), s(s(z)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[548, 13710])).
% 2.74/2.90 tff(13712,plain,
% 2.74/2.90 (~b(s(s(z)), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[3997, 550, 204, 535])).
% 2.74/2.90 tff(13713,plain,
% 2.74/2.90 (r(s(s(z)), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[437, 13712])).
% 2.74/2.90 tff(13714,plain,
% 2.74/2.90 (((~![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(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), 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(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(13715,plain,
% 2.74/2.90 (((~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(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(13716,plain,
% 2.74/2.90 (((~![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(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(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[13715])).
% 2.74/2.90 tff(13717,plain,
% 2.74/2.90 (((~![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(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(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 2.74/2.90 inference(transitivity,[status(thm)],[13716, 13714])).
% 2.74/2.90 tff(13718,plain,
% 2.74/2.90 ((~![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(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)))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(13719,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[13718, 13717])).
% 2.74/2.90 tff(13720,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13719, 97, 550, 204, 83, 535])).
% 2.74/2.90 tff(13721,plain,((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(13722,plain,
% 2.74/2.90 (~b(s(s(z)), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13721, 550, 204, 535])).
% 2.74/2.90 tff(13723,plain,
% 2.74/2.90 (r(s(s(z)), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[625, 13722])).
% 2.74/2.90 tff(13724,plain,
% 2.74/2.90 (~r(s(s(s(z))), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[12716, 13723, 2, 13713])).
% 2.74/2.90 tff(13725,plain,
% 2.74/2.90 (b(s(s(s(z))), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[402, 13724])).
% 2.74/2.90 tff(13726,plain,
% 2.74/2.90 (~b(s(s(s(z))), s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[11911, 13725, 204, 550])).
% 2.74/2.90 tff(13727,plain,
% 2.74/2.90 (r(s(s(s(z))), s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1358, 13726])).
% 2.74/2.90 tff(13728,plain,
% 2.74/2.90 (~r(s(z), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13230, 13723, 2, 13713])).
% 2.74/2.90 tff(13729,plain,
% 2.74/2.90 (b(s(z), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[253, 13728])).
% 2.74/2.90 tff(13730,plain,
% 2.74/2.90 (~b(z, s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13242, 13725, 550, 13729])).
% 2.74/2.90 tff(13731,plain,
% 2.74/2.90 (r(z, s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1318, 13730])).
% 2.74/2.90 tff(13732,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[9265, 155, 13723, 2, 13731, 13713, 13727])).
% 2.74/2.90 tff(13733,plain,((~b(s(z), z)) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(13734,plain,
% 2.74/2.90 (~b(s(z), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13733, 2, 204, 535])).
% 2.74/2.90 tff(13735,plain,
% 2.74/2.90 (r(s(z), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[568, 13734])).
% 2.74/2.90 tff(13736,plain,
% 2.74/2.90 (~r(s(s(z)), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[966, 155, 11419, 13735, 2])).
% 2.74/2.90 tff(13737,plain,
% 2.74/2.90 (b(s(s(z)), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[625, 13736])).
% 2.74/2.90 tff(13738,plain,
% 2.74/2.90 (~r(s(s(s(elem!1))), s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[11770, 13735, 288])).
% 2.74/2.90 tff(13739,plain,
% 2.74/2.90 (b(s(s(s(elem!1))), s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[493, 13738])).
% 2.74/2.90 tff(13740,plain,
% 2.74/2.90 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[11644, 13737, 535, 13739])).
% 2.74/2.90 tff(13741,plain,
% 2.74/2.90 (r(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[58, 13740])).
% 2.74/2.90 tff(13742,plain,
% 2.74/2.90 (~b(s(s(s(z))), s(s(z)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1339, 1330, 204, 13737])).
% 2.74/2.90 tff(13743,plain,
% 2.74/2.90 (r(s(s(s(z))), s(s(z)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[421, 13742])).
% 2.74/2.90 tff(13744,plain,
% 2.74/2.90 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[11644, 13737, 535, 1139])).
% 2.74/2.90 tff(13745,plain,
% 2.74/2.90 (r(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[58, 13744])).
% 2.74/2.90 tff(13746,plain,
% 2.74/2.90 (((~![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(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(13747,plain,
% 2.74/2.90 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(13748,plain,
% 2.74/2.90 (((~![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(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(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(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[13747])).
% 2.74/2.90 tff(13749,plain,
% 2.74/2.90 (((~![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(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(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(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.74/2.90 inference(transitivity,[status(thm)],[13748, 13746])).
% 2.74/2.90 tff(13750,plain,
% 2.74/2.90 ((~![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(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(13751,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[13750, 13749])).
% 2.74/2.90 tff(13752,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13751, 97, 204, 1361, 1330, 1216])).
% 2.74/2.90 tff(13753,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(13754,plain,
% 2.74/2.90 (~b(s(s(z)), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13753, 1216, 204, 1330])).
% 2.74/2.90 tff(13755,plain,
% 2.74/2.90 (r(s(s(z)), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[437, 13754])).
% 2.74/2.90 tff(13756,plain,
% 2.74/2.90 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[5794, 13755, 13745, 13743])).
% 2.74/2.90 tff(13757,plain,
% 2.74/2.90 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[2687, 13756, 2466])).
% 2.74/2.90 tff(13758,plain,
% 2.74/2.90 (((~![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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(13759,plain,
% 2.74/2.90 (((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(13760,plain,
% 2.74/2.90 (((~![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(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[13759])).
% 2.74/2.90 tff(13761,plain,
% 2.74/2.90 (((~![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(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.90 inference(transitivity,[status(thm)],[13760, 13758])).
% 2.74/2.90 tff(13762,plain,
% 2.74/2.90 ((~![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(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(13763,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[13762, 13761])).
% 2.74/2.90 tff(13764,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13763, 97, 1139, 83, 535, 86, 1216, 5941])).
% 2.74/2.90 tff(13765,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(13766,plain,
% 2.74/2.90 (~b(s(z), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13765, 1216, 13737, 535, 1139, 13757])).
% 2.74/2.90 tff(13767,plain,
% 2.74/2.90 (r(s(z), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[253, 13766])).
% 2.74/2.90 tff(13768,plain,
% 2.74/2.90 (~r(s(s(s(z))), s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[2940, 13767, 2, 13755])).
% 2.74/2.90 tff(13769,plain,
% 2.74/2.90 (b(s(s(s(z))), s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1358, 13768])).
% 2.74/2.90 tff(13770,plain,
% 2.74/2.90 (((~![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(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(13771,plain,
% 2.74/2.90 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(13772,plain,
% 2.74/2.90 (((~![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(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(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(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[13771])).
% 2.74/2.90 tff(13773,plain,
% 2.74/2.90 (((~![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(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(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(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.90 inference(transitivity,[status(thm)],[13772, 13770])).
% 2.74/2.90 tff(13774,plain,
% 2.74/2.90 ((~![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(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(13775,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[13774, 13773])).
% 2.74/2.90 tff(13776,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[13775, 97, 124, 13769, 1330, 13757])).
% 2.74/2.91 tff(13777,plain,((~b(s(s(s(z))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(13778,plain,
% 2.74/2.91 (~b(s(s(s(z))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[13777, 1330, 124, 2, 535, 13739, 2466, 204])).
% 2.74/2.91 tff(13779,plain,
% 2.74/2.91 (r(s(s(s(z))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[402, 13778])).
% 2.74/2.91 tff(13780,plain,
% 2.74/2.91 (~r(s(s(s(z))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[4334, 155, 11419, 13735, 13779])).
% 2.74/2.91 tff(13781,plain,
% 2.74/2.91 (b(s(s(s(z))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1358, 13780])).
% 2.74/2.91 tff(13782,plain,
% 2.74/2.91 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[11697, 13781, 13739, 124, 13737, 13743, 13741, 288])).
% 2.74/2.91 tff(13783,plain,
% 2.74/2.91 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2687, 13782, 2466])).
% 2.74/2.91 tff(13784,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[11487, 97, 13739, 535, 13781, 13783])).
% 2.74/2.91 tff(13785,plain,((~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(13786,plain,
% 2.74/2.91 (~b(z, s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[13785, 124, 2466, 535, 288, 2, 204])).
% 2.74/2.91 tff(13787,plain,
% 2.74/2.91 (r(z, s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1318, 13786])).
% 2.74/2.91 tff(13788,plain,
% 2.74/2.91 (~r(s(s(s(elem!1))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[11770, 81, 288])).
% 2.74/2.91 tff(13789,plain,
% 2.74/2.91 (b(s(s(s(elem!1))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[493, 13788])).
% 2.74/2.91 tff(13790,plain,
% 2.74/2.91 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[11644, 83, 535, 13789])).
% 2.74/2.91 tff(13791,plain,
% 2.74/2.91 (r(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[58, 13790])).
% 2.74/2.91 tff(13792,plain,
% 2.74/2.91 (~b(s(s(s(z))), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[11509, 1300, 535, 83])).
% 2.74/2.91 tff(13793,plain,
% 2.74/2.91 (r(s(s(s(z))), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[421, 13792])).
% 2.74/2.91 tff(13794,plain,
% 2.74/2.91 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[11697, 1360, 13789, 124, 83, 13793, 13791, 288])).
% 2.74/2.91 tff(13795,plain,
% 2.74/2.91 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2687, 13794, 2466])).
% 2.74/2.91 tff(13796,plain,
% 2.74/2.91 (~b(s(z), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[12294, 13795, 13789, 1360])).
% 2.74/2.91 tff(13797,plain,
% 2.74/2.91 (r(s(z), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[253, 13796])).
% 2.74/2.91 tff(13798,plain,
% 2.74/2.91 (~r(s(s(s(z))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1308, 13797, 81, 1300])).
% 2.74/2.91 tff(13799,plain,
% 2.74/2.91 (b(s(s(s(z))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[402, 13798])).
% 2.74/2.91 tff(13800,plain,
% 2.74/2.91 (((~![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(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(13801,plain,
% 2.74/2.91 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(13802,plain,
% 2.74/2.91 (((~![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(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[13801])).
% 2.74/2.91 tff(13803,plain,
% 2.74/2.91 (((~![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(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[13802, 13800])).
% 2.74/2.91 tff(13804,plain,
% 2.74/2.91 ((~![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(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(13805,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[13804, 13803])).
% 2.74/2.91 tff(13806,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[13805, 97, 13789, 204, 535, 1360, 13799, 13795])).
% 2.74/2.91 tff(13807,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(13808,plain,
% 2.74/2.91 (~b(s(s(s(z))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[13807, 13787, 535, 13735, 204, 2466, 124, 13737, 288])).
% 2.74/2.91 tff(13809,plain,
% 2.74/2.91 (r(s(s(s(z))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1358, 13808])).
% 2.74/2.91 tff(13810,plain,
% 2.74/2.91 (~r(s(s(s(z))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[4580, 155, 11419, 13735, 13809])).
% 2.74/2.91 tff(13811,plain,
% 2.74/2.91 (b(s(s(s(z))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[402, 13810])).
% 2.74/2.91 tff(13812,plain,
% 2.74/2.91 (~b(s(s(s(z))), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[11509, 13787, 535, 13737])).
% 2.74/2.91 tff(13813,plain,
% 2.74/2.91 (r(s(s(s(z))), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[421, 13812])).
% 2.74/2.91 tff(13814,plain,
% 2.74/2.91 (~b(s(s(z)), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[5211, 97, 204, 13737, 13811])).
% 2.74/2.91 tff(13815,plain,
% 2.74/2.91 (r(s(s(z)), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[437, 13814])).
% 2.74/2.91 tff(13816,plain,
% 2.74/2.91 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[5794, 13815, 13741, 13813])).
% 2.74/2.91 tff(13817,plain,
% 2.74/2.91 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2687, 13816, 2466])).
% 2.74/2.91 tff(13818,plain,
% 2.74/2.91 (~r(s(z), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2940, 13815, 2, 13809])).
% 2.74/2.91 tff(13819,plain,
% 2.74/2.91 (b(s(z), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[253, 13818])).
% 2.74/2.91 tff(13820,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[13765, 13819, 13817, 13737, 535, 13739, 13811])).
% 2.74/2.91 tff(13821,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(13822,plain,
% 2.74/2.91 (~b(z, s(s(s(elem!1))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[13821, 4228, 535, 2, 204, 288])).
% 2.74/2.91 tff(13823,plain,
% 2.74/2.91 (r(z, s(s(s(elem!1))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[590, 13822])).
% 2.74/2.91 tff(13824,plain,
% 2.74/2.91 (~r(s(z), s(s(s(elem!1))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1423, 155, 13823, 13735, 288])).
% 2.74/2.91 tff(13825,plain,
% 2.74/2.91 (b(s(z), s(s(s(elem!1))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[181, 13824])).
% 2.74/2.91 tff(13826,plain,
% 2.74/2.91 (~r(s(s(s(z))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[11541, 13825, 13739, 1, 13823, 288, 13735])).
% 2.74/2.91 tff(13827,plain,
% 2.74/2.91 (b(s(s(s(z))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[402, 13826])).
% 2.74/2.91 tff(13828,plain,
% 2.74/2.91 (((~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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(13829,plain,
% 2.74/2.91 (((~![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(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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[13828])).
% 2.74/2.91 tff(13830,plain,
% 2.74/2.91 (((~![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(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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 2.74/2.91 inference(transitivity,[status(thm)],[13829, 10178])).
% 2.74/2.91 tff(13831,plain,
% 2.74/2.91 ((~![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(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)))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(13832,plain,
% 2.74/2.91 ((~![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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[13831, 13830])).
% 2.74/2.91 tff(13833,plain,
% 2.74/2.91 (~b(s(s(s(z))), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[13832, 97, 204, 13737, 13827])).
% 2.74/2.91 tff(13834,plain,
% 2.74/2.91 (r(s(s(s(z))), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[421, 13833])).
% 2.74/2.91 tff(13835,plain,
% 2.74/2.91 (~b(s(s(z)), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[5211, 97, 204, 13737, 13827])).
% 2.74/2.91 tff(13836,plain,
% 2.74/2.91 (r(s(s(z)), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[437, 13835])).
% 2.74/2.91 tff(13837,plain,
% 2.74/2.91 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[5794, 13836, 13741, 13834])).
% 2.74/2.91 tff(13838,plain,
% 2.74/2.91 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2687, 13837, 4228])).
% 2.74/2.91 tff(13839,plain,
% 2.74/2.91 (~b(s(z), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[13765, 13838, 13737, 535, 13739, 13827])).
% 2.74/2.91 tff(13840,plain,
% 2.74/2.91 (r(s(z), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[253, 13839])).
% 2.74/2.91 tff(13841,plain,
% 2.74/2.91 (~r(s(s(s(z))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2940, 13840, 2, 13836])).
% 2.74/2.91 tff(13842,plain,
% 2.74/2.91 (b(s(s(s(z))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1358, 13841])).
% 2.74/2.91 tff(13843,plain,
% 2.74/2.91 (((~![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(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(13844,plain,
% 2.74/2.91 (((~b(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(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(13845,plain,
% 2.74/2.91 (((~![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(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(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[13844])).
% 2.74/2.91 tff(13846,plain,
% 2.74/2.91 (((~![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(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(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[13845, 13843])).
% 2.74/2.91 tff(13847,plain,
% 2.74/2.91 ((~![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(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(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(13848,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[13847, 13846])).
% 2.74/2.91 tff(13849,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[13848, 97, 13739, 13825, 13842, 13838])).
% 2.74/2.91 tff(13850,plain,((s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(13851,plain,
% 2.74/2.91 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[13850, 2, 13711, 11818, 2596])).
% 2.74/2.91 tff(13852,plain,
% 2.74/2.91 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[13851])).
% 2.74/2.91 tff(13853,plain,
% 2.74/2.91 (s(s(z)) = s(s(elem!1))),
% 2.74/2.91 inference(transitivity,[status(thm)],[73, 13852, 19])).
% 2.74/2.91 tff(13854,plain,
% 2.74/2.91 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[13853])).
% 2.74/2.91 tff(13855,plain,
% 2.74/2.91 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.74/2.91 inference(symmetry,[status(thm)],[13854])).
% 2.74/2.91 tff(13856,plain,
% 2.74/2.91 (s(elem!1) = s(z)),
% 2.74/2.91 inference(transitivity,[status(thm)],[30, 13855, 23])).
% 2.74/2.91 tff(13857,plain,
% 2.74/2.91 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[13856])).
% 2.74/2.91 tff(13858,plain,
% 2.74/2.91 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.74/2.91 inference(symmetry,[status(thm)],[13857])).
% 2.74/2.91 tff(13859,plain,
% 2.74/2.91 (~b(s(s(s(z))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[9913, 13851, 239])).
% 2.74/2.91 tff(13860,plain,
% 2.74/2.91 (r(s(s(s(z))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[402, 13859])).
% 2.74/2.91 tff(13861,plain,
% 2.74/2.91 (~b(s(z), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[13733, 2, 11818, 13711])).
% 2.74/2.91 tff(13862,plain,
% 2.74/2.91 (r(s(z), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[568, 13861])).
% 2.74/2.91 tff(13863,plain,
% 2.74/2.91 (~r(s(s(z)), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[966, 155, 11419, 13862, 2])).
% 2.74/2.91 tff(13864,plain,
% 2.74/2.91 (b(s(s(z)), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[625, 13863])).
% 2.74/2.91 tff(13865,plain,
% 2.74/2.91 (~r(s(s(s(elem!1))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[11770, 13862, 2596])).
% 2.74/2.91 tff(13866,plain,
% 2.74/2.91 (b(s(s(s(elem!1))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[493, 13865])).
% 2.74/2.91 tff(13867,plain,
% 2.74/2.91 (b(s(s(s(z))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1846, 1393, 1139])).
% 2.74/2.91 tff(13868,plain,
% 2.74/2.91 (~r(z, s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1308, 338, 81, 386])).
% 2.74/2.91 tff(13869,plain,
% 2.74/2.91 (b(z, s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1318, 13868])).
% 2.74/2.91 tff(13870,plain,
% 2.74/2.91 (~b(s(s(z)), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[11970, 13869, 204, 13867])).
% 2.74/2.91 tff(13871,plain,
% 2.74/2.91 (r(s(s(z)), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[437, 13870])).
% 2.74/2.91 tff(13872,plain,
% 2.74/2.91 (r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10091, 13871, 1393])).
% 2.74/2.91 tff(13873,plain,
% 2.74/2.91 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[11644, 83, 535, 1139])).
% 2.74/2.91 tff(13874,plain,
% 2.74/2.91 (r(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[58, 13873])).
% 2.74/2.91 tff(13875,plain,
% 2.74/2.91 (b(elem!1, s(s(s(elem!1))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[13869, 8106])).
% 2.74/2.91 tff(13876,plain,
% 2.74/2.91 (~r(z, s(s(s(elem!1))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[6374, 13868, 12684])).
% 2.74/2.91 tff(13877,plain,
% 2.74/2.91 (b(z, s(s(s(elem!1))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[590, 13876])).
% 2.74/2.91 tff(13878,plain,
% 2.74/2.91 (~r(s(s(s(s(elem!1)))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[11568, 495, 81])).
% 2.74/2.91 tff(13879,plain,
% 2.74/2.91 (b(s(s(s(s(elem!1)))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[842, 13878])).
% 2.74/2.91 tff(13880,plain,
% 2.74/2.91 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[884, 13879, 204, 83])).
% 2.74/2.91 tff(13881,plain,
% 2.74/2.91 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[452, 13880])).
% 2.74/2.91 tff(13882,plain,
% 2.74/2.91 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1822, 13881, 1393])).
% 2.74/2.91 tff(13883,plain,
% 2.74/2.91 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[5371, 13882, 145, 1393, 224])).
% 2.74/2.91 tff(13884,plain,
% 2.74/2.91 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[821, 13883, 4451])).
% 2.74/2.91 tff(13885,plain,
% 2.74/2.91 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[4474, 13879, 1444])).
% 2.74/2.91 tff(13886,plain,
% 2.74/2.91 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[4515, 97, 6315, 13885, 1899])).
% 2.74/2.91 tff(13887,plain,
% 2.74/2.91 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1631, 13886, 1508])).
% 2.74/2.91 tff(13888,plain,
% 2.74/2.91 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[4505, 13887, 5369, 13882])).
% 2.74/2.91 tff(13889,plain,
% 2.74/2.91 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[486, 13888, 1418])).
% 2.74/2.91 tff(13890,plain,
% 2.74/2.91 (~b(z, s(s(s(s(elem!1)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[9866, 13889, 124, 13884])).
% 2.74/2.91 tff(13891,plain,
% 2.74/2.91 (r(z, s(s(s(s(elem!1)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1093, 13890])).
% 2.74/2.91 tff(13892,plain,
% 2.74/2.91 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[5308, 13889, 1139, 13879])).
% 2.74/2.91 tff(13893,plain,
% 2.74/2.91 (r(s(z), s(s(s(s(elem!1)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[280, 13892])).
% 2.74/2.91 tff(13894,plain,
% 2.74/2.91 ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[5048, 11419])).
% 2.74/2.91 tff(13895,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[13894, 13893, 13891, 495])).
% 2.74/2.91 tff(13896,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(13897,plain,
% 2.74/2.91 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[13896, 13877, 1139, 13875, 13874, 1393, 13872, 204, 83, 81])).
% 2.74/2.91 tff(13898,plain,
% 2.74/2.91 (b(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[511, 13897])).
% 2.74/2.91 tff(13899,plain,
% 2.74/2.91 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[13898, 13433])).
% 2.74/2.91 tff(13900,plain,
% 2.74/2.91 (((~![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(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(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(13901,plain,
% 2.74/2.91 (((~b(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(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(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(elem!1)))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(13902,plain,
% 2.74/2.91 (((~![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(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(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(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(elem!1))))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[13901])).
% 2.74/2.91 tff(13903,plain,
% 2.74/2.91 (((~![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(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(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(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(elem!1)))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[13902, 13900])).
% 2.74/2.91 tff(13904,plain,
% 2.74/2.91 ((~![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(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(13905,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[13904, 13903])).
% 2.74/2.92 tff(13906,plain,
% 2.74/2.92 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[13905, 97, 13469, 9787, 13899])).
% 2.74/2.92 tff(13907,plain,
% 2.74/2.92 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[821, 13906, 4451])).
% 2.74/2.92 tff(13908,plain,
% 2.74/2.92 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[5371, 13907, 13874, 1393, 13872])).
% 2.74/2.92 tff(13909,plain,
% 2.74/2.92 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1822, 13908, 1393])).
% 2.74/2.92 tff(13910,plain,
% 2.74/2.92 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2129, 13898, 535, 1139])).
% 2.74/2.92 tff(13911,plain,
% 2.74/2.92 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[486, 13910, 1418])).
% 2.74/2.92 tff(13912,plain,
% 2.74/2.92 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[2508])).
% 2.74/2.92 tff(13913,plain,
% 2.74/2.92 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.74/2.92 inference(symmetry,[status(thm)],[13912])).
% 2.74/2.92 tff(13914,plain,
% 2.74/2.92 (r(s(z), s(s(s(elem!1))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[338, 13913])).
% 2.74/2.92 tff(13915,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[175, 13914])).
% 2.74/2.92 tff(13916,plain,((~r(s(z), s(s(s(z))))) | r(s(z), s(s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(13917,plain,
% 2.74/2.92 (r(s(z), s(s(s(elem!1))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[13916, 338, 12684])).
% 2.74/2.92 tff(13918,plain,
% 2.74/2.92 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[924, 13907, 13917, 13911])).
% 2.74/2.92 tff(13919,plain,
% 2.74/2.92 (b(s(z), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[280, 13918])).
% 2.74/2.92 tff(13920,plain,
% 2.74/2.92 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[12643, 13907, 13872, 13911])).
% 2.74/2.92 tff(13921,plain,
% 2.74/2.92 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[336, 13920])).
% 2.74/2.92 tff(13922,plain,
% 2.74/2.92 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3267, 13921, 535, 13919])).
% 2.74/2.92 tff(13923,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[452, 13922, 13909])).
% 2.74/2.92 tff(13924,plain,((~r(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(13925,plain,
% 2.74/2.92 (~r(s(z), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[13924, 13711, 13851, 13866, 11818, 13864, 13862, 13860])).
% 2.74/2.92 tff(13926,plain,
% 2.74/2.92 (b(s(z), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[253, 13925])).
% 2.74/2.92 tff(13927,plain,
% 2.74/2.92 (b(s(z), s(s(s(elem!1))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[6628, 13926, 13851])).
% 2.74/2.92 tff(13928,plain,
% 2.74/2.92 (b(s(elem!1), s(s(s(elem!1))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[13927, 13858])).
% 2.74/2.92 tff(13929,plain,
% 2.74/2.92 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[13851])).
% 2.74/2.92 tff(13930,plain,
% 2.74/2.92 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[13929, 1414])).
% 2.74/2.92 tff(13931,plain,
% 2.74/2.92 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[13930, 2507])).
% 2.74/2.92 tff(13932,plain,
% 2.74/2.92 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[13931])).
% 2.74/2.92 tff(13933,plain,
% 2.74/2.92 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[286, 13932])).
% 2.74/2.92 tff(13934,plain,
% 2.74/2.92 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[11339, 13927, 13711, 13866])).
% 2.74/2.92 tff(13935,plain,
% 2.74/2.92 (r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[143, 13934])).
% 2.74/2.92 tff(13936,plain,
% 2.74/2.92 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[11644, 13864, 13711, 13866])).
% 2.74/2.92 tff(13937,plain,
% 2.74/2.92 (r(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[58, 13936])).
% 2.74/2.92 tff(13938,plain,
% 2.74/2.92 (s(z) = s(elem!1)),
% 2.74/2.92 inference(transitivity,[status(thm)],[24, 13854, 29])).
% 2.74/2.92 tff(13939,plain,
% 2.74/2.92 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[13938])).
% 2.74/2.92 tff(13940,plain,
% 2.74/2.92 (z = elem!1),
% 2.74/2.92 inference(transitivity,[status(thm)],[1443, 13939, 85])).
% 2.74/2.92 tff(13941,plain,
% 2.74/2.92 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 2.74/2.92 inference(monotonicity,[status(thm)],[13940])).
% 2.74/2.92 tff(13942,plain,
% 2.74/2.92 (r(s(z), z) <=> r(s(elem!1), z)),
% 2.74/2.92 inference(monotonicity,[status(thm)],[13938])).
% 2.74/2.92 tff(13943,plain,
% 2.74/2.92 (r(s(elem!1), z)),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[13862, 13942])).
% 2.74/2.92 tff(13944,plain,
% 2.74/2.92 (r(s(elem!1), elem!1)),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[13943, 13941])).
% 2.74/2.92 tff(13945,plain,
% 2.74/2.92 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[13940])).
% 2.74/2.92 tff(13946,plain,
% 2.74/2.92 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[13853])).
% 2.74/2.92 tff(13947,plain,
% 2.74/2.92 (b(z, s(s(elem!1)))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[11818, 13946])).
% 2.74/2.92 tff(13948,plain,
% 2.74/2.92 (b(elem!1, s(s(elem!1)))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[13947, 13945])).
% 2.74/2.92 tff(13949,plain,
% 2.74/2.92 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.74/2.92 inference(monotonicity,[status(thm)],[13940])).
% 2.74/2.92 tff(13950,plain,
% 2.74/2.92 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 2.74/2.92 inference(monotonicity,[status(thm)],[13853])).
% 2.74/2.92 tff(13951,plain,
% 2.74/2.92 (b(s(s(elem!1)), z)),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[13864, 13950])).
% 2.74/2.92 tff(13952,plain,
% 2.74/2.92 (b(s(s(elem!1)), elem!1)),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[13951, 13949])).
% 2.74/2.92 tff(13953,plain,
% 2.74/2.92 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[6218, 1901])).
% 2.74/2.92 tff(13954,plain,
% 2.74/2.92 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[13953])).
% 2.74/2.92 tff(13955,plain,
% 2.74/2.92 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[837, 13954])).
% 2.74/2.92 tff(13956,plain,
% 2.74/2.92 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[11339, 193, 535, 1139])).
% 2.74/2.92 tff(13957,plain,
% 2.74/2.92 (r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[143, 13956])).
% 2.74/2.92 tff(13958,plain,
% 2.74/2.92 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[821, 1805, 4451])).
% 2.74/2.92 tff(13959,plain,
% 2.74/2.92 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[5371, 13958, 145, 1393, 13957])).
% 2.74/2.92 tff(13960,plain,
% 2.74/2.92 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1484, 13959, 1432])).
% 2.74/2.92 tff(13961,plain,
% 2.74/2.92 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1949, 13960, 1915, 6220, 13955, 1914, 1932])).
% 2.74/2.92 tff(13962,plain,
% 2.74/2.92 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1909, 13961, 1393])).
% 2.74/2.92 tff(13963,plain,
% 2.74/2.92 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2129, 513, 535, 1139])).
% 2.74/2.92 tff(13964,plain,
% 2.74/2.92 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[486, 13963, 1418])).
% 2.74/2.92 tff(13965,plain,
% 2.74/2.92 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[12643, 13958, 13957, 13964])).
% 2.74/2.92 tff(13966,plain,
% 2.74/2.92 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[336, 13965])).
% 2.74/2.92 tff(13967,plain,
% 2.74/2.92 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1822, 13959, 1393])).
% 2.74/2.92 tff(13968,plain,
% 2.74/2.92 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[452, 13967])).
% 2.74/2.92 tff(13969,plain,
% 2.74/2.92 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3267, 13968, 535, 13966])).
% 2.74/2.92 tff(13970,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[280, 13969, 13962])).
% 2.74/2.92 tff(13971,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(13972,plain,
% 2.74/2.92 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[13971, 13711, 13851, 13952, 13948, 13944, 13937, 13866, 13927])).
% 2.74/2.92 tff(13973,plain,
% 2.74/2.92 (r(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[511, 13972])).
% 2.74/2.92 tff(13974,plain,
% 2.74/2.92 (~r(s(s(s(s(elem!1)))), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[11568, 13973, 13862])).
% 2.74/2.92 tff(13975,plain,
% 2.74/2.92 (b(s(s(s(s(elem!1)))), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[842, 13974])).
% 2.74/2.92 tff(13976,plain,
% 2.74/2.92 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[884, 13975, 11818, 13864])).
% 2.74/2.92 tff(13977,plain,
% 2.74/2.92 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[452, 13976])).
% 2.74/2.92 tff(13978,plain,
% 2.74/2.92 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1822, 13977, 13851])).
% 2.74/2.92 tff(13979,plain,
% 2.74/2.92 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[5371, 13978, 13937, 13851, 13935])).
% 2.74/2.92 tff(13980,plain,
% 2.74/2.92 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[821, 13979, 13933])).
% 2.74/2.92 tff(13981,plain,
% 2.74/2.92 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[13930])).
% 2.74/2.92 tff(13982,plain,
% 2.74/2.92 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[286, 13981])).
% 2.74/2.92 tff(13983,plain,
% 2.74/2.92 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.74/2.92 inference(symmetry,[status(thm)],[13852])).
% 2.74/2.92 tff(13984,plain,
% 2.74/2.92 (s(s(elem!1)) = s(s(z))),
% 2.74/2.92 inference(transitivity,[status(thm)],[167, 13983, 72])).
% 2.74/2.92 tff(13985,plain,
% 2.74/2.92 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[13984])).
% 2.74/2.92 tff(13986,plain,
% 2.74/2.92 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.92 inference(symmetry,[status(thm)],[13985])).
% 2.74/2.92 tff(13987,plain,
% 2.74/2.92 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[13937, 13986])).
% 2.74/2.92 tff(13988,plain,
% 2.74/2.92 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[13853])).
% 2.74/2.92 tff(13989,plain,
% 2.74/2.92 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.74/2.92 inference(transitivity,[status(thm)],[13988, 1428])).
% 2.74/2.92 tff(13990,plain,
% 2.74/2.92 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[13989, 1505])).
% 2.74/2.92 tff(13991,plain,
% 2.74/2.92 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[13990])).
% 2.74/2.92 tff(13992,plain,
% 2.74/2.92 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[331, 13991])).
% 2.74/2.92 tff(13993,plain,
% 2.74/2.92 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4474, 13975, 13940])).
% 2.74/2.92 tff(13994,plain,
% 2.74/2.92 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[13576, 97, 13993, 13952, 13948])).
% 2.74/2.92 tff(13995,plain,
% 2.74/2.92 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1631, 13994, 13992])).
% 2.74/2.92 tff(13996,plain,
% 2.74/2.92 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4505, 13995, 13987, 13978])).
% 2.74/2.92 tff(13997,plain,
% 2.74/2.92 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[486, 13996, 13982])).
% 2.74/2.92 tff(13998,plain,
% 2.74/2.92 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10968, 97, 13997, 13980, 13928])).
% 2.74/2.92 tff(13999,plain,
% 2.74/2.92 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(z))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[13856])).
% 2.74/2.92 tff(14000,plain,
% 2.74/2.92 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(z) = s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[13999, 265])).
% 2.74/2.92 tff(14001,plain,
% 2.74/2.92 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.74/2.92 inference(symmetry,[status(thm)],[14000])).
% 2.74/2.92 tff(14002,plain,
% 2.74/2.92 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[14001])).
% 2.74/2.92 tff(14003,plain,
% 2.74/2.92 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[275, 14002])).
% 2.74/2.92 tff(14004,plain,
% 2.74/2.92 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1615, 53, 14003, 13998])).
% 2.74/2.92 tff(14005,plain,
% 2.74/2.92 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[5308, 13997, 13866, 13975])).
% 2.74/2.92 tff(14006,plain,
% 2.74/2.92 (r(s(z), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[280, 14005])).
% 2.74/2.92 tff(14007,plain,
% 2.74/2.92 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1909, 14006, 13851])).
% 2.74/2.92 tff(14008,plain,
% 2.74/2.92 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[13853, 13938])).
% 2.74/2.92 tff(14009,plain,
% 2.74/2.92 (r(s(s(elem!1)), s(elem!1))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[2, 14008])).
% 2.74/2.92 tff(14010,plain,
% 2.74/2.92 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(14011,plain,
% 2.74/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[14010])).
% 2.74/2.92 tff(14012,plain,
% 2.74/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[14011, 11126])).
% 2.74/2.92 tff(14013,plain,
% 2.74/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(14014,plain,
% 2.74/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[14013, 14012])).
% 2.74/2.92 tff(14015,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14014, 155, 13995, 14009, 14007, 14004])).
% 2.74/2.92 tff(14016,plain,((~r(s(s(z)), s(z))) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(14017,plain,
% 2.74/2.92 (~r(s(s(z)), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14016, 239])).
% 2.74/2.92 tff(14018,plain,
% 2.74/2.92 (b(s(s(z)), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[122, 14017])).
% 2.74/2.92 tff(14019,plain,
% 2.74/2.92 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[743, 155, 494, 11419, 288, 645])).
% 2.74/2.92 tff(14020,plain,
% 2.74/2.92 (b(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[58, 14019])).
% 2.74/2.92 tff(14021,plain,
% 2.74/2.92 (r(z, s(s(s(elem!1))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3954, 535, 4, 82, 550, 645, 226])).
% 2.74/2.92 tff(14022,plain,
% 2.74/2.92 (~r(s(z), s(s(s(elem!1))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[11807, 14021, 494])).
% 2.74/2.92 tff(14023,plain,
% 2.74/2.92 (b(s(z), s(s(s(elem!1))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[181, 14022])).
% 2.74/2.92 tff(14024,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[5699, 97, 14023, 59, 87, 535])).
% 2.74/2.92 tff(14025,plain,((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | r(s(s(s(elem!1))), s(s(z))) | b(s(s(s(elem!1))), s(z)) | (~b(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(14026,plain,
% 2.74/2.92 (~b(s(z), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14025, 226, 14019, 82, 11772, 645, 87])).
% 2.74/2.92 tff(14027,plain,
% 2.74/2.92 (r(s(z), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[548, 14026])).
% 2.74/2.92 tff(14028,plain,
% 2.74/2.92 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[743, 155, 125, 11419, 288, 645])).
% 2.74/2.92 tff(14029,plain,
% 2.74/2.92 (b(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[58, 14028])).
% 2.74/2.92 tff(14030,plain,
% 2.74/2.92 (~r(s(s(s(z))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[6467, 386, 226, 645])).
% 2.74/2.92 tff(14031,plain,
% 2.74/2.92 (b(s(s(s(z))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[421, 14030])).
% 2.74/2.92 tff(14032,plain,
% 2.74/2.92 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3662, 14031, 87, 60])).
% 2.74/2.92 tff(14033,plain,
% 2.74/2.92 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3089, 14032, 1])).
% 2.74/2.92 tff(14034,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3623, 97, 550, 87, 1360, 1331])).
% 2.74/2.92 tff(14035,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(14036,plain,
% 2.74/2.92 (~b(s(s(s(z))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14035, 14031, 87, 550])).
% 2.74/2.92 tff(14037,plain,
% 2.74/2.92 (r(s(s(s(z))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1358, 14036])).
% 2.74/2.92 tff(14038,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[12512, 155, 11419, 288, 14037, 386, 14033])).
% 2.74/2.92 tff(14039,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(14040,plain,
% 2.74/2.92 (~r(s(s(s(z))), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14039, 1, 288, 87, 14029, 11901, 226, 645])).
% 2.74/2.92 tff(14041,plain,
% 2.74/2.92 (b(s(s(s(z))), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[402, 14040])).
% 2.74/2.92 tff(14042,plain,
% 2.74/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(14043,plain,
% 2.74/2.92 (((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(14044,plain,
% 2.74/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[14043])).
% 2.74/2.92 tff(14045,plain,
% 2.74/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[14044, 14042])).
% 2.74/2.92 tff(14046,plain,
% 2.74/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(14047,plain,
% 2.74/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[14046, 14045])).
% 2.74/2.92 tff(14048,plain,
% 2.74/2.92 (~r(z, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14047, 155, 11419, 226, 3, 2597])).
% 2.74/2.92 tff(14049,plain,
% 2.74/2.92 (b(z, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1318, 14048])).
% 2.74/2.92 tff(14050,plain,
% 2.74/2.92 (~b(s(z), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[13242, 14049, 550, 1216])).
% 2.74/2.92 tff(14051,plain,
% 2.74/2.92 (~r(s(s(s(z))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[6518, 3, 2597, 125, 1, 226])).
% 2.74/2.92 tff(14052,plain,
% 2.74/2.92 (b(s(s(s(z))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[421, 14051])).
% 2.74/2.92 tff(14053,plain,
% 2.74/2.92 (((~![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(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(14054,plain,
% 2.74/2.92 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~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(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(14055,plain,
% 2.74/2.92 (((~![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(z)), s(z))) | (~b(s(s(z)), s(z))) | (~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(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(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[14054])).
% 2.74/2.92 tff(14056,plain,
% 2.74/2.92 (((~![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(z)), s(z))) | (~b(s(s(z)), s(z))) | (~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(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(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[14055, 14053])).
% 2.74/2.92 tff(14057,plain,
% 2.74/2.92 ((~![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(z)), s(z))) | (~b(s(s(z)), s(z))) | (~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(elem!1))), s(s(s(z))))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(14058,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[14057, 14056])).
% 2.74/2.92 tff(14059,plain,
% 2.74/2.92 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14058, 97, 60, 87, 14052])).
% 2.74/2.92 tff(14060,plain,
% 2.74/2.92 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2687, 14059, 4228])).
% 2.74/2.92 tff(14061,plain,
% 2.74/2.92 (~r(s(z), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2638, 14060, 125, 2597])).
% 2.74/2.92 tff(14062,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[253, 14061, 14050])).
% 2.74/2.92 tff(14063,plain,((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(14064,plain,
% 2.74/2.92 (~r(s(s(s(z))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14063, 14041, 125, 11901, 3, 14029, 87, 226, 1])).
% 2.74/2.92 tff(14065,plain,
% 2.74/2.92 (b(s(s(s(z))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1358, 14064])).
% 2.74/2.92 tff(14066,plain,
% 2.74/2.92 (~b(s(s(z)), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[7010, 14065, 87, 11901])).
% 2.74/2.92 tff(14067,plain,
% 2.74/2.92 (r(s(s(z)), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[437, 14066])).
% 2.74/2.92 tff(14068,plain,
% 2.74/2.92 (~b(s(s(s(z))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14035, 14065, 87, 11901])).
% 2.74/2.92 tff(14069,plain,
% 2.74/2.92 (r(s(s(s(z))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[421, 14068])).
% 2.74/2.92 tff(14070,plain,
% 2.74/2.92 (~r(z, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1969, 14069, 226, 14067])).
% 2.74/2.92 tff(14071,plain,
% 2.74/2.92 (b(z, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1318, 14070])).
% 2.74/2.92 tff(14072,plain,
% 2.74/2.92 (~r(s(z), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2641, 14067, 3, 14069])).
% 2.74/2.92 tff(14073,plain,
% 2.74/2.92 (b(s(z), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[253, 14072])).
% 2.74/2.92 tff(14074,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[13242, 14073, 14071, 11901, 14041])).
% 2.74/2.92 tff(14075,plain,((s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(14076,plain,
% 2.74/2.92 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[14075, 14027, 226, 87, 494, 288, 645])).
% 2.74/2.92 tff(14077,plain,
% 2.74/2.92 (b(s(s(elem!1)), s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[9687, 14076, 87])).
% 2.74/2.92 tff(14078,plain,
% 2.74/2.92 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[14076])).
% 2.74/2.92 tff(14079,plain,
% 2.74/2.92 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[14078, 1414])).
% 2.74/2.92 tff(14080,plain,
% 2.74/2.92 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[14079, 2507])).
% 2.74/2.92 tff(14081,plain,
% 2.74/2.92 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[14080])).
% 2.74/2.92 tff(14082,plain,
% 2.74/2.92 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[286, 14081])).
% 2.74/2.93 tff(14083,plain,
% 2.74/2.93 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[11529, 14076])).
% 2.74/2.93 tff(14084,plain,
% 2.74/2.93 (b(s(s(s(z))), s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[2677, 14076, 14020])).
% 2.74/2.93 tff(14085,plain,
% 2.74/2.93 ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[4590, 11419])).
% 2.74/2.93 tff(14086,plain,
% 2.74/2.93 (~r(z, s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14085, 14027, 226, 494])).
% 2.74/2.93 tff(14087,plain,
% 2.74/2.93 (~r(z, s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[6652, 14076, 14086])).
% 2.74/2.93 tff(14088,plain,
% 2.74/2.93 (b(z, s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1318, 14087])).
% 2.74/2.93 tff(14089,plain,
% 2.74/2.93 (~b(s(z), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[7835, 14088, 14084, 11772])).
% 2.74/2.93 tff(14090,plain,
% 2.74/2.93 (r(s(z), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[253, 14089])).
% 2.74/2.93 tff(14091,plain,
% 2.74/2.93 (r(s(z), s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[13916, 14090, 14083])).
% 2.74/2.93 tff(14092,plain,
% 2.74/2.93 (b(z, s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[590, 14086])).
% 2.74/2.93 tff(14093,plain,
% 2.74/2.93 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3240, 513, 87, 550])).
% 2.74/2.93 tff(14094,plain,
% 2.74/2.93 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[336, 14093])).
% 2.74/2.93 tff(14095,plain,
% 2.74/2.93 (b(s(s(elem!1)), s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9687, 1393, 87])).
% 2.74/2.93 tff(14096,plain,
% 2.74/2.93 (((~![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(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14097,plain,
% 2.74/2.93 (((~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(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)))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14098,plain,
% 2.74/2.93 (((~![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(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(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))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14097])).
% 2.74/2.93 tff(14099,plain,
% 2.74/2.93 (((~![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(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(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)))),
% 2.74/2.93 inference(transitivity,[status(thm)],[14098, 14096])).
% 2.74/2.93 tff(14100,plain,
% 2.74/2.93 ((~![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(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)))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(14101,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), elem!1))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[14100, 14099])).
% 2.74/2.93 tff(14102,plain,
% 2.74/2.93 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14101, 97, 10805, 14095, 13508])).
% 2.74/2.93 tff(14103,plain,
% 2.74/2.93 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1484, 14102, 1432])).
% 2.74/2.93 tff(14104,plain,
% 2.74/2.93 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[7352, 14103, 1393])).
% 2.74/2.93 tff(14105,plain,
% 2.74/2.93 (~r(z, s(s(s(s(elem!1)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3852, 14104, 226, 1393, 14094])).
% 2.74/2.93 tff(14106,plain,
% 2.74/2.93 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3652, 14104, 125, 550, 4, 645, 124, 226])).
% 2.74/2.93 tff(14107,plain,
% 2.74/2.93 (~b(z, s(s(s(s(elem!1)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[701, 14106, 124, 513])).
% 2.74/2.93 tff(14108,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1093, 14107, 14105])).
% 2.74/2.93 tff(14109,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | r(s(s(s(elem!1))), s(s(z))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(14110,plain,
% 2.74/2.93 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14109, 14092, 226, 14076, 494, 11772, 14019, 645, 87])).
% 2.74/2.93 tff(14111,plain,
% 2.74/2.93 (r(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[511, 14110])).
% 2.74/2.93 tff(14112,plain,
% 2.74/2.93 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1136, 14111, 494, 14091])).
% 2.74/2.93 tff(14113,plain,
% 2.74/2.93 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[821, 14112, 14082])).
% 2.74/2.93 tff(14114,plain,
% 2.74/2.93 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14076])).
% 2.74/2.93 tff(14115,plain,
% 2.74/2.93 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.74/2.93 inference(symmetry,[status(thm)],[14114])).
% 2.74/2.93 tff(14116,plain,
% 2.74/2.93 (s(s(elem!1)) = s(s(z))),
% 2.74/2.93 inference(transitivity,[status(thm)],[167, 14115, 72])).
% 2.74/2.93 tff(14117,plain,
% 2.74/2.93 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14116])).
% 2.74/2.93 tff(14118,plain,
% 2.74/2.93 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.93 inference(symmetry,[status(thm)],[14117])).
% 2.74/2.93 tff(14119,plain,
% 2.74/2.93 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[14020, 14118])).
% 2.74/2.93 tff(14120,plain,
% 2.74/2.93 (s(s(z)) = s(s(elem!1))),
% 2.74/2.93 inference(transitivity,[status(thm)],[73, 14114, 19])).
% 2.74/2.93 tff(14121,plain,
% 2.74/2.93 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14120])).
% 2.74/2.93 tff(14122,plain,
% 2.74/2.93 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.74/2.93 inference(transitivity,[status(thm)],[14121, 1428])).
% 2.74/2.93 tff(14123,plain,
% 2.74/2.93 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14122])).
% 2.74/2.93 tff(14124,plain,
% 2.74/2.93 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[331, 14123])).
% 2.74/2.93 tff(14125,plain,
% 2.74/2.93 ((~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[5351, 11419])).
% 2.74/2.93 tff(14126,plain,
% 2.74/2.93 (~r(z, s(s(s(s(elem!1)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14125, 14111, 226, 14027])).
% 2.74/2.93 tff(14127,plain,
% 2.74/2.93 (b(z, s(s(s(s(elem!1)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1093, 14126])).
% 2.74/2.93 tff(14128,plain,
% 2.74/2.93 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9866, 14127, 14092, 14113])).
% 2.74/2.93 tff(14129,plain,
% 2.74/2.93 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3652, 14128, 494, 11772, 14019, 645, 14092, 226])).
% 2.74/2.93 tff(14130,plain,
% 2.74/2.93 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[7352, 14129, 14076])).
% 2.74/2.93 tff(14131,plain,
% 2.74/2.93 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1484, 14130, 14124])).
% 2.74/2.93 tff(14132,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[8222, 97, 14131, 14119, 14113, 14077])).
% 2.74/2.93 tff(14133,plain,((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), z)) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(14134,plain,
% 2.74/2.93 (~r(z, s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14133, 645, 87, 288, 82])).
% 2.74/2.93 tff(14135,plain,
% 2.74/2.93 (b(z, s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[222, 14134])).
% 2.74/2.93 tff(14136,plain,
% 2.74/2.93 (~b(z, s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[212, 14135, 87, 14020])).
% 2.74/2.93 tff(14137,plain,
% 2.74/2.93 (r(z, s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[590, 14136])).
% 2.74/2.93 tff(14138,plain,
% 2.74/2.93 (~r(s(z), s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[11807, 14137, 494])).
% 2.74/2.93 tff(14139,plain,
% 2.74/2.93 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[735, 155, 14137, 288, 645])).
% 2.74/2.93 tff(14140,plain,
% 2.74/2.93 (~b(s(z), s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3966, 204, 87, 550])).
% 2.74/2.93 tff(14141,plain,
% 2.74/2.93 (r(s(z), s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[548, 14140])).
% 2.74/2.93 tff(14142,plain,
% 2.74/2.93 ((~b(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[6717, 11419])).
% 2.74/2.93 tff(14143,plain,
% 2.74/2.93 (~r(s(s(s(z))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14142, 1960, 125, 14141, 570, 550])).
% 2.74/2.93 tff(14144,plain,
% 2.74/2.93 (b(s(s(s(z))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1358, 14143])).
% 2.74/2.93 tff(14145,plain,
% 2.74/2.93 (~b(s(s(s(z))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[11911, 14144, 550, 204])).
% 2.74/2.93 tff(14146,plain,
% 2.74/2.93 (r(s(s(s(z))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[402, 14145])).
% 2.74/2.93 tff(14147,plain,
% 2.74/2.93 (~b(s(s(z)), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[7010, 14144, 87, 550])).
% 2.74/2.93 tff(14148,plain,
% 2.74/2.93 (r(s(s(z)), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[437, 14147])).
% 2.74/2.93 tff(14149,plain,
% 2.74/2.93 (~r(z, s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[6410, 14148, 645, 14146])).
% 2.74/2.93 tff(14150,plain,
% 2.74/2.93 (~r(s(z), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[5675, 3, 125])).
% 2.74/2.93 tff(14151,plain,
% 2.74/2.93 (b(s(z), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[568, 14150])).
% 2.74/2.93 tff(14152,plain,
% 2.74/2.93 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10091, 1961, 137])).
% 2.74/2.93 tff(14153,plain,
% 2.74/2.93 (~r(s(s(s(z))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[6039, 14152, 14151, 1960, 1330, 3, 1961, 125])).
% 2.74/2.93 tff(14154,plain,
% 2.74/2.93 (~b(s(s(s(z))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[12599, 12701, 1330, 14151])).
% 2.74/2.93 tff(14155,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1358, 14154, 14153])).
% 2.74/2.93 tff(14156,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | r(s(s(z)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(14157,plain,
% 2.74/2.93 (~b(z, s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14156, 14148, 125, 14141, 137, 1960])).
% 2.74/2.93 tff(14158,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1318, 14157, 14149])).
% 2.74/2.93 tff(14159,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | r(s(s(z)), s(s(s(elem!1)))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(14160,plain,
% 2.74/2.93 (~r(s(s(s(z))), s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14159, 14139, 494, 645, 87, 11772, 14135, 14137])).
% 2.74/2.93 tff(14161,plain,
% 2.74/2.93 (b(s(s(s(z))), s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[421, 14160])).
% 2.74/2.93 tff(14162,plain,
% 2.74/2.93 (~b(s(s(s(z))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14035, 14161, 87, 11772])).
% 2.74/2.93 tff(14163,plain,
% 2.74/2.93 (r(s(s(s(z))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1358, 14162])).
% 2.74/2.93 tff(14164,plain,
% 2.74/2.93 (~b(z, s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[4725, 97, 14135, 87, 14161])).
% 2.74/2.93 tff(14165,plain,
% 2.74/2.93 (r(z, s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1318, 14164])).
% 2.74/2.93 tff(14166,plain,
% 2.74/2.93 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[7978, 14165, 494, 14137, 14161, 14163, 14020, 288, 645])).
% 2.74/2.93 tff(14167,plain,
% 2.74/2.93 (~r(s(z), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[13916, 14166, 14138])).
% 2.74/2.93 tff(14168,plain,
% 2.74/2.93 (b(s(z), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[253, 14167])).
% 2.74/2.93 tff(14169,plain,
% 2.74/2.93 (~b(s(s(s(z))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[4717, 97, 14135, 87, 14161])).
% 2.74/2.93 tff(14170,plain,
% 2.74/2.93 (r(s(s(s(z))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[402, 14169])).
% 2.74/2.93 tff(14171,plain,
% 2.74/2.93 (~r(s(s(z)), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[6410, 14165, 645, 14170])).
% 2.74/2.93 tff(14172,plain,
% 2.74/2.93 (b(s(s(z)), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[437, 14171])).
% 2.74/2.93 tff(14173,plain,
% 2.74/2.93 (((~![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(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14174,plain,
% 2.74/2.93 (((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14175,plain,
% 2.74/2.93 (((~![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(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14174])).
% 2.74/2.93 tff(14176,plain,
% 2.74/2.93 (((~![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(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[14175, 14173])).
% 2.74/2.93 tff(14177,plain,
% 2.74/2.93 ((~![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(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(14178,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[14177, 14176])).
% 2.74/2.93 tff(14179,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14178, 97, 11772, 14135, 87, 14172, 14161, 14168])).
% 2.74/2.93 tff(14180,plain,((~r(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), z)) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(14181,plain,
% 2.74/2.93 (~r(s(s(z)), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14180, 82, 288, 87])).
% 2.74/2.93 tff(14182,plain,
% 2.74/2.93 (b(s(s(z)), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[625, 14181])).
% 2.74/2.93 tff(14183,plain,
% 2.74/2.93 (((~![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(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14184,plain,
% 2.74/2.93 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(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(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14185,plain,
% 2.74/2.93 (((~![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(z, s(s(s(elem!1))))) | (~b(z, s(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(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14184])).
% 2.74/2.93 tff(14186,plain,
% 2.74/2.93 (((~![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(z, s(s(s(elem!1))))) | (~b(z, s(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(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.74/2.93 inference(transitivity,[status(thm)],[14185, 14183])).
% 2.74/2.93 tff(14187,plain,
% 2.74/2.93 ((~![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(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(14188,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[14187, 14186])).
% 2.74/2.93 tff(14189,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14188, 97, 550, 124, 83, 87])).
% 2.74/2.93 tff(14190,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(14191,plain,
% 2.74/2.93 (~b(z, s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14190, 11772, 14182, 87])).
% 2.74/2.93 tff(14192,plain,
% 2.74/2.93 (r(z, s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[590, 14191])).
% 2.74/2.93 tff(14193,plain,
% 2.74/2.93 (((~![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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), 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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14194,plain,
% 2.74/2.93 (((~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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14195,plain,
% 2.74/2.93 (((~![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(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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14194])).
% 2.74/2.93 tff(14196,plain,
% 2.74/2.93 (((~![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(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(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[14195, 14193])).
% 2.74/2.93 tff(14197,plain,
% 2.74/2.93 ((~![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(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))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(14198,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[14197, 14196])).
% 2.74/2.93 tff(14199,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14198, 97, 550, 204, 83, 87])).
% 2.74/2.93 tff(14200,plain,((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(14201,plain,
% 2.74/2.93 (~b(z, s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14200, 11772, 14182, 87])).
% 2.74/2.93 tff(14202,plain,
% 2.74/2.93 (r(z, s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[222, 14201])).
% 2.74/2.93 tff(14203,plain,
% 2.74/2.93 (~r(s(z), s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14085, 14202, 14192, 494])).
% 2.74/2.93 tff(14204,plain,
% 2.74/2.93 (b(s(z), s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[548, 14203])).
% 2.74/2.93 tff(14205,plain,
% 2.74/2.93 (~b(z, s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[2972, 535, 550, 83])).
% 2.74/2.93 tff(14206,plain,
% 2.74/2.93 (~r(z, s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[11509, 535, 1331, 83])).
% 2.74/2.93 tff(14207,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1318, 14206, 14205])).
% 2.74/2.93 tff(14208,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(14209,plain,
% 2.74/2.93 (~b(s(s(s(z))), s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14208, 14204, 14182, 11772])).
% 2.74/2.93 tff(14210,plain,
% 2.74/2.93 (r(s(s(s(z))), s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[421, 14209])).
% 2.74/2.93 tff(14211,plain,
% 2.74/2.93 (~b(z, s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[2972, 14204, 11772, 14182])).
% 2.74/2.93 tff(14212,plain,
% 2.74/2.93 (r(z, s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1318, 14211])).
% 2.74/2.93 tff(14213,plain,
% 2.74/2.93 (~b(z, s(s(s(s(elem!1)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[11776, 14204, 11772, 14182])).
% 2.74/2.93 tff(14214,plain,
% 2.74/2.93 (r(z, s(s(s(s(elem!1)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1093, 14213])).
% 2.74/2.93 tff(14215,plain,
% 2.74/2.93 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[6995, 14214, 14202, 14212, 14210])).
% 2.74/2.93 tff(14216,plain,
% 2.74/2.93 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[336, 14215])).
% 2.74/2.93 tff(14217,plain,
% 2.74/2.93 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3240, 14216, 87, 11772])).
% 2.74/2.93 tff(14218,plain,
% 2.74/2.93 (r(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[511, 14217])).
% 2.74/2.93 tff(14219,plain,
% 2.74/2.93 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[13894, 14218, 14214])).
% 2.74/2.93 tff(14220,plain,
% 2.74/2.93 (b(s(z), s(s(s(s(elem!1)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[280, 14219])).
% 2.74/2.93 tff(14221,plain,
% 2.74/2.93 (~b(s(s(s(s(elem!1)))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3812, 14220, 14204, 14216])).
% 2.74/2.93 tff(14222,plain,
% 2.74/2.93 (r(s(s(s(s(elem!1)))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[842, 14221])).
% 2.74/2.93 tff(14223,plain,
% 2.74/2.93 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[832, 14222, 14192, 288])).
% 2.74/2.93 tff(14224,plain,
% 2.74/2.93 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[11802, 14202, 494, 14192])).
% 2.74/2.93 tff(14225,plain,
% 2.74/2.93 (b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[143, 14224])).
% 2.74/2.93 tff(14226,plain,
% 2.74/2.93 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1872, 14222, 288, 14214])).
% 2.74/2.93 tff(14227,plain,
% 2.74/2.93 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[4129, 14226, 14216, 14225, 14223])).
% 2.74/2.93 tff(14228,plain,
% 2.74/2.93 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[349, 14227])).
% 2.74/2.93 tff(14229,plain,
% 2.74/2.93 (s(s(s(s(elem!1)))) = elem!1),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1734, 14228])).
% 2.74/2.93 tff(14230,plain,
% 2.74/2.93 (elem!1 = s(s(s(s(elem!1))))),
% 2.74/2.93 inference(symmetry,[status(thm)],[14229])).
% 2.74/2.93 tff(14231,plain,
% 2.74/2.93 (elem!1 = s(s(elem!1))),
% 2.74/2.93 inference(transitivity,[status(thm)],[14230, 14228])).
% 2.74/2.93 tff(14232,plain,
% 2.74/2.93 (r(elem!1, elem!1) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[14230, 14231])).
% 2.74/2.93 tff(14233,plain,
% 2.74/2.93 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(elem!1, elem!1)),
% 2.74/2.93 inference(symmetry,[status(thm)],[14232])).
% 2.74/2.93 tff(14234,plain,
% 2.74/2.93 (~r(s(s(z)), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1969, 14212, 14202, 14210])).
% 2.74/2.93 tff(14235,plain,
% 2.74/2.93 (b(s(s(z)), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[437, 14234])).
% 2.74/2.93 tff(14236,plain,
% 2.74/2.93 (~b(s(s(s(z))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[7010, 14235, 87, 11772])).
% 2.74/2.93 tff(14237,plain,
% 2.74/2.93 (r(s(s(s(z))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1358, 14236])).
% 2.74/2.93 tff(14238,plain,
% 2.74/2.93 (~r(s(z), s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[11807, 14192, 494])).
% 2.74/2.93 tff(14239,plain,
% 2.74/2.93 (b(s(z), s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[181, 14238])).
% 2.74/2.93 tff(14240,plain,
% 2.74/2.93 (((~![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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), 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(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14241,plain,
% 2.74/2.93 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(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(s(z)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(14242,plain,
% 2.74/2.93 (((~![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(z)), s(s(s(z))))) | (~b(s(s(z)), s(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(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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14241])).
% 2.74/2.94 tff(14243,plain,
% 2.74/2.94 (((~![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(z)), s(s(s(z))))) | (~b(s(s(z)), s(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(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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[14242, 14240])).
% 2.74/2.94 tff(14244,plain,
% 2.74/2.94 ((~![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(z)), s(s(s(z))))) | (~b(s(s(z)), s(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(s(z)))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(14245,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[14244, 14243])).
% 2.74/2.94 tff(14246,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14245, 97, 193, 60, 535, 1361])).
% 2.74/2.94 tff(14247,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(14248,plain,
% 2.74/2.94 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14247, 14235, 14204, 14239])).
% 2.74/2.94 tff(14249,plain,
% 2.74/2.94 (r(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[58, 14248])).
% 2.74/2.94 tff(14250,plain,
% 2.74/2.94 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[6049, 14249, 14202, 494, 14210, 14237])).
% 2.74/2.94 tff(14251,plain,
% 2.74/2.94 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[3267, 14220, 14204, 14216])).
% 2.74/2.94 tff(14252,plain,
% 2.74/2.94 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[452, 14251])).
% 2.74/2.94 tff(14253,plain,
% 2.74/2.94 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1822, 14252, 14250])).
% 2.74/2.94 tff(14254,plain,
% 2.74/2.94 (r(elem!1, elem!1)),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[14253, 14233])).
% 2.74/2.94 tff(14255,plain,
% 2.74/2.94 ((~![X: $i] : (~r(X, X))) | (~r(elem!1, elem!1))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(14256,plain,
% 2.74/2.94 (~r(elem!1, elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14255, 8005])).
% 2.74/2.94 tff(14257,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14256, 14254])).
% 2.74/2.94 tff(14258,plain,(b(s(s(s(elem!1))), s(z)) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(14259,plain,
% 2.74/2.94 (b(s(s(s(elem!1))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14258, 288, 87])).
% 2.74/2.94 tff(14260,plain,
% 2.74/2.94 (~r(s(z), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[5580, 81, 288, 87])).
% 2.74/2.94 tff(14261,plain,
% 2.74/2.94 (b(s(z), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[548, 14260])).
% 2.74/2.94 tff(14262,plain,
% 2.74/2.94 (~r(s(s(s(z))), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[4580, 155, 11419, 81, 2597])).
% 2.74/2.94 tff(14263,plain,
% 2.74/2.94 (b(s(s(s(z))), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[402, 14262])).
% 2.74/2.94 tff(14264,plain,
% 2.74/2.94 (((~![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(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14265,plain,
% 2.74/2.94 (((~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(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14266,plain,
% 2.74/2.94 (((~![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(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(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14265])).
% 2.74/2.94 tff(14267,plain,
% 2.74/2.94 (((~![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(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(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[14266, 14264])).
% 2.74/2.94 tff(14268,plain,
% 2.74/2.94 ((~![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(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))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(14269,plain,
% 2.74/2.94 ((~![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(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[14268, 14267])).
% 2.74/2.94 tff(14270,plain,
% 2.74/2.94 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14269, 97, 14259, 87, 14261])).
% 2.74/2.94 tff(14271,plain,
% 2.74/2.94 (r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[143, 14270])).
% 2.74/2.94 tff(14272,plain,
% 2.74/2.94 (((~![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(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14273,plain,
% 2.74/2.94 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~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(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14274,plain,
% 2.74/2.94 (((~![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(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~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(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14273])).
% 2.74/2.94 tff(14275,plain,
% 2.74/2.94 (((~![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(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~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(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[14274, 14272])).
% 2.74/2.94 tff(14276,plain,
% 2.74/2.94 ((~![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(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~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)))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(14277,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[14276, 14275])).
% 2.74/2.94 tff(14278,plain,
% 2.74/2.94 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14277, 97, 14259, 87, 14261])).
% 2.74/2.94 tff(14279,plain,
% 2.74/2.94 (r(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[58, 14278])).
% 2.74/2.94 tff(14280,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[735, 155, 570, 288, 645, 224])).
% 2.74/2.94 tff(14281,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(14282,plain,
% 2.74/2.94 (~r(z, s(s(s(elem!1))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14281, 645, 288, 14271])).
% 2.74/2.94 tff(14283,plain,
% 2.74/2.94 (b(z, s(s(s(elem!1))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[590, 14282])).
% 2.74/2.94 tff(14284,plain,
% 2.74/2.94 (~r(z, s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2671, 645, 288, 14279])).
% 2.74/2.94 tff(14285,plain,
% 2.74/2.94 (b(z, s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[222, 14284])).
% 2.74/2.94 tff(14286,plain,
% 2.74/2.94 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(z, s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[4739, 11419])).
% 2.74/2.94 tff(14287,plain,
% 2.74/2.94 (~b(s(s(s(z))), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14286, 204, 87, 81])).
% 2.74/2.94 tff(14288,plain,
% 2.74/2.94 (r(s(s(s(z))), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[421, 14287])).
% 2.74/2.94 tff(14289,plain,
% 2.74/2.94 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[4382, 155, 14279, 14271, 14288])).
% 2.74/2.94 tff(14290,plain,
% 2.74/2.94 (((~![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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14291,plain,
% 2.74/2.94 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14292,plain,
% 2.74/2.94 (((~![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(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14291])).
% 2.74/2.94 tff(14293,plain,
% 2.74/2.94 (((~![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(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[14292, 14290])).
% 2.74/2.94 tff(14294,plain,
% 2.74/2.94 ((~![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(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(14295,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[14294, 14293])).
% 2.74/2.94 tff(14296,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14295, 97, 1139, 124, 1330, 1702])).
% 2.74/2.94 tff(14297,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(14298,plain,
% 2.74/2.94 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14297, 1330, 124, 14259])).
% 2.74/2.94 tff(14299,plain,
% 2.74/2.94 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[3089, 14298, 14289])).
% 2.74/2.94 tff(14300,plain,
% 2.74/2.94 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14299])).
% 2.74/2.94 tff(14301,plain,
% 2.74/2.94 (s(s(z)) = s(s(elem!1))),
% 2.74/2.94 inference(transitivity,[status(thm)],[73, 14300, 19])).
% 2.74/2.94 tff(14302,plain,
% 2.74/2.94 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14301])).
% 2.74/2.94 tff(14303,plain,
% 2.74/2.94 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.74/2.94 inference(symmetry,[status(thm)],[14302])).
% 2.74/2.94 tff(14304,plain,
% 2.74/2.94 (s(elem!1) = s(z)),
% 2.74/2.94 inference(transitivity,[status(thm)],[30, 14303, 23])).
% 2.74/2.94 tff(14305,plain,
% 2.74/2.94 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14304])).
% 2.74/2.94 tff(14306,plain,
% 2.74/2.94 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.74/2.94 inference(symmetry,[status(thm)],[14305])).
% 2.74/2.94 tff(14307,plain,
% 2.74/2.94 (b(s(s(s(z))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1846, 14299, 14259])).
% 2.74/2.94 tff(14308,plain,
% 2.74/2.94 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[4806, 876, 87, 204])).
% 2.74/2.94 tff(14309,plain,
% 2.74/2.94 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[452, 14308])).
% 2.74/2.94 tff(14310,plain,
% 2.74/2.94 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1822, 14309, 1393])).
% 2.74/2.94 tff(14311,plain,
% 2.74/2.94 (((~![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(z)), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14312,plain,
% 2.74/2.94 (((~b(s(s(s(z))), s(z))) | (~b(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(z)))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(14313,plain,
% 2.74/2.94 (((~![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(z))), s(z))) | (~b(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(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(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14312])).
% 2.74/2.94 tff(14314,plain,
% 2.74/2.94 (((~![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(z))), s(z))) | (~b(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(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(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[14313, 14311])).
% 2.74/2.94 tff(14315,plain,
% 2.74/2.94 ((~![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(z))), s(z))) | (~b(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(z)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(14316,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[14315, 14314])).
% 2.74/2.94 tff(14317,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14316, 97, 204, 876, 87, 1360, 371, 1330])).
% 2.74/2.94 tff(14318,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(14319,plain,
% 2.74/2.94 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14318, 876, 87, 204, 1360, 1330])).
% 2.74/2.94 tff(14320,plain,
% 2.74/2.94 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10862, 14319, 1889])).
% 2.74/2.94 tff(14321,plain,
% 2.74/2.94 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[821, 14320, 4451])).
% 2.74/2.94 tff(14322,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[5371, 14321, 14310, 145, 1393, 224])).
% 2.74/2.94 tff(14323,plain,((~b(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(14324,plain,
% 2.74/2.94 (~b(s(s(s(s(elem!1)))), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14323, 14299, 14279, 14271, 87, 204, 14307, 1330])).
% 2.74/2.94 tff(14325,plain,
% 2.74/2.94 (r(s(s(s(s(elem!1)))), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[842, 14324])).
% 2.74/2.94 tff(14326,plain,
% 2.74/2.94 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[11568, 14325, 81])).
% 2.74/2.94 tff(14327,plain,
% 2.74/2.94 (b(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[511, 14326])).
% 2.74/2.94 tff(14328,plain,
% 2.74/2.94 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[14327, 14306])).
% 2.74/2.94 tff(14329,plain,
% 2.74/2.94 (b(s(s(elem!1)), s(elem!1))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[9687, 14299, 87])).
% 2.74/2.94 tff(14330,plain,
% 2.74/2.94 (s(z) = s(elem!1)),
% 2.74/2.94 inference(transitivity,[status(thm)],[24, 14302, 29])).
% 2.74/2.94 tff(14331,plain,
% 2.74/2.94 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14330, 14301])).
% 2.74/2.94 tff(14332,plain,
% 2.74/2.94 (b(s(elem!1), s(s(elem!1)))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[14261, 14331])).
% 2.74/2.94 tff(14333,plain,
% 2.74/2.94 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14301])).
% 2.74/2.94 tff(14334,plain,
% 2.74/2.94 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.74/2.94 inference(transitivity,[status(thm)],[14333, 1428])).
% 2.74/2.94 tff(14335,plain,
% 2.74/2.94 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[14334, 1505])).
% 2.74/2.94 tff(14336,plain,
% 2.74/2.94 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14335])).
% 2.74/2.94 tff(14337,plain,
% 2.74/2.94 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[331, 14336])).
% 2.74/2.94 tff(14338,plain,
% 2.74/2.94 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[3107, 14325, 14299])).
% 2.74/2.94 tff(14339,plain,
% 2.74/2.94 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14330])).
% 2.74/2.94 tff(14340,plain,
% 2.74/2.94 (z = elem!1),
% 2.74/2.94 inference(transitivity,[status(thm)],[1443, 14339, 85])).
% 2.74/2.94 tff(14341,plain,
% 2.74/2.94 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14340])).
% 2.74/2.94 tff(14342,plain,
% 2.74/2.94 (r(s(s(s(elem!1))), elem!1)),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[288, 14341])).
% 2.74/2.94 tff(14343,plain,
% 2.74/2.94 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.74/2.94 inference(symmetry,[status(thm)],[14300])).
% 2.74/2.94 tff(14344,plain,
% 2.74/2.94 (s(s(elem!1)) = s(s(z))),
% 2.74/2.94 inference(transitivity,[status(thm)],[167, 14343, 72])).
% 2.74/2.94 tff(14345,plain,
% 2.74/2.94 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14344])).
% 2.74/2.94 tff(14346,plain,
% 2.74/2.94 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.94 inference(symmetry,[status(thm)],[14345])).
% 2.74/2.94 tff(14347,plain,
% 2.74/2.94 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[14279, 14346])).
% 2.74/2.94 tff(14348,plain,
% 2.74/2.94 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14299])).
% 2.74/2.94 tff(14349,plain,
% 2.74/2.94 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[14348, 1414])).
% 2.74/2.94 tff(14350,plain,
% 2.74/2.94 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[14349])).
% 2.74/2.94 tff(14351,plain,
% 2.74/2.94 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[286, 14350])).
% 2.74/2.94 tff(14352,plain,
% 2.74/2.94 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2129, 14327, 14261, 14259])).
% 2.74/2.94 tff(14353,plain,
% 2.74/2.94 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[486, 14352, 14351])).
% 2.74/2.94 tff(14354,plain,
% 2.74/2.94 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[7805, 14353, 14347, 14342, 14338])).
% 2.74/2.95 tff(14355,plain,
% 2.74/2.95 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[1631, 14354, 14337])).
% 2.74/2.95 tff(14356,plain,
% 2.74/2.95 (((~![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(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(14357,plain,
% 2.74/2.95 (((~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(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)))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(14358,plain,
% 2.74/2.95 (((~![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), 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(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))))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[14357])).
% 2.74/2.95 tff(14359,plain,
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% 2.74/2.95 tff(14373,plain,
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% 2.74/2.95 tff(14386,plain,
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% 2.74/2.95 tff(14391,plain,
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% 2.74/2.95 (r(s(s(z)), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[437, 14430])).
% 2.74/2.95 tff(14432,plain,
% 2.74/2.95 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[5794, 14431, 14279, 14408])).
% 2.74/2.95 tff(14433,plain,
% 2.74/2.95 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[2687, 14432, 4228])).
% 2.74/2.95 tff(14434,plain,
% 2.74/2.95 (~b(s(z), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[13765, 14433, 14259, 14261, 14392, 14263])).
% 2.74/2.95 tff(14435,plain,
% 2.74/2.95 (r(s(z), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[253, 14434])).
% 2.74/2.95 tff(14436,plain,
% 2.74/2.95 (~r(z, s(s(z)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[6929, 155, 14414, 14279, 14271])).
% 2.74/2.95 tff(14437,plain,
% 2.74/2.95 (b(z, s(s(z)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[222, 14436])).
% 2.74/2.95 tff(14438,plain,
% 2.74/2.95 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[8998, 155, 338, 2597, 13308])).
% 2.74/2.95 tff(14439,plain,
% 2.74/2.95 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[4169, 14438])).
% 2.74/2.95 tff(14440,plain,
% 2.74/2.95 (((~![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, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(14441,plain,
% 2.74/2.95 (((~b(z, s(s(z)))) | (~b(z, 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(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(14442,plain,
% 2.74/2.95 (((~![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, s(s(z)))) | (~b(z, 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(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[14441])).
% 2.74/2.95 tff(14443,plain,
% 2.74/2.95 (((~![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, s(s(z)))) | (~b(z, 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(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.74/2.95 inference(transitivity,[status(thm)],[14442, 14440])).
% 2.74/2.95 tff(14444,plain,
% 2.74/2.95 ((~![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, s(s(z)))) | (~b(z, 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))))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(14445,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[14444, 14443])).
% 2.74/2.95 tff(14446,plain,
% 2.74/2.95 ($false),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[14445, 97, 204, 14263, 14439, 13316])).
% 2.74/2.95 tff(14447,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.95 tff(14448,plain,
% 2.74/2.95 (~r(s(s(s(s(z)))), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[14447, 14437, 14435, 2597, 81])).
% 2.74/2.95 tff(14449,plain,
% 2.74/2.95 (b(s(s(s(s(z)))), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[13335, 14448])).
% 2.74/2.95 tff(14450,plain,
% 2.74/2.95 (b(s(z), s(s(s(s(elem!1)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[1248, 14422, 14419])).
% 2.74/2.95 tff(14451,plain,
% 2.74/2.95 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[13343, 97, 14450, 14417, 14449])).
% 2.74/2.95 tff(14452,plain,
% 2.74/2.95 (~b(s(s(s(s(z)))), elem!1)),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[14451, 14429])).
% 2.74/2.95 tff(14453,plain,
% 2.74/2.95 (r(s(s(s(s(z)))), elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[2873, 14452, 14427])).
% 2.74/2.95 tff(14454,plain,
% 2.74/2.95 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[14453, 14426])).
% 2.74/2.95 tff(14455,plain,
% 2.74/2.95 (((~![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(s(s(s(elem!1)))))) | (~b(s(s(s(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(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(14456,plain,
% 2.74/2.95 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(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(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(14457,plain,
% 2.74/2.95 (((~![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(s(s(s(elem!1)))))) | (~b(s(z), s(s(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(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[14456])).
% 2.74/2.95 tff(14458,plain,
% 2.74/2.95 (((~![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(s(s(s(elem!1)))))) | (~b(s(z), s(s(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(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.74/2.95 inference(transitivity,[status(thm)],[14457, 14455])).
% 2.74/2.95 tff(14459,plain,
% 2.74/2.95 ((~![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(s(s(s(elem!1)))))) | (~b(s(z), s(s(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)))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(14460,plain,
% 2.74/2.95 ((~![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(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[14459, 14458])).
% 2.74/2.95 tff(14461,plain,
% 2.74/2.95 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[14460, 97, 14450, 87, 14449])).
% 2.74/2.95 tff(14462,plain,
% 2.74/2.95 (r(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[13323, 14461])).
% 2.74/2.95 tff(14463,plain,
% 2.74/2.95 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[444, 14422, 14278])).
% 2.74/2.95 tff(14464,plain,
% 2.74/2.95 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[452, 14463])).
% 2.74/2.95 tff(14465,plain,
% 2.74/2.95 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[2161, 14422, 14270])).
% 2.74/2.95 tff(14466,plain,
% 2.74/2.95 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[336, 14465])).
% 2.74/2.95 tff(14467,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(14468,plain,
% 2.74/2.95 (((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(14469,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[14468])).
% 2.74/2.95 tff(14470,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.74/2.95 inference(transitivity,[status(thm)],[14469, 14467])).
% 2.74/2.95 tff(14471,plain,
% 2.74/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(14472,plain,
% 2.74/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[14471, 14470])).
% 2.74/2.95 tff(14473,plain,
% 2.74/2.95 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[14472, 155, 14466, 14464, 14462])).
% 2.74/2.95 tff(14474,plain,
% 2.74/2.95 ($false),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[14473, 14454])).
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% 2.74/2.95 tff(14476,plain,
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% 2.74/2.95 (b(s(s(s(z))), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[1358, 14476])).
% 2.74/2.95 tff(14478,plain,
% 2.74/2.95 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[14372, 14477, 14261, 14259])).
% 2.74/2.95 tff(14479,plain,
% 2.74/2.95 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[3089, 14478, 1])).
% 2.74/2.95 tff(14480,plain,
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% 2.74/2.95 inference(unit_resolution,[status(thm)],[11501, 14477, 14261, 14259, 1])).
% 2.74/2.95 tff(14481,plain,
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% 2.74/2.96 inference(unit_resolution,[status(thm)],[421, 14480])).
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% 2.74/2.96 inference(unit_resolution,[status(thm)],[4382, 155, 14279, 14271, 14481, 14479])).
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% 2.74/2.96 tff(14484,plain,
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% 2.74/2.96 inference(unit_resolution,[status(thm)],[14483, 81, 2596, 14018])).
% 2.74/2.96 tff(14485,plain,
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% 2.74/2.96 inference(monotonicity,[status(thm)],[14484])).
% 2.74/2.96 tff(14486,plain,
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% 2.74/2.96 tff(14487,plain,
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% 2.74/2.96 inference(monotonicity,[status(thm)],[14486])).
% 2.74/2.96 tff(14488,plain,
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% 2.74/2.96 inference(transitivity,[status(thm)],[24, 14487, 29])).
% 2.74/2.96 tff(14489,plain,
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% 2.74/2.96 inference(monotonicity,[status(thm)],[14488])).
% 2.74/2.96 tff(14490,plain,
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% 2.74/2.96 inference(transitivity,[status(thm)],[1443, 14489, 85])).
% 2.74/2.96 tff(14491,plain,
% 2.74/2.96 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.74/2.96 inference(monotonicity,[status(thm)],[14490])).
% 2.74/2.96 tff(14492,plain,
% 2.74/2.96 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 2.74/2.96 inference(monotonicity,[status(thm)],[14486])).
% 2.74/2.96 tff(14493,plain,
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% 2.74/2.96 inference(unit_resolution,[status(thm)],[14390, 81, 14018, 2596])).
% 2.74/2.96 tff(14494,plain,
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% 2.74/2.96 inference(unit_resolution,[status(thm)],[625, 14493])).
% 2.74/2.96 tff(14495,plain,
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% 2.74/2.96 inference(modus_ponens,[status(thm)],[14494, 14492])).
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% 2.74/2.96 (b(s(s(elem!1)), elem!1)),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[14495, 14491])).
% 2.74/2.96 tff(14497,plain,
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% 2.74/2.96 inference(unit_resolution,[status(thm)],[11529, 14484])).
% 2.74/2.96 tff(14498,plain,
% 2.74/2.96 (~b(s(s(s(z))), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[9913, 14484, 239])).
% 2.74/2.96 tff(14499,plain,
% 2.74/2.96 (r(s(s(s(z))), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[402, 14498])).
% 2.74/2.96 tff(14500,plain,
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% 2.74/2.96 inference(unit_resolution,[status(thm)],[5580, 81, 2596, 14018])).
% 2.74/2.96 tff(14501,plain,
% 2.74/2.96 (b(s(z), s(s(z)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[548, 14500])).
% 2.74/2.96 tff(14502,plain,
% 2.74/2.96 (b(s(s(s(elem!1))), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[14258, 2596, 14018])).
% 2.74/2.96 tff(14503,plain,
% 2.74/2.96 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[1401])).
% 2.74/2.96 tff(14504,plain,
% 2.74/2.96 (b(s(s(s(s(s(elem!1))))), s(elem!1)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 2.74/2.96 inference(symmetry,[status(thm)],[14503])).
% 2.74/2.96 tff(14505,plain,
% 2.74/2.96 ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) <=> (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[14504])).
% 2.74/2.96 tff(14506,plain,
% 2.74/2.96 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[14269, 97, 1139, 87, 535])).
% 2.74/2.96 tff(14507,plain,
% 2.74/2.96 (r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[143, 14506])).
% 2.74/2.96 tff(14508,plain,
% 2.74/2.96 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[14277, 97, 1139, 87, 535])).
% 2.74/2.96 tff(14509,plain,
% 2.74/2.96 (r(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[58, 14508])).
% 2.74/2.96 tff(14510,plain,
% 2.74/2.96 (r(s(s(s(z))), s(s(z)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[8734, 1393, 14509])).
% 2.74/2.96 tff(14511,plain,
% 2.74/2.96 (r(s(s(z)), s(s(s(z))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[14507, 8045])).
% 2.74/2.96 tff(14512,plain,
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% 2.74/2.96 inference(unit_resolution,[status(thm)],[1969, 1300, 14511, 14510])).
% 2.74/2.96 tff(14513,plain,
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% 2.74/2.96 inference(unit_resolution,[status(thm)],[222, 14512])).
% 2.74/2.96 tff(14514,plain,
% 2.74/2.96 (~r(s(z), s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[1308, 1300, 81, 386])).
% 2.74/2.96 tff(14515,plain,
% 2.74/2.96 (b(s(z), s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[253, 14514])).
% 2.74/2.96 tff(14516,plain,
% 2.74/2.96 (b(s(z), s(s(s(elem!1))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[6628, 14515, 1393])).
% 2.74/2.96 tff(14517,plain,
% 2.74/2.96 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 2.74/2.96 inference(transitivity,[status(thm)],[1890, 11844])).
% 2.74/2.96 tff(14518,plain,
% 2.74/2.96 (b(elem!1, s(s(elem!1)))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[14513, 14517])).
% 2.74/2.96 tff(14519,plain,
% 2.74/2.96 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[13971, 14518, 535, 1393, 1915, 1448, 14509, 1139, 14516])).
% 2.74/2.96 tff(14520,plain,
% 2.74/2.96 (r(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[511, 14519])).
% 2.74/2.96 tff(14521,plain,
% 2.74/2.96 (~r(s(s(s(s(elem!1)))), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[11568, 14520, 81])).
% 2.74/2.96 tff(14522,plain,
% 2.74/2.96 (b(s(s(s(s(elem!1)))), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[842, 14521])).
% 2.74/2.96 tff(14523,plain,
% 2.74/2.96 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[4806, 14522, 87, 14513])).
% 2.74/2.96 tff(14524,plain,
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% 2.74/2.96 inference(unit_resolution,[status(thm)],[452, 14523])).
% 2.74/2.96 tff(14525,plain,
% 2.74/2.96 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[1822, 14524, 1393])).
% 2.74/2.96 tff(14526,plain,
% 2.74/2.96 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[5371, 14525, 14509, 1393, 14507])).
% 2.74/2.96 tff(14527,plain,
% 2.74/2.96 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[821, 14526, 4451])).
% 2.74/2.96 tff(14528,plain,
% 2.74/2.96 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[14509, 5368])).
% 2.74/2.96 tff(14529,plain,
% 2.74/2.96 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[4474, 14522, 1444])).
% 2.74/2.96 tff(14530,plain,
% 2.74/2.96 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[13576, 97, 14529, 1915, 14518])).
% 2.74/2.96 tff(14531,plain,
% 2.74/2.96 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[1631, 14530, 1508])).
% 2.74/2.96 tff(14532,plain,
% 2.74/2.96 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[4505, 14531, 14528, 14525])).
% 2.74/2.96 tff(14533,plain,
% 2.74/2.96 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[486, 14532, 1418])).
% 2.74/2.96 tff(14534,plain,
% 2.74/2.96 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[14507, 5365])).
% 2.74/2.96 tff(14535,plain,
% 2.74/2.96 (b(s(elem!1), s(s(s(elem!1))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[14516, 1514])).
% 2.74/2.96 tff(14536,plain,
% 2.74/2.96 ((s(s(z)) = s(s(s(s(s(elem!1)))))) <=> (s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[1399])).
% 2.74/2.96 tff(14537,plain,
% 2.74/2.96 ((s(s(z)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.74/2.96 inference(transitivity,[status(thm)],[14536, 11819])).
% 2.74/2.96 tff(14538,plain,
% 2.74/2.96 ((~(s(s(z)) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[14537])).
% 2.74/2.96 tff(14539,plain,
% 2.74/2.96 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[13386, 14538])).
% 2.74/2.96 tff(14540,plain,
% 2.74/2.96 (((~![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(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(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(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(14541,plain,
% 2.74/2.96 (((~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(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(14542,plain,
% 2.74/2.96 (((~![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(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(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[14541])).
% 2.74/2.96 tff(14543,plain,
% 2.74/2.96 (((~![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(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(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[14542, 14540])).
% 2.74/2.96 tff(14544,plain,
% 2.74/2.96 ((~![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(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)))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(14545,plain,
% 2.74/2.96 ((~![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(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(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[14544, 14543])).
% 2.74/2.96 tff(14546,plain,
% 2.74/2.96 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[14545, 97, 1617, 8216, 13629])).
% 2.74/2.96 tff(14547,plain,
% 2.74/2.96 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[6269, 14546, 14539])).
% 2.74/2.96 tff(14548,plain,
% 2.74/2.96 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[6283, 155, 4497, 6277, 14547])).
% 2.74/2.96 tff(14549,plain,
% 2.74/2.96 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[14548, 13628])).
% 2.74/2.96 tff(14550,plain,
% 2.74/2.96 (((~![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(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(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(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(14551,plain,
% 2.74/2.96 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(14552,plain,
% 2.74/2.96 (((~![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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[14551])).
% 2.74/2.96 tff(14553,plain,
% 2.74/2.96 (((~![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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[14552, 14550])).
% 2.74/2.96 tff(14554,plain,
% 2.74/2.96 ((~![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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(14555,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[14554, 14553])).
% 2.74/2.96 tff(14556,plain,
% 2.74/2.96 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[14555, 97, 473, 805, 2423, 1617, 13629])).
% 2.74/2.96 tff(14557,plain,
% 2.74/2.96 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[14556, 7493])).
% 2.74/2.96 tff(14558,plain,
% 2.74/2.96 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[6289, 14557, 7492])).
% 2.74/2.96 tff(14559,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[14558, 14549])).
% 2.74/2.96 tff(14560,plain,((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(14561,plain,
% 2.74/2.96 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[14560, 14535, 14528, 14534, 1393, 14095, 14533, 14527, 13469])).
% 2.74/2.96 tff(14562,plain,
% 2.74/2.96 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[14561, 14505])).
% 2.74/2.96 tff(14563,plain,
% 2.74/2.96 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[6239, 14562, 6223])).
% 2.74/2.96 tff(14564,plain,
% 2.74/2.96 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[14563, 6213])).
% 2.74/2.96 tff(14565,plain,
% 2.74/2.96 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10968, 97, 14533, 14527, 14535])).
% 2.74/2.96 tff(14566,plain,
% 2.74/2.96 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[1615, 53, 1612, 14565])).
% 2.74/2.96 tff(14567,plain,
% 2.74/2.96 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[5308, 14533, 1139, 14522])).
% 2.74/2.96 tff(14568,plain,
% 2.74/2.96 (r(s(z), s(s(s(s(elem!1)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[280, 14567])).
% 2.74/2.96 tff(14569,plain,
% 2.74/2.96 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[1909, 14568, 1393])).
% 2.74/2.96 tff(14570,plain,
% 2.74/2.96 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~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)))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(14571,plain,
% 2.74/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(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))))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[14570])).
% 2.74/2.96 tff(14572,plain,
% 2.74/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(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)))))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[14571, 6256])).
% 2.74/2.96 tff(14573,plain,
% 2.74/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(14574,plain,
% 2.74/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(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))))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[14573, 14572])).
% 2.74/2.96 tff(14575,plain,
% 2.74/2.96 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[14574, 155, 14569, 14566, 14564])).
% 2.74/2.96 tff(14576,plain,
% 2.74/2.96 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[6254, 14575, 8167])).
% 2.74/2.96 tff(14577,plain,
% 2.74/2.96 (r(elem!1, s(elem!1))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[11419, 4430])).
% 2.74/2.96 tff(14578,plain,
% 2.74/2.96 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[13688, 155, 1448, 14577, 14564])).
% 2.74/2.96 tff(14579,plain,
% 2.74/2.96 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[6313, 14578, 6300])).
% 2.74/2.96 tff(14580,plain,
% 2.74/2.96 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[1401])).
% 2.74/2.96 tff(14581,plain,
% 2.74/2.96 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 2.74/2.96 inference(symmetry,[status(thm)],[14580])).
% 2.74/2.96 tff(14582,plain,
% 2.74/2.96 (r(z, s(z)) <=> r(elem!1, s(z))),
% 2.74/2.96 inference(transitivity,[status(thm)],[4430, 14581])).
% 2.74/2.96 tff(14583,plain,
% 2.74/2.96 (r(elem!1, s(z))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[11419, 14582])).
% 2.74/2.96 tff(14584,assumption,(r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.74/2.96 tff(14585,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 2.74/2.96 tff(14586,plain,
% 2.74/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(14587,plain,
% 2.74/2.96 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(14588,plain,
% 2.74/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[14587])).
% 2.74/2.96 tff(14589,plain,
% 2.74/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[14588, 14586])).
% 2.74/2.96 tff(14590,plain,
% 2.74/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(14591,plain,
% 2.74/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[14590, 14589])).
% 2.74/2.96 tff(14592,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[14591, 155, 14585, 287, 14584, 495])).
% 2.74/2.96 tff(14593,plain,((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(14594,plain,
% 2.74/2.96 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[14593, 14568, 14583, 14520])).
% 2.74/2.96 tff(14595,plain,
% 2.74/2.96 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[1930, 14594, 13955])).
% 2.74/2.96 tff(14596,plain,
% 2.74/2.96 (((~![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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(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(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(14597,plain,
% 2.74/2.96 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(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(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(14598,plain,
% 2.74/2.96 (((~![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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(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(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))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[14597])).
% 2.74/2.96 tff(14599,plain,
% 2.74/2.96 (((~![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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(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(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))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.74/2.97 inference(transitivity,[status(thm)],[14598, 14596])).
% 2.74/2.97 tff(14600,plain,
% 2.74/2.97 ((~![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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(14601,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[14600, 14599])).
% 2.74/2.97 tff(14602,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14601, 97, 14533, 14529, 14527, 14595, 14579, 14576])).
% 2.74/2.97 tff(14603,plain,((~r(z, s(s(s(z))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(s(z), s(s(z)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(14604,plain,
% 2.74/2.97 (~r(z, s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14603, 14484, 14502, 14496, 14018, 81, 14501, 14499])).
% 2.74/2.97 tff(14605,plain,
% 2.74/2.97 (~r(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[6374, 14604, 14497])).
% 2.74/2.97 tff(14606,plain,
% 2.74/2.97 (b(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[590, 14605])).
% 2.74/2.97 tff(14607,plain,
% 2.74/2.97 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.74/2.97 inference(symmetry,[status(thm)],[14485])).
% 2.74/2.97 tff(14608,plain,
% 2.74/2.97 (s(s(elem!1)) = s(s(z))),
% 2.74/2.97 inference(transitivity,[status(thm)],[167, 14607, 72])).
% 2.74/2.97 tff(14609,plain,
% 2.74/2.97 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[14608])).
% 2.74/2.97 tff(14610,plain,
% 2.74/2.97 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.97 inference(symmetry,[status(thm)],[14609])).
% 2.74/2.97 tff(14611,plain,
% 2.74/2.97 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14277, 97, 14502, 14018, 14501])).
% 2.74/2.97 tff(14612,plain,
% 2.74/2.97 (r(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[58, 14611])).
% 2.74/2.97 tff(14613,plain,
% 2.74/2.97 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[14612, 14610])).
% 2.74/2.97 tff(14614,plain,
% 2.74/2.97 (b(z, s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1318, 14604])).
% 2.74/2.97 tff(14615,plain,
% 2.74/2.97 (~b(z, s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14363, 14606, 14018, 81, 2596, 14614])).
% 2.74/2.97 tff(14616,plain,
% 2.74/2.97 (r(z, s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[222, 14615])).
% 2.74/2.97 tff(14617,plain,
% 2.74/2.97 (~b(s(s(s(s(elem!1)))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[11740, 14616, 14613, 14501, 14606, 14484, 14496])).
% 2.74/2.97 tff(14618,plain,
% 2.74/2.97 (r(s(s(s(s(elem!1)))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[842, 14617])).
% 2.74/2.97 tff(14619,plain,
% 2.74/2.97 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[11568, 14618, 81])).
% 2.74/2.97 tff(14620,plain,
% 2.74/2.97 (b(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[511, 14619])).
% 2.74/2.97 tff(14621,plain,
% 2.74/2.97 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2129, 14620, 14501, 14502])).
% 2.74/2.97 tff(14622,plain,
% 2.74/2.97 (~r(z, s(s(s(s(elem!1)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[3464, 14621, 2596, 14605, 14618])).
% 2.74/2.97 tff(14623,plain,
% 2.74/2.97 (b(z, s(s(s(s(elem!1)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1093, 14622])).
% 2.74/2.97 tff(14624,plain,
% 2.74/2.97 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[14484])).
% 2.74/2.97 tff(14625,plain,
% 2.74/2.97 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[14624, 1414])).
% 2.74/2.97 tff(14626,plain,
% 2.74/2.97 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[14625])).
% 2.74/2.97 tff(14627,plain,
% 2.74/2.97 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[286, 14626])).
% 2.74/2.97 tff(14628,plain,
% 2.74/2.97 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[486, 14621, 14627])).
% 2.74/2.97 tff(14629,plain,
% 2.74/2.97 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[5339, 14628, 2596, 14612, 14616])).
% 2.74/2.97 tff(14630,plain,
% 2.74/2.97 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[336, 14629])).
% 2.74/2.97 tff(14631,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[669, 14630, 14623, 14494, 14620])).
% 2.74/2.97 tff(14632,plain,((~r(s(z), z)) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(14633,plain,
% 2.74/2.97 (~r(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14632, 239])).
% 2.74/2.97 tff(14634,plain,
% 2.74/2.97 (b(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[568, 14633])).
% 2.74/2.97 tff(14635,plain,
% 2.74/2.97 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[6908, 97, 14502, 14634, 14018])).
% 2.74/2.97 tff(14636,plain,
% 2.74/2.97 (r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[143, 14635])).
% 2.74/2.97 tff(14637,plain,
% 2.74/2.97 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[6908, 97, 14259, 550, 87])).
% 2.74/2.97 tff(14638,plain,
% 2.74/2.97 (r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[143, 14637])).
% 2.74/2.97 tff(14639,plain,
% 2.74/2.97 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10654, 550, 87, 14259])).
% 2.74/2.97 tff(14640,plain,
% 2.74/2.97 (r(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[58, 14639])).
% 2.74/2.97 tff(14641,plain,
% 2.74/2.97 (~r(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2671, 226, 288, 14640])).
% 2.74/2.97 tff(14642,plain,
% 2.74/2.97 (b(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[625, 14641])).
% 2.74/2.97 tff(14643,plain,
% 2.74/2.97 (~b(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14190, 14642, 550, 87])).
% 2.74/2.97 tff(14644,plain,
% 2.74/2.97 (r(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[590, 14643])).
% 2.74/2.97 tff(14645,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[5182, 155, 14644, 226, 14640, 14638])).
% 2.74/2.97 tff(14646,plain,((~r(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(14647,plain,
% 2.74/2.97 (~r(z, s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14646, 14634, 14018, 2596])).
% 2.74/2.97 tff(14648,plain,
% 2.74/2.97 (b(z, s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[222, 14647])).
% 2.74/2.97 tff(14649,plain,
% 2.74/2.97 (~b(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14200, 14648, 14634, 14018])).
% 2.74/2.97 tff(14650,plain,
% 2.74/2.97 (r(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[625, 14649])).
% 2.74/2.97 tff(14651,plain,
% 2.74/2.97 (~r(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14281, 14650, 2596, 14636])).
% 2.74/2.97 tff(14652,plain,
% 2.74/2.97 (b(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[590, 14651])).
% 2.74/2.97 tff(14653,plain,
% 2.74/2.97 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10654, 14634, 14018, 14502])).
% 2.74/2.97 tff(14654,plain,
% 2.74/2.97 (r(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[58, 14653])).
% 2.74/2.97 tff(14655,plain,
% 2.74/2.97 (~b(s(z), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[3966, 14648, 14018, 14634])).
% 2.74/2.97 tff(14656,plain,
% 2.74/2.97 (r(s(z), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[548, 14655])).
% 2.74/2.97 tff(14657,plain,
% 2.74/2.97 (~r(s(z), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[5875, 14656, 14654, 14636])).
% 2.74/2.97 tff(14658,plain,
% 2.74/2.97 (b(s(z), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[181, 14657])).
% 2.74/2.97 tff(14659,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[12791, 97, 14502, 14658, 14634, 14652])).
% 2.74/2.97 tff(14660,plain,(b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(14661,plain,
% 2.74/2.97 ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[4567, 14660])).
% 2.74/2.97 tff(14662,plain,
% 2.74/2.97 (~b(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14661, 11429, 60])).
% 2.74/2.97 tff(14663,plain,
% 2.74/2.97 (r(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[625, 14662])).
% 2.74/2.97 tff(14664,plain,
% 2.74/2.97 (~r(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[11825, 14663, 3])).
% 2.74/2.97 tff(14665,plain,
% 2.74/2.97 (b(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[568, 14664])).
% 2.74/2.97 tff(14666,plain,
% 2.74/2.97 ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10212, 14660])).
% 2.74/2.97 tff(14667,plain,
% 2.74/2.97 (~b(s(s(s(elem!1))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14666, 14665, 11429])).
% 2.74/2.97 tff(14668,plain,
% 2.74/2.97 (r(s(s(s(elem!1))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[493, 14667])).
% 2.74/2.97 tff(14669,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2261, 97, 14660, 204, 60, 127])).
% 2.74/2.97 tff(14670,plain,((~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(14671,plain,
% 2.74/2.97 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14670, 11429, 60])).
% 2.74/2.97 tff(14672,plain,
% 2.74/2.97 (r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[143, 14671])).
% 2.74/2.97 tff(14673,plain,
% 2.74/2.97 (~r(s(z), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1273, 14672, 2, 14668])).
% 2.74/2.97 tff(14674,plain,
% 2.74/2.97 (b(s(z), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[181, 14673])).
% 2.74/2.97 tff(14675,plain,
% 2.74/2.97 (~r(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2253, 14672, 2, 14663, 14668])).
% 2.74/2.97 tff(14676,plain,
% 2.74/2.97 (b(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[590, 14675])).
% 2.74/2.97 tff(14677,plain,
% 2.74/2.97 ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[5838, 14660])).
% 2.74/2.97 tff(14678,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14677, 14676, 14674, 14665])).
% 2.74/2.97 tff(14679,plain,((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(14680,plain,
% 2.74/2.97 (~r(s(z), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14679, 59, 2])).
% 2.74/2.97 tff(14681,plain,
% 2.74/2.97 (b(s(z), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[548, 14680])).
% 2.74/2.97 tff(14682,plain,
% 2.74/2.97 (~b(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14661, 204, 60])).
% 2.74/2.97 tff(14683,plain,
% 2.74/2.97 (r(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[625, 14682])).
% 2.74/2.97 tff(14684,plain,
% 2.74/2.97 (~r(s(z), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14679, 60, 2])).
% 2.74/2.97 tff(14685,plain,
% 2.74/2.97 (b(s(z), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[548, 14684])).
% 2.74/2.97 tff(14686,plain,
% 2.74/2.97 (~b(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[13733, 204, 2, 14685])).
% 2.74/2.97 tff(14687,plain,
% 2.74/2.97 (r(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[568, 14686])).
% 2.74/2.97 tff(14688,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[966, 155, 11419, 14687, 14683, 2])).
% 2.74/2.97 tff(14689,plain,((~b(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(14690,plain,
% 2.74/2.97 (~b(z, s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14689, 59, 2])).
% 2.74/2.97 tff(14691,plain,
% 2.74/2.97 (r(z, s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[222, 14690])).
% 2.74/2.97 tff(14692,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[11814, 97, 193, 60, 535, 127])).
% 2.74/2.97 tff(14693,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(14694,plain,
% 2.74/2.97 (~b(s(z), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14693, 127, 14681, 59])).
% 2.74/2.97 tff(14695,plain,
% 2.74/2.97 (r(s(z), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[181, 14694])).
% 2.74/2.97 tff(14696,plain,
% 2.74/2.97 (~r(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[11807, 14695, 494])).
% 2.74/2.97 tff(14697,plain,
% 2.74/2.97 (b(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[590, 14696])).
% 2.74/2.97 tff(14698,plain,
% 2.74/2.97 ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[4987, 14660])).
% 2.74/2.97 tff(14699,plain,
% 2.74/2.97 (~b(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14698, 14697, 127])).
% 2.74/2.97 tff(14700,plain,
% 2.74/2.97 (r(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[625, 14699])).
% 2.74/2.97 tff(14701,plain,
% 2.74/2.97 (~b(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[3945, 14700, 14681, 4, 14694, 82, 14696, 226])).
% 2.74/2.97 tff(14702,plain,
% 2.74/2.97 (r(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[568, 14701])).
% 2.74/2.97 tff(14703,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[966, 155, 11419, 14702, 14700, 2])).
% 2.74/2.97 tff(14704,plain,((~b(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | r(s(s(s(elem!1))), s(s(z))) | b(s(s(s(elem!1))), s(z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(14705,plain,
% 2.74/2.97 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14704, 226, 4, 82, 2])).
% 2.74/2.97 tff(14706,plain,
% 2.74/2.97 (r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[143, 14705])).
% 2.74/2.97 tff(14707,plain,
% 2.74/2.97 (~r(s(z), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1273, 14706, 2, 494])).
% 2.74/2.97 tff(14708,plain,
% 2.74/2.97 (b(s(z), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[181, 14707])).
% 2.74/2.97 tff(14709,plain,
% 2.74/2.97 (~r(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[11802, 14706, 494, 226])).
% 2.74/2.97 tff(14710,plain,
% 2.74/2.97 (b(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[590, 14709])).
% 2.74/2.97 tff(14711,plain,
% 2.74/2.97 (~b(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14677, 14710, 14708])).
% 2.74/2.97 tff(14712,plain,
% 2.74/2.97 (r(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[568, 14711])).
% 2.74/2.97 tff(14713,plain,
% 2.74/2.97 (~r(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[966, 155, 11419, 14712, 2])).
% 2.74/2.97 tff(14714,plain,
% 2.74/2.97 (b(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[625, 14713])).
% 2.74/2.97 tff(14715,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[4312, 97, 14660, 14710, 59, 14714])).
% 2.74/2.97 tff(14716,plain,((~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | r(s(s(s(elem!1))), s(s(z))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(14717,plain,
% 2.74/2.97 (b(s(s(s(elem!1))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14716, 14691, 4, 2])).
% 2.74/2.97 tff(14718,plain,
% 2.74/2.97 (~b(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[11644, 14717, 59, 14681])).
% 2.74/2.97 tff(14719,plain,
% 2.74/2.97 (r(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[625, 14718])).
% 2.74/2.97 tff(14720,plain,
% 2.74/2.97 (~b(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[11644, 1139, 60, 14685])).
% 2.74/2.97 tff(14721,plain,
% 2.74/2.97 (r(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[625, 14720])).
% 2.74/2.97 tff(14722,plain,
% 2.74/2.97 (~b(z, s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14689, 60, 2])).
% 2.74/2.97 tff(14723,plain,
% 2.74/2.97 (r(z, s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[222, 14722])).
% 2.74/2.97 tff(14724,plain,
% 2.74/2.97 ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[12878, 14660])).
% 2.74/2.97 tff(14725,plain,
% 2.74/2.97 (~b(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14724, 550, 1139])).
% 2.74/2.97 tff(14726,plain,
% 2.74/2.97 (r(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[590, 14725])).
% 2.74/2.97 tff(14727,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[11631, 155, 11419, 570, 226, 2, 225])).
% 2.74/2.97 tff(14728,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(14729,plain,
% 2.74/2.97 (~r(s(z), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14728, 14726, 14723, 2])).
% 2.74/2.97 tff(14730,plain,
% 2.74/2.97 (b(s(z), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[181, 14729])).
% 2.74/2.97 tff(14731,plain,
% 2.74/2.97 (~b(s(s(z)), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14247, 14730, 60, 14685])).
% 2.74/2.97 tff(14732,plain,
% 2.74/2.97 (r(s(s(z)), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[437, 14731])).
% 2.74/2.97 tff(14733,plain,
% 2.74/2.97 (~r(s(z), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[13230, 14732, 2, 14721])).
% 2.74/2.97 tff(14734,plain,
% 2.74/2.97 (b(s(z), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[253, 14733])).
% 2.74/2.97 tff(14735,plain,
% 2.74/2.97 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1710, 14734, 1139, 14730])).
% 2.74/2.97 tff(14736,plain,
% 2.74/2.97 (~r(s(s(s(z))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[12716, 14732, 2, 14721])).
% 2.74/2.97 tff(14737,plain,
% 2.74/2.97 (b(s(s(s(z))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[402, 14736])).
% 2.74/2.97 tff(14738,plain,
% 2.74/2.97 (~b(z, s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[13242, 14734, 550, 14737])).
% 2.74/2.97 tff(14739,plain,
% 2.74/2.97 (r(z, s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1318, 14738])).
% 2.74/2.97 tff(14740,plain,
% 2.74/2.97 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[5852, 14739, 1, 14726, 14735])).
% 2.74/2.97 tff(14741,plain,
% 2.74/2.97 (~r(s(s(s(z))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[11460, 14739, 14723, 14732])).
% 2.74/2.97 tff(14742,plain,
% 2.74/2.97 (b(s(s(s(z))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1358, 14741])).
% 2.74/2.97 tff(14743,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[12294, 14742, 14740, 1139, 14734])).
% 2.74/2.97 tff(14744,plain,((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(14745,plain,
% 2.74/2.97 (~b(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14744, 14717, 1, 2, 59])).
% 2.74/2.97 tff(14746,plain,
% 2.74/2.97 (r(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[568, 14745])).
% 2.74/2.97 tff(14747,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[966, 155, 11419, 14746, 14719, 2])).
% 2.74/2.97 tff(14748,plain,(r(s(s(s(elem!1))), s(s(z))) | (~r(s(s(z)), s(z))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(14749,plain,
% 2.74/2.97 (r(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14748, 2, 1])).
% 2.74/2.97 tff(14750,plain,
% 2.74/2.97 (~r(s(s(s(elem!1))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2313, 3, 2, 14749])).
% 2.74/2.97 tff(14751,plain,
% 2.74/2.97 (b(s(s(s(elem!1))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[493, 14750])).
% 2.74/2.97 tff(14752,plain,
% 2.74/2.97 (b(s(s(s(z))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[12659, 14751, 2, 14749, 1, 3])).
% 2.74/2.97 tff(14753,plain,
% 2.74/2.97 (~b(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14666, 11429, 14751])).
% 2.74/2.97 tff(14754,plain,
% 2.74/2.97 (r(s(z), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[568, 14753])).
% 2.74/2.97 tff(14755,plain,
% 2.74/2.97 (~r(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[11825, 14754, 3])).
% 2.74/2.97 tff(14756,plain,
% 2.74/2.97 (b(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[625, 14755])).
% 2.74/2.97 tff(14757,plain,
% 2.74/2.97 (~b(s(s(s(z))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10183, 97, 11429, 14756, 14752])).
% 2.74/2.97 tff(14758,plain,
% 2.74/2.97 (r(s(s(s(z))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[402, 14757])).
% 2.74/2.97 tff(14759,plain,
% 2.74/2.97 (~b(z, s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1339, 14756, 11429, 14752])).
% 2.74/2.97 tff(14760,plain,
% 2.74/2.97 (r(z, s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1318, 14759])).
% 2.74/2.97 tff(14761,plain,
% 2.74/2.97 (b(s(z), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[12098, 14754, 3])).
% 2.74/2.97 tff(14762,plain,
% 2.74/2.97 (~r(s(z), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1308, 14758, 14754, 14760])).
% 2.74/2.97 tff(14763,plain,
% 2.74/2.97 (b(s(z), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[253, 14762])).
% 2.74/2.97 tff(14764,plain,
% 2.74/2.97 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1710, 14763, 14751, 14761])).
% 2.74/2.97 tff(14765,plain,
% 2.74/2.97 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[3089, 14764, 1])).
% 2.74/2.97 tff(14766,plain,
% 2.74/2.97 (~r(s(s(s(z))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[4334, 155, 11419, 14754, 14758])).
% 2.74/2.97 tff(14767,plain,
% 2.74/2.97 (b(s(s(s(z))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1358, 14766])).
% 2.74/2.97 tff(14768,plain,
% 2.74/2.97 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[11923, 14767, 14761, 14763])).
% 2.74/2.97 tff(14769,plain,
% 2.74/2.97 (~r(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[5852, 14768, 1, 14760, 14764])).
% 2.74/2.97 tff(14770,plain,
% 2.74/2.97 (b(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[590, 14769])).
% 2.74/2.97 tff(14771,plain,
% 2.74/2.97 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2687, 14768, 4228])).
% 2.74/2.97 tff(14772,plain,
% 2.74/2.97 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[4557, 97, 14660, 11429, 14756])).
% 2.74/2.97 tff(14773,plain,
% 2.74/2.97 (r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[143, 14772])).
% 2.74/2.97 tff(14774,plain,
% 2.74/2.97 (b(s(z), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[12047, 3, 1331, 81])).
% 2.74/2.97 tff(14775,plain,
% 2.74/2.97 (~b(z, s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2452, 3, 1331, 81])).
% 2.74/2.97 tff(14776,plain,
% 2.74/2.97 (r(z, s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[723, 14775])).
% 2.74/2.97 tff(14777,plain,
% 2.74/2.97 (~r(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[966, 155, 14776, 81, 5667])).
% 2.74/2.97 tff(14778,plain,
% 2.74/2.97 (b(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[625, 14777])).
% 2.74/2.97 tff(14779,plain,
% 2.74/2.97 (~b(z, s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1339, 14778, 1331, 204])).
% 2.74/2.97 tff(14780,plain,
% 2.74/2.97 (r(z, s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1318, 14779])).
% 2.74/2.97 tff(14781,plain,
% 2.74/2.97 (~b(s(s(s(z))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10183, 97, 204, 14778, 1331])).
% 2.74/2.97 tff(14782,plain,
% 2.74/2.97 (r(s(s(s(z))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[402, 14781])).
% 2.74/2.97 tff(14783,plain,
% 2.74/2.97 (~r(s(z), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1308, 14782, 81, 14780])).
% 2.74/2.97 tff(14784,plain,
% 2.74/2.97 (b(s(z), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[253, 14783])).
% 2.74/2.97 tff(14785,plain,
% 2.74/2.97 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1710, 14784, 1139, 14774])).
% 2.74/2.97 tff(14786,plain,
% 2.74/2.97 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[12294, 14784, 1360, 1139])).
% 2.74/2.97 tff(14787,plain,
% 2.74/2.97 (~r(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[5852, 14786, 14780, 1, 14785])).
% 2.74/2.97 tff(14788,plain,
% 2.74/2.97 (b(z, s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[590, 14787])).
% 2.74/2.97 tff(14789,plain,
% 2.74/2.97 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[3089, 14785, 1])).
% 2.74/2.97 tff(14790,plain,
% 2.74/2.97 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2687, 14786, 4228])).
% 2.74/2.97 tff(14791,plain,
% 2.74/2.97 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[5749, 155, 1961, 14790, 14789])).
% 2.74/2.97 tff(14792,plain,
% 2.74/2.97 (b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[143, 14791])).
% 2.74/2.97 tff(14793,plain,
% 2.74/2.97 (~r(s(s(s(elem!1))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[12026, 155, 14780, 14782, 14790])).
% 2.74/2.97 tff(14794,plain,
% 2.74/2.97 (b(s(s(s(elem!1))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[246, 14793])).
% 2.74/2.97 tff(14795,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[4987, 14794, 14792, 14778, 14788])).
% 2.74/2.97 tff(14796,plain,((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(14797,plain,
% 2.74/2.97 (~r(s(s(z)), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14796, 14767, 3, 11429, 14751, 1, 14752, 14754])).
% 2.74/2.97 tff(14798,plain,
% 2.74/2.97 (b(s(s(z)), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[437, 14797])).
% 2.74/2.97 tff(14799,plain,
% 2.74/2.97 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[523, 3022])).
% 2.74/2.97 tff(14800,plain,
% 2.74/2.97 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(14801,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[14800])).
% 2.74/2.97 tff(14802,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[14801, 4094])).
% 2.74/2.97 tff(14803,plain,
% 2.74/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(14804,plain,
% 2.74/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[14803, 14802])).
% 2.74/2.97 tff(14805,plain,
% 2.74/2.97 (~r(s(s(s(s(elem!1)))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14804, 155, 387, 1300, 386])).
% 2.74/2.97 tff(14806,plain,
% 2.74/2.97 (b(s(s(s(s(elem!1)))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[842, 14805])).
% 2.74/2.97 tff(14807,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(14808,plain,
% 2.74/2.97 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(14809,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[14808])).
% 2.74/2.97 tff(14810,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[14809, 14807])).
% 2.74/2.97 tff(14811,plain,
% 2.74/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(14812,plain,
% 2.74/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[14811, 14810])).
% 2.74/2.97 tff(14813,plain,
% 2.74/2.97 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14812, 155, 387, 2630, 4252])).
% 2.74/2.97 tff(14814,plain,
% 2.74/2.97 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[821, 14813, 802])).
% 2.74/2.97 tff(14815,plain,
% 2.74/2.97 (~r(s(s(s(elem!1))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[12026, 155, 1300, 386, 2630])).
% 2.74/2.97 tff(14816,plain,
% 2.74/2.97 (b(s(s(s(elem!1))), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[246, 14815])).
% 2.74/2.97 tff(14817,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[12801, 97, 1139, 193, 14816, 124, 14814, 14806])).
% 2.74/2.97 tff(14818,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(14819,plain,
% 2.74/2.97 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14818, 14799, 193, 3008, 1139, 2630, 4252, 1300, 386])).
% 2.74/2.97 tff(14820,plain,
% 2.74/2.97 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2747, 14819])).
% 2.74/2.97 tff(14821,plain,
% 2.74/2.97 (~r(s(z), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1308, 386, 81, 1300])).
% 2.74/2.97 tff(14822,plain,
% 2.74/2.97 (b(s(z), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[253, 14821])).
% 2.74/2.97 tff(14823,plain,
% 2.74/2.97 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[3031, 155, 488, 309, 2, 495])).
% 2.74/2.97 tff(14824,plain,
% 2.74/2.97 (b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[141, 53, 42, 14823])).
% 2.74/2.97 tff(14825,plain,
% 2.74/2.97 ((~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2151, 155, 463, 309, 81])).
% 2.74/2.97 tff(14826,plain,
% 2.74/2.97 (~r(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[14825, 2])).
% 2.74/2.97 tff(14827,plain,
% 2.74/2.97 (b(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[625, 14826])).
% 2.74/2.97 tff(14828,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[13040, 97, 1139, 124, 14827, 14824])).
% 2.74/2.97 tff(14829,plain,((~r(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(14830,plain,
% 2.74/2.98 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14829, 495, 1139, 2, 81, 463, 309, 124])).
% 2.74/2.98 tff(14831,plain,
% 2.74/2.98 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[486, 14830, 472])).
% 2.74/2.98 tff(14832,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[3290, 12153, 14831, 124, 126])).
% 2.74/2.98 tff(14833,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(14834,plain,
% 2.74/2.98 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14833, 309, 126, 472, 81, 729, 1139, 2, 463, 124])).
% 2.74/2.98 tff(14835,plain,
% 2.74/2.98 (b(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[511, 14834])).
% 2.74/2.98 tff(14836,plain,
% 2.74/2.98 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[7696, 14835, 1361, 1360, 1331, 86])).
% 2.74/2.98 tff(14837,plain,
% 2.74/2.98 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1804, 14835, 1139, 193])).
% 2.74/2.98 tff(14838,plain,
% 2.74/2.98 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[821, 14837, 3701])).
% 2.74/2.98 tff(14839,plain,
% 2.74/2.98 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[12643, 309, 14838, 224])).
% 2.74/2.98 tff(14840,plain,
% 2.74/2.98 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[486, 14839, 472])).
% 2.74/2.98 tff(14841,plain,
% 2.74/2.98 (~b(s(s(s(s(elem!1)))), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[3290, 14840, 124, 126])).
% 2.74/2.98 tff(14842,plain,
% 2.74/2.98 (r(s(s(s(s(elem!1)))), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[842, 14841])).
% 2.74/2.98 tff(14843,plain,
% 2.74/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(14844,plain,
% 2.74/2.98 (((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~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))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(14845,plain,
% 2.74/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[14844])).
% 2.74/2.98 tff(14846,plain,
% 2.74/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[14845, 14843])).
% 2.74/2.98 tff(14847,plain,
% 2.74/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~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)))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(14848,plain,
% 2.74/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[14847, 14846])).
% 2.74/2.98 tff(14849,plain,
% 2.74/2.98 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14848, 155, 14842, 14838, 1300, 4252])).
% 2.74/2.98 tff(14850,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[384, 53, 14849, 14836, 286])).
% 2.74/2.98 tff(14851,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(14852,plain,
% 2.74/2.98 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14851, 3022, 4252, 3008, 14816, 1300, 224, 1361, 1360, 1331, 14822, 1139, 193, 81, 729, 2, 463])).
% 2.74/2.98 tff(14853,plain,
% 2.74/2.98 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[336, 14852])).
% 2.74/2.98 tff(14854,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1985, 97, 14853, 1361, 1360, 14820])).
% 2.74/2.98 tff(14855,plain,((~r(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(14856,plain,
% 2.74/2.98 ((~r(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | r(z, s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14855, 11419])).
% 2.74/2.98 tff(14857,plain,
% 2.74/2.98 (~r(z, s(s(s(s(elem!1)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14856, 14771, 14751, 14767, 14761, 14798, 14765, 14760, 14758, 14773, 14752, 14754, 2, 14769])).
% 2.74/2.98 tff(14858,plain,
% 2.74/2.98 (b(z, s(s(s(s(elem!1)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1093, 14857])).
% 2.74/2.98 tff(14859,plain,
% 2.74/2.98 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[7696, 371, 1361, 1360, 1331, 86])).
% 2.74/2.98 tff(14860,plain,
% 2.74/2.98 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1154, 14859, 1139])).
% 2.74/2.98 tff(14861,plain,
% 2.74/2.98 (r(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[511, 14859])).
% 2.74/2.98 tff(14862,plain,
% 2.74/2.98 (~r(s(s(s(s(elem!1)))), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[4414, 14861, 81, 729])).
% 2.74/2.98 tff(14863,plain,
% 2.74/2.98 (b(s(s(s(s(elem!1)))), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[842, 14862])).
% 2.74/2.98 tff(14864,plain,
% 2.74/2.98 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[3290, 14863, 124, 126])).
% 2.74/2.98 tff(14865,plain,
% 2.74/2.98 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[4987, 126, 83, 124])).
% 2.74/2.98 tff(14866,plain,
% 2.74/2.98 (r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[143, 14865])).
% 2.74/2.98 tff(14867,plain,
% 2.74/2.98 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[380, 371, 83, 372])).
% 2.74/2.98 tff(14868,plain,
% 2.74/2.98 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[336, 14867])).
% 2.74/2.98 tff(14869,plain,
% 2.74/2.98 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[523, 14860])).
% 2.74/2.98 tff(14870,plain,
% 2.74/2.98 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[821, 14869, 6059])).
% 2.74/2.98 tff(14871,plain,
% 2.74/2.98 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[12643, 14870, 14868, 14866])).
% 2.74/2.98 tff(14872,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[486, 14871, 14864, 14860])).
% 2.74/2.98 tff(14873,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(14874,plain,
% 2.74/2.98 ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14873, 11419])).
% 2.74/2.98 tff(14875,plain,
% 2.74/2.98 ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14874, 14660])).
% 2.74/2.98 tff(14876,plain,
% 2.74/2.98 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14875, 14770, 14751, 14754, 14798, 14767, 14752, 14763, 14756, 14858])).
% 2.74/2.98 tff(14877,plain,
% 2.74/2.98 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[2747, 14876])).
% 2.74/2.98 tff(14878,plain,
% 2.74/2.98 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14818, 14877, 14751, 14771, 14761, 14770, 14765, 14760, 14758])).
% 2.74/2.98 tff(14879,plain,
% 2.74/2.98 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[523, 14878])).
% 2.74/2.98 tff(14880,plain,
% 2.74/2.98 (~(s(s(s(s(z)))) = elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[2786, 14879])).
% 2.74/2.98 tff(14881,plain,
% 2.74/2.98 (b(s(z), s(s(s(s(elem!1)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1248, 14879, 14761])).
% 2.74/2.98 tff(14882,plain,
% 2.74/2.98 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14679, 3, 2])).
% 2.74/2.98 tff(14883,plain,
% 2.74/2.98 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[444, 14879, 14882])).
% 2.74/2.98 tff(14884,plain,
% 2.74/2.98 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[452, 14883])).
% 2.74/2.98 tff(14885,plain,
% 2.74/2.98 (b(s(s(s(s(elem!1)))), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1154, 14879, 14751])).
% 2.74/2.98 tff(14886,plain,
% 2.74/2.98 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[7433, 14758, 14752, 14756, 11429])).
% 2.74/2.98 tff(14887,plain,
% 2.74/2.98 (r(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[13323, 14886])).
% 2.74/2.98 tff(14888,plain,
% 2.74/2.98 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[349, 14879])).
% 2.74/2.98 tff(14889,plain,
% 2.74/2.98 (s(s(s(s(elem!1)))) = elem!1),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1734, 14888])).
% 2.74/2.98 tff(14890,plain,
% 2.74/2.98 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[2161, 14879, 14772])).
% 2.74/2.98 tff(14891,plain,
% 2.74/2.98 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[336, 14890])).
% 2.74/2.98 tff(14892,plain,
% 2.74/2.98 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14472, 155, 309, 1170, 10481])).
% 2.74/2.98 tff(14893,plain,
% 2.74/2.98 (~r(s(s(s(s(z)))), elem!1)),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[14892, 4152])).
% 2.74/2.98 tff(14894,plain,
% 2.74/2.98 (b(s(s(s(s(z)))), elem!1)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[2873, 14893, 4150])).
% 2.74/2.98 tff(14895,plain,
% 2.74/2.98 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[14894, 4149])).
% 2.74/2.98 tff(14896,assumption,(~(s(s(s(s(z)))) = s(z))), introduced(assumption)).
% 2.74/2.98 tff(14897,plain,
% 2.74/2.98 (b(s(s(s(s(z)))), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[2807, 10482, 14896])).
% 2.74/2.98 tff(14898,plain,
% 2.74/2.98 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[13343, 97, 255, 513, 14897])).
% 2.74/2.98 tff(14899,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14898, 14895])).
% 2.74/2.98 tff(14900,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (s(s(s(s(z)))) = s(z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(14901,plain,
% 2.74/2.98 ((~r(s(s(s(s(z)))), s(s(z)))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14900, 2795])).
% 2.74/2.98 tff(14902,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14901, 14891, 14889, 3, 14887, 14885, 2, 14884, 14881, 14880])).
% 2.74/2.98 tff(14903,plain,((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(14904,plain,
% 2.74/2.98 (~r(s(z), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14903, 2, 1])).
% 2.74/2.98 tff(14905,plain,
% 2.74/2.98 (b(s(z), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[548, 14904])).
% 2.74/2.98 tff(14906,plain,
% 2.74/2.98 (~b(s(z), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[13733, 204, 2, 14905])).
% 2.74/2.98 tff(14907,plain,
% 2.74/2.98 (r(s(z), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[568, 14906])).
% 2.74/2.98 tff(14908,plain,
% 2.74/2.98 (~r(s(s(z)), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[966, 155, 11419, 14907, 2])).
% 2.74/2.98 tff(14909,plain,
% 2.74/2.98 (b(s(s(z)), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[625, 14908])).
% 2.74/2.98 tff(14910,plain,
% 2.74/2.98 (~b(s(s(s(z))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1339, 1330, 204, 14909])).
% 2.74/2.98 tff(14911,plain,
% 2.74/2.98 (r(s(s(s(z))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[421, 14910])).
% 2.74/2.98 tff(14912,plain,
% 2.74/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(14913,plain,
% 2.74/2.98 (((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~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(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(14914,plain,
% 2.74/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[14913])).
% 2.74/2.98 tff(14915,plain,
% 2.74/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[14914, 14912])).
% 2.74/2.98 tff(14916,plain,
% 2.74/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(14917,plain,
% 2.74/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[14916, 14915])).
% 2.74/2.98 tff(14918,plain,
% 2.74/2.98 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14917, 155, 125, 2, 14749, 14911])).
% 2.74/2.98 tff(14919,plain,
% 2.74/2.98 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[2687, 14918, 4228])).
% 2.74/2.98 tff(14920,plain,
% 2.74/2.98 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[4557, 97, 14660, 204, 14909])).
% 2.74/2.98 tff(14921,plain,
% 2.74/2.98 (r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[143, 14920])).
% 2.74/2.98 tff(14922,plain,
% 2.74/2.98 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[4382, 155, 14749, 14921, 14911])).
% 2.74/2.98 tff(14923,plain,
% 2.74/2.98 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[3089, 14922, 1])).
% 2.74/2.98 tff(14924,plain,
% 2.74/2.98 (((~![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(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(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(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(14925,plain,
% 2.74/2.98 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(14926,plain,
% 2.74/2.98 (((~![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(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(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))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[14925])).
% 2.74/2.98 tff(14927,plain,
% 2.74/2.98 (((~![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(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(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))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[14926, 14924])).
% 2.74/2.98 tff(14928,plain,
% 2.74/2.98 ((~![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(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(14929,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[14928, 14927])).
% 2.74/2.98 tff(14930,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14929, 97, 14660, 1330, 14923, 14919])).
% 2.74/2.98 tff(14931,plain,((~b(z, s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(14932,plain,
% 2.74/2.98 (~b(z, s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14931, 204, 125, 2, 1])).
% 2.74/2.98 tff(14933,plain,
% 2.74/2.98 (r(z, s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1318, 14932])).
% 2.74/2.98 tff(14934,plain,
% 2.74/2.98 (~b(s(s(s(z))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[11509, 14933, 14905, 14909])).
% 2.74/2.98 tff(14935,plain,
% 2.74/2.98 (r(s(s(s(z))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[421, 14934])).
% 2.74/2.98 tff(14936,plain,
% 2.74/2.98 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14917, 155, 125, 2, 14749, 14935])).
% 2.74/2.98 tff(14937,plain,
% 2.74/2.98 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[2687, 14936, 4228])).
% 2.74/2.98 tff(14938,plain,
% 2.74/2.98 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[4382, 155, 14749, 14921, 14935])).
% 2.74/2.98 tff(14939,plain,
% 2.74/2.98 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[3089, 14938, 1])).
% 2.74/2.98 tff(14940,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[4777, 97, 14660, 204, 1216, 1702])).
% 2.74/2.98 tff(14941,plain,((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(14942,plain,
% 2.74/2.98 (~b(s(s(s(z))), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14941, 204, 14939])).
% 2.74/2.98 tff(14943,plain,
% 2.74/2.98 (r(s(s(s(z))), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[402, 14942])).
% 2.74/2.98 tff(14944,plain,
% 2.74/2.98 (~r(s(z), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1308, 14943, 14907, 14933])).
% 2.74/2.98 tff(14945,plain,
% 2.74/2.98 (b(s(z), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[253, 14944])).
% 2.74/2.98 tff(14946,plain,
% 2.74/2.98 (~r(s(z), s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1273, 14921, 2, 125])).
% 2.74/2.98 tff(14947,plain,
% 2.74/2.98 (b(s(z), s(s(s(elem!1))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[181, 14946])).
% 2.74/2.98 tff(14948,plain,
% 2.74/2.98 (((~![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(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(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(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(14949,plain,
% 2.74/2.98 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(14950,plain,
% 2.74/2.98 (((~![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(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[14949])).
% 2.74/2.98 tff(14951,plain,
% 2.74/2.98 (((~![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(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[14950, 14948])).
% 2.74/2.98 tff(14952,plain,
% 2.74/2.98 ((~![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(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(14953,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[14952, 14951])).
% 2.74/2.98 tff(14954,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14953, 97, 14947, 14945, 14939, 14937])).
% 2.74/2.98 tff(14955,plain,((~b(z, s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(14956,plain,
% 2.74/2.98 (~b(z, s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14955, 125, 1, 2])).
% 2.74/2.98 tff(14957,plain,
% 2.74/2.98 (r(z, s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[222, 14956])).
% 2.74/2.98 tff(14958,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[11652, 155, 11419, 226, 2, 1300, 1960])).
% 2.74/2.98 tff(14959,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(14960,plain,
% 2.74/2.98 (~r(z, s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14959, 1960, 2, 14957])).
% 2.74/2.98 tff(14961,plain,
% 2.74/2.98 (b(z, s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[1318, 14960])).
% 2.74/2.98 tff(14962,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[966, 155, 11419, 81, 645, 2])).
% 2.74/2.98 tff(14963,plain,((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(14964,plain,
% 2.74/2.98 (~r(s(z), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14963, 645, 2])).
% 2.74/2.98 tff(14965,plain,
% 2.74/2.98 (b(s(z), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[568, 14964])).
% 2.74/2.98 tff(14966,plain,
% 2.74/2.98 (~r(s(s(s(z))), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[6467, 1960, 226, 645])).
% 2.74/2.98 tff(14967,plain,
% 2.74/2.98 (b(s(s(s(z))), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[402, 14966])).
% 2.74/2.98 tff(14968,plain,
% 2.74/2.98 (~r(z, s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[14959, 1960, 2, 226])).
% 2.74/2.99 tff(14969,plain,
% 2.74/2.99 (b(z, s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1318, 14968])).
% 2.74/2.99 tff(14970,plain,
% 2.74/2.99 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(14971,plain,
% 2.74/2.99 (((~![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(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[14970])).
% 2.74/2.99 tff(14972,plain,
% 2.74/2.99 (((~![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(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.99 inference(transitivity,[status(thm)],[14971, 5717])).
% 2.74/2.99 tff(14973,plain,
% 2.74/2.99 ((~![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(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(14974,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[14973, 14972])).
% 2.74/2.99 tff(14975,plain,
% 2.74/2.99 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[14974, 97, 14660, 14969, 14967])).
% 2.74/2.99 tff(14976,plain,
% 2.74/2.99 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[14917, 155, 125, 2, 145, 1960])).
% 2.74/2.99 tff(14977,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[2687, 14976, 14975, 2466])).
% 2.74/2.99 tff(14978,plain,((~r(s(s(s(z))), s(s(z)))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(14979,plain,
% 2.74/2.99 (~r(s(s(s(z))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[14978, 645, 125, 2, 145, 226, 2466])).
% 2.74/2.99 tff(14980,plain,
% 2.74/2.99 (b(s(s(s(z))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[421, 14979])).
% 2.74/2.99 tff(14981,plain,
% 2.74/2.99 ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[7847, 14660])).
% 2.74/2.99 tff(14982,plain,
% 2.74/2.99 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[14981, 1330, 1331])).
% 2.74/2.99 tff(14983,plain,
% 2.74/2.99 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[2687, 14982, 2466])).
% 2.74/2.99 tff(14984,plain,
% 2.74/2.99 (~b(s(z), s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[7835, 1330, 1331, 14965])).
% 2.74/2.99 tff(14985,plain,
% 2.74/2.99 (r(s(z), s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[253, 14984])).
% 2.74/2.99 tff(14986,plain,
% 2.74/2.99 (~r(s(s(z)), s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[13230, 338, 2, 645])).
% 2.74/2.99 tff(14987,plain,
% 2.74/2.99 (b(s(s(z)), s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[437, 14986])).
% 2.74/2.99 tff(14988,plain,
% 2.74/2.99 (~r(s(s(s(z))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[2638, 338, 125, 2630])).
% 2.74/2.99 tff(14989,plain,
% 2.74/2.99 (b(s(s(s(z))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1358, 14988])).
% 2.74/2.99 tff(14990,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[3585, 14989, 14987, 535, 1331])).
% 2.74/2.99 tff(14991,plain,((~r(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(14992,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[14991, 14985, 14983, 1331, 125, 535, 2, 645])).
% 2.74/2.99 tff(14993,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (s(s(s(elem!1))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(14994,plain,
% 2.74/2.99 (~b(z, s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[14993, 14980, 125, 535, 2, 645, 2466])).
% 2.74/2.99 tff(14995,plain,
% 2.74/2.99 (r(z, s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1318, 14994])).
% 2.74/2.99 tff(14996,plain,
% 2.74/2.99 (~r(s(s(s(z))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11471, 14995, 226, 535, 14980])).
% 2.74/2.99 tff(14997,plain,
% 2.74/2.99 (b(s(s(s(z))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1358, 14996])).
% 2.74/2.99 tff(14998,plain,
% 2.74/2.99 ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[3625, 11419])).
% 2.74/2.99 tff(14999,plain,
% 2.74/2.99 (~b(z, s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[14998, 14997, 535, 14980, 14965, 645])).
% 2.74/2.99 tff(15000,plain,
% 2.74/2.99 (r(z, s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[590, 14999])).
% 2.74/2.99 tff(15001,plain,
% 2.74/2.99 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11802, 15000, 125, 226])).
% 2.74/2.99 tff(15002,plain,
% 2.74/2.99 (~r(s(s(s(z))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[8978, 1331, 2, 535, 125, 570, 645, 2466])).
% 2.74/2.99 tff(15003,plain,
% 2.74/2.99 (b(s(s(s(z))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1358, 15002])).
% 2.74/2.99 tff(15004,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11499, 97, 535, 15003, 1331, 127])).
% 2.74/2.99 tff(15005,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (s(s(s(elem!1))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(15006,plain,
% 2.74/2.99 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15005, 15000, 535, 2, 125, 14980, 645, 2466])).
% 2.74/2.99 tff(15007,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[143, 15006, 15001])).
% 2.74/2.99 tff(15008,plain,((~r(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(15009,plain,
% 2.74/2.99 (~r(s(s(z)), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15008, 125, 2, 14905, 4228, 14957, 14749])).
% 2.74/2.99 tff(15010,plain,
% 2.74/2.99 (b(s(s(z)), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[625, 15009])).
% 2.74/2.99 tff(15011,plain,
% 2.74/2.99 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[4547, 97, 14660, 15010, 14961])).
% 2.74/2.99 tff(15012,plain,
% 2.74/2.99 (r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[143, 15011])).
% 2.74/2.99 tff(15013,plain,
% 2.74/2.99 (~b(s(z), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[2972, 14961, 14905, 15010])).
% 2.74/2.99 tff(15014,plain,
% 2.74/2.99 (r(s(z), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[568, 15013])).
% 2.74/2.99 tff(15015,plain,
% 2.74/2.99 (~r(s(z), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1273, 15012, 2, 125])).
% 2.74/2.99 tff(15016,plain,
% 2.74/2.99 (b(s(z), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[181, 15015])).
% 2.74/2.99 tff(15017,plain,
% 2.74/2.99 (~r(z, s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11802, 15012, 125, 14957])).
% 2.74/2.99 tff(15018,plain,
% 2.74/2.99 (b(z, s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[590, 15017])).
% 2.74/2.99 tff(15019,plain,
% 2.74/2.99 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1678, 53, 1, 5373])).
% 2.74/2.99 tff(15020,plain,
% 2.74/2.99 (~b(s(s(s(z))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[4352, 97, 193, 126, 15019])).
% 2.74/2.99 tff(15021,plain,
% 2.74/2.99 (r(s(s(s(z))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1358, 15020])).
% 2.74/2.99 tff(15022,plain,
% 2.74/2.99 (~b(s(s(s(z))), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[4360, 97, 126, 124, 15019])).
% 2.74/2.99 tff(15023,plain,
% 2.74/2.99 (r(s(s(s(z))), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[402, 15022])).
% 2.74/2.99 tff(15024,plain,
% 2.74/2.99 ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[4290, 155, 226, 81, 1960])).
% 2.74/2.99 tff(15025,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15024, 15023, 15021])).
% 2.74/2.99 tff(15026,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(15027,plain,
% 2.74/2.99 ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15026, 14660])).
% 2.74/2.99 tff(15028,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15027, 15018, 15016, 14749, 14957, 15014, 1960, 1, 15012])).
% 2.74/2.99 tff(15029,plain,((~r(s(s(s(z))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(15030,plain,
% 2.74/2.99 (~r(s(s(s(z))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15029, 125, 1, 2])).
% 2.74/2.99 tff(15031,plain,
% 2.74/2.99 (b(s(s(s(z))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[421, 15030])).
% 2.74/2.99 tff(15032,plain,
% 2.74/2.99 (~r(z, s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11509, 15031, 14905, 15010])).
% 2.74/2.99 tff(15033,plain,
% 2.74/2.99 (b(z, s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1318, 15032])).
% 2.74/2.99 tff(15034,plain,
% 2.74/2.99 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[14981, 15033, 15031])).
% 2.74/2.99 tff(15035,plain,
% 2.74/2.99 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[2687, 15034, 4228])).
% 2.74/2.99 tff(15036,plain,
% 2.74/2.99 (~b(s(s(s(z))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[8529, 97, 15010, 14905, 15031])).
% 2.74/2.99 tff(15037,plain,
% 2.74/2.99 (r(s(s(s(z))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1358, 15036])).
% 2.74/2.99 tff(15038,plain,
% 2.74/2.99 (~b(s(z), s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[9363, 97, 15010, 14905, 15031])).
% 2.74/2.99 tff(15039,plain,
% 2.74/2.99 (r(s(z), s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[253, 15038])).
% 2.74/2.99 tff(15040,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[2638, 15039, 15037, 125, 15035])).
% 2.74/2.99 tff(15041,plain,((~r(s(s(s(elem!1))), s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(15042,plain,
% 2.74/2.99 (~r(s(s(s(elem!1))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15041, 2, 1])).
% 2.74/2.99 tff(15043,plain,
% 2.74/2.99 (b(s(s(s(elem!1))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[493, 15042])).
% 2.74/2.99 tff(15044,plain,
% 2.74/2.99 (~b(s(s(s(z))), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[14941, 1702, 204])).
% 2.74/2.99 tff(15045,plain,
% 2.74/2.99 (r(s(s(s(z))), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[402, 15044])).
% 2.74/2.99 tff(15046,plain,
% 2.74/2.99 (~b(s(s(s(z))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[14372, 1702, 535, 1139])).
% 2.74/2.99 tff(15047,plain,
% 2.74/2.99 (r(s(s(s(z))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1358, 15046])).
% 2.74/2.99 tff(15048,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[4580, 155, 11419, 81, 15047, 15045])).
% 2.74/2.99 tff(15049,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(15050,plain,
% 2.74/2.99 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15049, 14907, 204, 14905, 15043])).
% 2.74/2.99 tff(15051,plain,
% 2.74/2.99 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[3089, 15050, 1])).
% 2.74/2.99 tff(15052,plain,
% 2.74/2.99 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[4557, 97, 14660, 204, 83])).
% 2.74/2.99 tff(15053,plain,
% 2.74/2.99 (r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[143, 15052])).
% 2.74/2.99 tff(15054,plain,
% 2.74/2.99 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), 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))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(15055,plain,
% 2.74/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), 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)))))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[15054])).
% 2.74/2.99 tff(15056,plain,
% 2.74/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), 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))))))),
% 2.74/2.99 inference(transitivity,[status(thm)],[15055, 4377])).
% 2.74/2.99 tff(15057,plain,
% 2.74/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(15058,plain,
% 2.74/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[15057, 15056])).
% 2.74/2.99 tff(15059,plain,
% 2.74/2.99 (~r(s(s(s(z))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15058, 155, 14749, 15053, 15051])).
% 2.74/2.99 tff(15060,plain,
% 2.74/2.99 (b(s(s(s(z))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[421, 15059])).
% 2.74/2.99 tff(15061,plain,
% 2.74/2.99 (~r(z, s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11509, 15060, 14905, 83])).
% 2.74/2.99 tff(15062,plain,
% 2.74/2.99 (~b(z, s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1339, 15060, 204, 83])).
% 2.74/2.99 tff(15063,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1318, 15062, 15061])).
% 2.74/2.99 tff(15064,plain,((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(15065,plain,
% 2.74/2.99 (~b(z, s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15064, 83, 1, 2])).
% 2.74/2.99 tff(15066,plain,
% 2.74/2.99 (r(z, s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[222, 15065])).
% 2.74/2.99 tff(15067,plain,
% 2.74/2.99 (~b(z, s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[2972, 550, 535, 83])).
% 2.74/2.99 tff(15068,plain,
% 2.74/2.99 (r(z, s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1318, 15067])).
% 2.74/2.99 tff(15069,plain,
% 2.74/2.99 (~b(s(s(s(z))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[14208, 550, 535, 83])).
% 2.74/2.99 tff(15070,plain,
% 2.74/2.99 (r(s(s(s(z))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[421, 15069])).
% 2.74/2.99 tff(15071,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[14959, 15070, 15068, 2, 226])).
% 2.74/2.99 tff(15072,plain,((~b(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(15073,plain,
% 2.74/2.99 (~b(s(z), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15072, 15066, 2, 14905, 83])).
% 2.74/2.99 tff(15074,plain,
% 2.74/2.99 (r(s(z), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[568, 15073])).
% 2.74/2.99 tff(15075,plain,
% 2.74/2.99 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[4547, 97, 14660, 83, 1330])).
% 2.74/2.99 tff(15076,plain,
% 2.74/2.99 (r(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[143, 15075])).
% 2.74/2.99 tff(15077,plain,
% 2.74/2.99 (~r(z, s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[5182, 155, 226, 145, 15076])).
% 2.74/2.99 tff(15078,plain,
% 2.74/2.99 (b(z, s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[590, 15077])).
% 2.74/2.99 tff(15079,plain,
% 2.74/2.99 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[14297, 15078, 1139, 1330])).
% 2.74/2.99 tff(15080,plain,
% 2.74/2.99 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[3089, 15079, 1])).
% 2.74/2.99 tff(15081,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[4382, 155, 145, 224, 1960, 4252])).
% 2.74/2.99 tff(15082,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(15083,plain,
% 2.74/2.99 (~r(s(s(s(z))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15082, 15076, 145, 15080])).
% 2.74/2.99 tff(15084,plain,
% 2.74/2.99 (b(s(s(s(z))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[421, 15083])).
% 2.74/2.99 tff(15085,plain,
% 2.74/2.99 (~b(s(s(s(z))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11501, 15084, 535, 1139, 1])).
% 2.74/2.99 tff(15086,plain,
% 2.74/2.99 (r(s(s(s(z))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1358, 15085])).
% 2.74/2.99 tff(15087,plain,
% 2.74/2.99 (~r(s(s(s(z))), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[4580, 155, 11419, 81, 15086])).
% 2.74/2.99 tff(15088,plain,
% 2.74/2.99 (b(s(s(s(z))), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[402, 15087])).
% 2.74/2.99 tff(15089,plain,
% 2.74/2.99 (((~![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(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(15090,plain,
% 2.74/2.99 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~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(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(15091,plain,
% 2.74/2.99 (((~![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(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~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(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[15090])).
% 2.74/2.99 tff(15092,plain,
% 2.74/2.99 (((~![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(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~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(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 2.74/2.99 inference(transitivity,[status(thm)],[15091, 15089])).
% 2.74/2.99 tff(15093,plain,
% 2.74/2.99 ((~![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(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(15094,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[15093, 15092])).
% 2.74/2.99 tff(15095,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15094, 97, 15078, 83, 15084, 15088])).
% 2.74/2.99 tff(15096,plain,((~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~r(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(15097,plain,
% 2.74/2.99 (~b(z, s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15096, 83, 15074, 14905, 15043, 1, 14749, 15066])).
% 2.74/2.99 tff(15098,plain,
% 2.74/2.99 (r(z, s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1318, 15097])).
% 2.74/2.99 tff(15099,plain,
% 2.74/2.99 (~r(s(s(s(z))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[14959, 15098, 2, 15066])).
% 2.74/2.99 tff(15100,plain,
% 2.74/2.99 (~b(s(s(s(z))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11509, 15098, 14905, 83])).
% 2.74/2.99 tff(15101,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[421, 15100, 15099])).
% 2.74/2.99 tff(15102,plain,((~b(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(15103,plain,
% 2.74/2.99 (~b(s(s(z)), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15102, 2, 1])).
% 2.74/2.99 tff(15104,plain,
% 2.74/2.99 (r(s(s(z)), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[625, 15103])).
% 2.74/2.99 tff(15105,plain,
% 2.74/2.99 (~r(s(z), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[14963, 15104, 2])).
% 2.74/2.99 tff(15106,plain,
% 2.74/2.99 (b(s(z), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[568, 15105])).
% 2.74/2.99 tff(15107,plain,
% 2.74/2.99 (~b(z, s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[13733, 15106, 2, 14905])).
% 2.74/2.99 tff(15108,plain,
% 2.74/2.99 (r(z, s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[222, 15107])).
% 2.74/2.99 tff(15109,plain,
% 2.74/2.99 (~b(z, s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[14724, 15106, 15043])).
% 2.74/2.99 tff(15110,plain,
% 2.74/2.99 (r(z, s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[590, 15109])).
% 2.74/2.99 tff(15111,plain,
% 2.74/2.99 (~r(s(z), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[14728, 15110, 15108, 2])).
% 2.74/2.99 tff(15112,plain,
% 2.74/2.99 (b(s(z), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[181, 15111])).
% 2.74/2.99 tff(15113,plain,
% 2.74/2.99 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11339, 15112, 14905, 15043])).
% 2.74/2.99 tff(15114,plain,
% 2.74/2.99 (~r(s(s(s(elem!1))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[4539, 8546, 570, 729, 224])).
% 2.74/2.99 tff(15115,plain,
% 2.74/2.99 (~b(s(s(s(elem!1))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[5184, 8546, 570, 255, 87])).
% 2.74/2.99 tff(15116,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[493, 15115, 15114])).
% 2.74/2.99 tff(15117,plain,((~b(s(s(z)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(15118,plain,
% 2.74/2.99 (~b(s(s(z)), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15117, 255, 570, 729, 2105, 550, 535])).
% 2.74/2.99 tff(15119,plain,
% 2.74/2.99 (r(s(s(z)), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[122, 15118])).
% 2.74/2.99 tff(15120,plain,
% 2.74/2.99 (~b(s(s(z)), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[15117, 255, 570, 729, 224, 550, 535])).
% 2.74/2.99 tff(15121,plain,
% 2.74/3.00 (r(s(s(z)), s(z))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[122, 15120])).
% 2.74/3.00 tff(15122,plain,
% 2.74/3.00 (~b(s(s(z)), z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[13721, 204, 550, 535])).
% 2.74/3.00 tff(15123,plain,
% 2.74/3.00 (r(s(s(z)), z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[625, 15122])).
% 2.74/3.00 tff(15124,plain,
% 2.74/3.00 (~r(s(s(s(elem!1))), s(z))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[2253, 15123, 570, 15121, 224])).
% 2.74/3.00 tff(15125,plain,
% 2.74/3.00 (b(s(s(s(elem!1))), s(z))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[493, 15124])).
% 2.74/3.00 tff(15126,plain,
% 2.74/3.00 (((~![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), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(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(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15127,plain,
% 2.74/3.00 (((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(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(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15128,plain,
% 2.74/3.00 (((~![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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(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(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z))))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[15127])).
% 2.74/3.00 tff(15129,plain,
% 2.74/3.00 (((~![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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(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(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[15128, 15126])).
% 2.74/3.00 tff(15130,plain,
% 2.74/3.00 ((~![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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(15131,plain,
% 2.74/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15130, 15129])).
% 2.74/3.00 tff(15132,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15131, 97, 550, 339, 204, 535])).
% 2.74/3.00 tff(15133,plain,((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(15134,plain,
% 2.74/3.00 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15133, 204, 550, 535])).
% 2.74/3.00 tff(15135,plain,
% 2.74/3.00 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[336, 15134])).
% 2.74/3.00 tff(15136,plain,
% 2.74/3.00 (~r(s(s(s(elem!1))), s(z))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[4539, 226, 570, 729, 224])).
% 2.74/3.00 tff(15137,plain,
% 2.74/3.00 (b(s(s(s(elem!1))), s(z))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[493, 15136])).
% 2.74/3.00 tff(15138,plain,
% 2.74/3.00 (~b(s(s(z)), s(z))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[5184, 15137, 570, 255, 226])).
% 2.74/3.00 tff(15139,plain,
% 2.74/3.00 (r(s(s(z)), s(z))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[122, 15138])).
% 2.74/3.00 tff(15140,plain,
% 2.74/3.00 (~b(s(s(z)), s(s(s(z))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[3067, 441, 255, 535])).
% 2.74/3.00 tff(15141,plain,
% 2.74/3.00 (r(s(s(z)), s(s(s(z))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[437, 15140])).
% 2.74/3.00 tff(15142,plain,
% 2.74/3.00 (~r(s(s(s(z))), z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[3595, 645, 729, 15139, 15141])).
% 2.74/3.00 tff(15143,plain,
% 2.74/3.00 (b(s(s(s(z))), z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[402, 15142])).
% 2.74/3.00 tff(15144,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[995, 155, 570, 488, 309, 645, 224])).
% 2.74/3.00 tff(15145,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(15146,plain,
% 2.74/3.00 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15145, 645, 309, 570, 224])).
% 2.74/3.00 tff(15147,plain,
% 2.74/3.00 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[486, 15146, 2718])).
% 2.74/3.00 tff(15148,plain,
% 2.74/3.00 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[349, 15147])).
% 2.74/3.00 tff(15149,plain,
% 2.74/3.00 (s(s(s(s(elem!1)))) = elem!1),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1734, 15148])).
% 2.74/3.00 tff(15150,plain,
% 2.74/3.00 (elem!1 = s(s(s(s(elem!1))))),
% 2.74/3.00 inference(symmetry,[status(thm)],[15149])).
% 2.74/3.00 tff(15151,plain,
% 2.74/3.00 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[15150])).
% 2.74/3.00 tff(15152,plain,
% 2.74/3.00 (b(s(s(s(s(elem!1)))), s(z))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1154, 15147, 15137])).
% 2.74/3.00 tff(15153,plain,
% 2.74/3.00 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.74/3.00 inference(symmetry,[status(thm)],[15148])).
% 2.74/3.00 tff(15154,plain,
% 2.74/3.00 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[15153])).
% 2.74/3.00 tff(15155,plain,
% 2.74/3.00 (s(elem!1) = s(s(s(s(elem!1))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[30, 15154, 270, 15147])).
% 2.74/3.00 tff(15156,plain,
% 2.74/3.00 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[15155])).
% 2.74/3.00 tff(15157,plain,
% 2.74/3.00 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(elem!1))),
% 2.74/3.00 inference(symmetry,[status(thm)],[15156])).
% 2.74/3.00 tff(15158,plain,
% 2.74/3.00 (r(s(s(z)), s(elem!1))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[309, 15157])).
% 2.74/3.00 tff(15159,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 2.74/3.00 tff(15160,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15161,plain,
% 2.74/3.00 (((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15162,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1)))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[15161])).
% 2.74/3.00 tff(15163,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[15162, 15160])).
% 2.74/3.00 tff(15164,plain,
% 2.74/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(15165,plain,
% 2.74/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1)))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15164, 15163])).
% 2.74/3.00 tff(15166,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15165, 155, 729, 645, 2, 1433, 15159])).
% 2.74/3.00 tff(15167,plain,((~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(15168,plain,
% 2.74/3.00 (~r(s(elem!1), z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15167, 15158, 645, 15139, 729])).
% 2.74/3.00 tff(15169,plain,
% 2.74/3.00 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.74/3.00 inference(symmetry,[status(thm)],[350])).
% 2.74/3.00 tff(15170,plain,
% 2.74/3.00 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[15169])).
% 2.74/3.00 tff(15171,plain,
% 2.74/3.00 (s(elem!1) = s(s(s(s(elem!1))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[30, 15170, 270, 340])).
% 2.74/3.00 tff(15172,plain,
% 2.74/3.00 (r(s(elem!1), z) <=> r(s(s(s(s(elem!1)))), z)),
% 2.74/3.00 inference(monotonicity,[status(thm)],[15171])).
% 2.74/3.00 tff(15173,plain,
% 2.74/3.00 (r(s(s(s(s(elem!1)))), z) <=> r(s(elem!1), z)),
% 2.74/3.00 inference(symmetry,[status(thm)],[15172])).
% 2.74/3.00 tff(15174,plain,
% 2.74/3.00 (r(s(elem!1), z)),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[824, 15173])).
% 2.74/3.00 tff(15175,assumption,(~r(s(elem!1), z)), introduced(assumption)).
% 2.74/3.00 tff(15176,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15175, 15174])).
% 2.74/3.00 tff(15177,plain,((~r(s(s(s(s(elem!1)))), z)) | r(s(elem!1), z) | (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(15178,plain,
% 2.74/3.00 (~r(s(s(s(s(elem!1)))), z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15177, 15168, 15147])).
% 2.74/3.00 tff(15179,plain,
% 2.74/3.00 (b(s(s(s(s(elem!1)))), z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[842, 15178])).
% 2.74/3.00 tff(15180,assumption,(b(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.74/3.00 tff(15181,plain,
% 2.74/3.00 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[5197, 97, 255, 513])).
% 2.74/3.00 tff(15182,plain,
% 2.74/3.00 (~b(s(s(s(z))), s(z))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15181, 15180])).
% 2.74/3.00 tff(15183,plain,
% 2.74/3.00 (r(s(s(s(z))), s(z))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1358, 15182])).
% 2.74/3.00 tff(15184,plain,
% 2.74/3.00 ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z)))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1773, 97, 255, 513])).
% 2.74/3.00 tff(15185,plain,
% 2.74/3.00 (~b(s(z), s(s(s(z))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15184, 15180])).
% 2.74/3.00 tff(15186,plain,
% 2.74/3.00 (r(s(z), s(s(s(z))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[253, 15185])).
% 2.74/3.00 tff(15187,plain,
% 2.74/3.00 (~r(z, s(s(s(z))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[5909, 155, 729, 15186, 15183])).
% 2.74/3.00 tff(15188,plain,
% 2.74/3.00 (b(z, s(s(s(z))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1318, 15187])).
% 2.74/3.00 tff(15189,plain,
% 2.74/3.00 (~r(s(s(z)), s(s(s(z))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[2938, 155, 2, 15186, 15183])).
% 2.74/3.00 tff(15190,plain,
% 2.74/3.00 (b(s(s(z)), s(s(s(z))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[437, 15189])).
% 2.74/3.00 tff(15191,plain,
% 2.74/3.00 (((~![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(z)))) | (~b(s(s(s(s(elem!1)))), 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(s(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(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15192,plain,
% 2.74/3.00 (((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(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)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15193,plain,
% 2.74/3.00 (((~![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(s(s(z))))) | (~b(z, s(s(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)))), 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(z)))) | (~b(s(s(s(s(elem!1)))), 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(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[15192])).
% 2.74/3.00 tff(15194,plain,
% 2.74/3.00 (((~![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(s(s(z))))) | (~b(z, s(s(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)))), 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(z)))) | (~b(s(s(s(s(elem!1)))), 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(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[15193, 15191])).
% 2.74/3.00 tff(15195,plain,
% 2.74/3.00 ((~![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(s(s(z))))) | (~b(z, s(s(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)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(15196,plain,
% 2.74/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15195, 15194])).
% 2.74/3.00 tff(15197,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15196, 97, 255, 876, 441, 535, 15190, 15188])).
% 2.74/3.00 tff(15198,plain,((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(15199,plain,
% 2.74/3.00 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15198, 15179, 15152, 441, 535, 15139, 729, 255])).
% 2.74/3.00 tff(15200,plain,
% 2.74/3.00 (~b(s(s(s(z))), elem!1)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1764, 15199, 15149])).
% 2.74/3.00 tff(15201,plain,
% 2.74/3.00 (~(s(s(s(z))) = elem!1)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1742, 15147])).
% 2.74/3.00 tff(15202,plain,
% 2.74/3.00 (r(s(s(s(z))), elem!1)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1755, 15201, 15200])).
% 2.74/3.00 tff(15203,plain,
% 2.74/3.00 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15202, 15151])).
% 2.74/3.00 tff(15204,plain,
% 2.74/3.00 (r(z, s(s(s(s(elem!1)))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[4141, 15147, 570])).
% 2.74/3.00 tff(15205,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15206,plain,
% 2.74/3.00 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15207,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[15206])).
% 2.74/3.00 tff(15208,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[15207, 15205])).
% 2.74/3.00 tff(15209,plain,
% 2.74/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(15210,plain,
% 2.74/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15209, 15208])).
% 2.74/3.00 tff(15211,plain,
% 2.74/3.00 (~r(z, s(s(s(z))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15210, 155, 15204, 226, 15203, 15141])).
% 2.74/3.00 tff(15212,plain,
% 2.74/3.00 (b(z, s(s(s(z))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1318, 15211])).
% 2.74/3.00 tff(15213,plain,
% 2.74/3.00 (~r(s(z), s(s(s(z))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[3605, 645, 729, 15139, 15141])).
% 2.74/3.00 tff(15214,plain,
% 2.74/3.00 (b(s(z), s(s(s(z))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[253, 15213])).
% 2.74/3.00 tff(15215,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[13240, 97, 550, 15214, 15212, 15143])).
% 2.74/3.00 tff(15216,plain,((~r(s(s(z)), z)) | (~b(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(15217,plain,
% 2.74/3.00 (~r(s(s(z)), z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15216, 441, 729, 226, 550, 535, 255, 309, 570, 2718, 224])).
% 2.74/3.00 tff(15218,plain,
% 2.74/3.00 (b(s(s(z)), z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[625, 15217])).
% 2.74/3.00 tff(15219,plain,
% 2.74/3.00 (((~![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(z)))) | (~b(s(s(z)), 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(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15220,plain,
% 2.74/3.00 (((~b(s(s(z)), z)) | (~b(s(s(z)), 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(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15221,plain,
% 2.74/3.00 (((~![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)), z)) | (~b(s(s(z)), 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(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[15220])).
% 2.74/3.00 tff(15222,plain,
% 2.74/3.00 (((~![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)), z)) | (~b(s(s(z)), 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(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[15221, 15219])).
% 2.74/3.00 tff(15223,plain,
% 2.74/3.00 ((~![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)), z)) | (~b(s(s(z)), 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)))))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(15224,plain,
% 2.74/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[15223, 15222])).
% 2.74/3.00 tff(15225,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15224, 97, 255, 15218, 441, 535])).
% 2.74/3.00 tff(15226,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~b(s(z), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(15227,plain,
% 2.74/3.00 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[15226, 226, 535, 729, 255, 550, 309, 570, 2718, 224])).
% 2.74/3.00 tff(15228,plain,
% 2.74/3.00 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[452, 15227])).
% 2.74/3.00 tff(15229,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(15230,plain,
% 2.74/3.00 (((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(15231,plain,
% 2.74/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z))))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[15230])).
% 2.74/3.01 tff(15232,plain,
% 2.74/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.74/3.01 inference(transitivity,[status(thm)],[15231, 15229])).
% 2.74/3.01 tff(15233,plain,
% 2.74/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.74/3.01 inference(quant_inst,[status(thm)],[])).
% 2.74/3.01 tff(15234,plain,
% 2.74/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z))))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[15233, 15232])).
% 2.74/3.01 tff(15235,plain,
% 2.74/3.01 (~r(z, s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15234, 155, 729, 226, 15228, 15139])).
% 2.74/3.01 tff(15236,plain,
% 2.74/3.01 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[4141, 15235, 570])).
% 2.74/3.01 tff(15237,plain,
% 2.74/3.01 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[486, 15236, 2718])).
% 2.74/3.01 tff(15238,plain,
% 2.74/3.01 (~r(s(s(z)), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15145, 15237, 309, 570, 224])).
% 2.74/3.01 tff(15239,plain,
% 2.74/3.01 (b(s(s(z)), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[625, 15238])).
% 2.74/3.01 tff(15240,plain,
% 2.74/3.01 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1044, 155, 15237, 309, 15228])).
% 2.74/3.01 tff(15241,plain,
% 2.74/3.01 (b(s(s(s(elem!1))), s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[58, 15240])).
% 2.74/3.01 tff(15242,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[11642, 97, 15137, 15241, 15239, 535])).
% 2.74/3.01 tff(15243,plain,((~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(15244,plain,
% 2.74/3.01 (~r(z, s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15243, 309, 535, 570, 224, 2718, 729, 255, 550])).
% 2.74/3.01 tff(15245,plain,
% 2.74/3.01 (b(z, s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[222, 15244])).
% 2.74/3.01 tff(15246,plain,
% 2.74/3.01 (~b(s(s(z)), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[13721, 15245, 550, 535])).
% 2.74/3.01 tff(15247,plain,
% 2.74/3.01 (r(s(s(z)), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[625, 15246])).
% 2.74/3.01 tff(15248,plain,
% 2.74/3.01 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15145, 15247, 309, 570, 224])).
% 2.74/3.01 tff(15249,plain,
% 2.74/3.01 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[486, 15248, 2718])).
% 2.74/3.01 tff(15250,plain,
% 2.74/3.01 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.74/3.01 inference(monotonicity,[status(thm)],[15249])).
% 2.74/3.01 tff(15251,plain,
% 2.74/3.01 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(elem!1))), z)),
% 2.74/3.01 inference(symmetry,[status(thm)],[15250])).
% 2.74/3.01 tff(15252,plain,
% 2.74/3.01 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[349, 15249])).
% 2.74/3.01 tff(15253,plain,
% 2.74/3.01 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.74/3.01 inference(symmetry,[status(thm)],[15252])).
% 2.74/3.01 tff(15254,plain,
% 2.74/3.01 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[15253])).
% 2.74/3.01 tff(15255,plain,
% 2.74/3.01 (s(elem!1) = s(s(s(s(elem!1))))),
% 2.74/3.01 inference(transitivity,[status(thm)],[30, 15254, 270, 15249])).
% 2.74/3.01 tff(15256,plain,
% 2.74/3.01 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[15255])).
% 2.74/3.01 tff(15257,plain,
% 2.74/3.01 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(elem!1))),
% 2.74/3.01 inference(symmetry,[status(thm)],[15256])).
% 2.74/3.01 tff(15258,plain,
% 2.74/3.01 (r(s(s(z)), s(elem!1))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[309, 15257])).
% 2.74/3.01 tff(15259,plain,
% 2.74/3.01 (~b(s(s(z)), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3966, 15245, 550, 535])).
% 2.74/3.01 tff(15260,plain,
% 2.74/3.01 (r(s(s(z)), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[122, 15259])).
% 2.74/3.01 tff(15261,plain,
% 2.74/3.01 (~r(s(elem!1), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15167, 15260, 15247, 15258, 729])).
% 2.74/3.01 tff(15262,plain,
% 2.74/3.01 (~r(s(s(s(s(elem!1)))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15177, 15261, 15249])).
% 2.74/3.01 tff(15263,plain,
% 2.74/3.01 (b(s(s(s(s(elem!1)))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[842, 15262])).
% 2.74/3.01 tff(15264,plain,
% 2.74/3.01 (b(s(s(s(elem!1))), z)),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[15263, 15251])).
% 2.74/3.01 tff(15265,plain,
% 2.74/3.01 (~b(s(s(s(elem!1))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[10212, 15264, 550, 15245])).
% 2.74/3.01 tff(15266,plain,
% 2.74/3.01 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[518, 15265, 15249])).
% 2.74/3.01 tff(15267,plain,
% 2.74/3.01 (r(s(s(s(s(elem!1)))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[511, 15266])).
% 2.74/3.01 tff(15268,plain,
% 2.74/3.01 (r(z, s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[4141, 15249, 570])).
% 2.74/3.01 tff(15269,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3040, 155, 15268, 309, 15247, 15260, 15267])).
% 2.74/3.01 tff(15270,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~r(z, s(z))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(15271,plain,
% 2.74/3.01 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15270, 15135, 729, 535, 570, 550, 224, 255])).
% 2.74/3.01 tff(15272,plain,
% 2.74/3.01 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[2129, 473, 535, 1139])).
% 2.74/3.01 tff(15273,plain,
% 2.74/3.01 (r(s(s(s(s(elem!1)))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[511, 15272])).
% 2.74/3.01 tff(15274,plain,
% 2.74/3.01 (~r(s(s(s(s(elem!1)))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3835, 15273, 729, 645, 1170])).
% 2.74/3.01 tff(15275,plain,
% 2.74/3.01 (b(s(s(s(s(elem!1)))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[842, 15274])).
% 2.74/3.01 tff(15276,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[5306, 97, 1139, 255, 473, 15275])).
% 2.74/3.01 tff(15277,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(15278,plain,
% 2.74/3.01 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15277, 15271, 255, 729, 15123, 15125, 535])).
% 2.74/3.01 tff(15279,plain,
% 2.74/3.01 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[452, 15278])).
% 2.74/3.01 tff(15280,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1)))))) | (~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(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(15281,plain,
% 2.74/3.01 (((~b(s(s(s(s(elem!1)))), 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(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(15282,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(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(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[15281])).
% 2.74/3.01 tff(15283,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(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(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.74/3.01 inference(transitivity,[status(thm)],[15282, 15280])).
% 2.74/3.01 tff(15284,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.74/3.01 inference(quant_inst,[status(thm)],[])).
% 2.74/3.01 tff(15285,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[15284, 15283])).
% 2.74/3.01 tff(15286,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15285, 97, 15125, 255, 15271, 15279])).
% 2.74/3.01 tff(15287,plain,((~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(15288,plain,
% 2.74/3.01 (~b(z, s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15287, 255, 729, 535, 570, 550, 2105])).
% 2.74/3.01 tff(15289,plain,
% 2.74/3.01 (r(z, s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[222, 15288])).
% 2.74/3.01 tff(15290,plain,
% 2.74/3.01 (~r(s(s(s(elem!1))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[4539, 15289, 570, 729, 2105])).
% 2.74/3.01 tff(15291,plain,
% 2.74/3.01 (b(s(s(s(elem!1))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[493, 15290])).
% 2.74/3.01 tff(15292,plain,
% 2.74/3.01 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15270, 2718, 729, 535, 570, 550, 2105, 255])).
% 2.74/3.01 tff(15293,plain,
% 2.74/3.01 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[336, 15292])).
% 2.74/3.01 tff(15294,plain,
% 2.74/3.01 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[2161, 15293, 138])).
% 2.74/3.01 tff(15295,plain,
% 2.74/3.01 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[486, 15294, 2718])).
% 2.74/3.01 tff(15296,plain,
% 2.74/3.01 (~r(z, s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[8403, 15295, 15289, 570, 2105])).
% 2.74/3.01 tff(15297,plain,
% 2.74/3.01 (b(z, s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1093, 15296])).
% 2.74/3.01 tff(15298,plain,
% 2.74/3.01 (~b(s(s(s(s(elem!1)))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3812, 15293, 535, 255])).
% 2.74/3.01 tff(15299,plain,
% 2.74/3.01 (r(s(s(s(s(elem!1)))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[842, 15298])).
% 2.74/3.01 tff(15300,plain,
% 2.74/3.01 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3267, 15293, 255, 535])).
% 2.74/3.01 tff(15301,plain,
% 2.74/3.01 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[452, 15300])).
% 2.74/3.01 tff(15302,plain,
% 2.74/3.01 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3278, 15301, 15119, 15289, 15299])).
% 2.74/3.01 tff(15303,plain,
% 2.74/3.01 (b(s(s(s(s(elem!1)))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[511, 15302])).
% 2.74/3.01 tff(15304,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[669, 15303, 15297, 83, 15293])).
% 2.74/3.01 tff(15305,plain,(b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | b(s(s(z)), s(s(s(elem!1)))) | (~r(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(15306,plain,
% 2.74/3.01 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15305, 83, 570, 255, 535, 138, 729, 550])).
% 2.74/3.01 tff(15307,plain,
% 2.74/3.01 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[2129, 15306, 535, 15291])).
% 2.74/3.01 tff(15308,plain,
% 2.74/3.01 (r(s(s(s(s(elem!1)))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[511, 15307])).
% 2.74/3.01 tff(15309,plain,
% 2.74/3.01 (~b(z, s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[11776, 83, 550, 535])).
% 2.74/3.01 tff(15310,plain,
% 2.74/3.01 (r(z, s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1093, 15309])).
% 2.74/3.01 tff(15311,plain,
% 2.74/3.01 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[12838, 15310, 729, 15289, 15308])).
% 2.74/3.01 tff(15312,plain,
% 2.74/3.01 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[336, 15311])).
% 2.74/3.01 tff(15313,plain,
% 2.74/3.01 (~b(s(s(s(s(elem!1)))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3812, 15312, 535, 255])).
% 2.74/3.01 tff(15314,plain,
% 2.74/3.01 (r(s(s(s(s(elem!1)))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[842, 15313])).
% 2.74/3.01 tff(15315,plain,
% 2.74/3.01 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3267, 15312, 255, 535])).
% 2.74/3.01 tff(15316,plain,
% 2.74/3.01 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[452, 15315])).
% 2.74/3.01 tff(15317,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3278, 15316, 15314, 15119, 15289, 15308])).
% 2.74/3.01 tff(15318,plain,((~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~r(z, s(z))) | (~b(s(z), z)) | (~r(z, s(s(s(elem!1))))) | b(s(s(z)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(15319,plain,
% 2.74/3.01 (~b(s(s(z)), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15318, 255, 535, 729, 550, 570, 138])).
% 2.74/3.01 tff(15320,plain,
% 2.74/3.01 (r(s(s(z)), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[625, 15319])).
% 2.74/3.01 tff(15321,plain,
% 2.74/3.01 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3835, 15301, 729, 15320, 15299])).
% 2.74/3.01 tff(15322,plain,
% 2.74/3.01 (b(s(s(s(s(elem!1)))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[511, 15321])).
% 2.74/3.01 tff(15323,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), 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), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(15324,plain,
% 2.74/3.01 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(15325,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[15324])).
% 2.74/3.01 tff(15326,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.74/3.01 inference(transitivity,[status(thm)],[15325, 15323])).
% 2.74/3.01 tff(15327,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)))),
% 2.74/3.01 inference(quant_inst,[status(thm)],[])).
% 2.74/3.01 tff(15328,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[15327, 15326])).
% 2.74/3.01 tff(15329,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15328, 97, 550, 255, 15297, 15322])).
% 2.74/3.01 tff(15330,plain,(b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | b(s(s(z)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(15331,plain,
% 2.74/3.01 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15330, 255, 550, 729, 570, 535, 138])).
% 2.74/3.01 tff(15332,plain,
% 2.74/3.01 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15277, 15331, 255, 729, 15320, 15291, 535])).
% 2.74/3.01 tff(15333,plain,
% 2.74/3.01 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[452, 15332])).
% 2.74/3.01 tff(15334,plain,
% 2.74/3.01 (~b(s(s(z)), s(s(s(z))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3067, 15333, 255, 535])).
% 2.74/3.01 tff(15335,plain,
% 2.74/3.01 (r(s(s(z)), s(s(s(z))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[437, 15334])).
% 2.74/3.01 tff(15336,plain,
% 2.74/3.01 (~r(s(s(s(z))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3595, 15335, 729, 15320, 15119])).
% 2.74/3.01 tff(15337,plain,
% 2.74/3.01 (b(s(s(s(z))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[402, 15336])).
% 2.74/3.01 tff(15338,plain,
% 2.74/3.01 (~r(s(z), s(s(s(z))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3605, 15335, 729, 15320, 15119])).
% 2.74/3.01 tff(15339,plain,
% 2.74/3.01 (b(s(z), s(s(s(z))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[253, 15338])).
% 2.74/3.01 tff(15340,plain,
% 2.74/3.01 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[2129, 15331, 535, 15291])).
% 2.74/3.01 tff(15341,plain,
% 2.74/3.01 (r(s(s(s(s(elem!1)))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[511, 15340])).
% 2.74/3.01 tff(15342,plain,
% 2.74/3.01 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3267, 15333, 255, 535])).
% 2.74/3.01 tff(15343,plain,
% 2.74/3.01 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[336, 15342])).
% 2.74/3.01 tff(15344,plain,
% 2.74/3.01 (~r(z, s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[12838, 15343, 729, 15289, 15341])).
% 2.74/3.01 tff(15345,plain,
% 2.74/3.01 (b(z, s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1093, 15344])).
% 2.74/3.01 tff(15346,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $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(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(15347,plain,
% 2.74/3.01 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(15348,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[15347])).
% 2.74/3.01 tff(15349,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.74/3.01 inference(transitivity,[status(thm)],[15348, 15346])).
% 2.74/3.01 tff(15350,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.74/3.01 inference(quant_inst,[status(thm)],[])).
% 2.74/3.01 tff(15351,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[15350, 15349])).
% 2.74/3.01 tff(15352,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15351, 97, 550, 15345, 15339, 15337])).
% 2.74/3.01 tff(15353,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~r(z, s(z))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | b(s(s(z)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(15354,plain,
% 2.74/3.01 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | b(s(s(z)), s(s(s(elem!1))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15353, 11419])).
% 2.74/3.01 tff(15355,plain,
% 2.74/3.01 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15354, 15113, 14905, 15106, 15110])).
% 2.74/3.01 tff(15356,plain,
% 2.74/3.01 (r(s(z), s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[280, 15355])).
% 2.74/3.01 tff(15357,plain,
% 2.74/3.01 (~r(z, s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[11787, 15356, 2, 15108])).
% 2.74/3.01 tff(15358,plain,
% 2.74/3.01 (b(z, s(s(s(s(elem!1)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1093, 15357])).
% 2.74/3.01 tff(15359,plain,
% 2.74/3.01 (r(s(s(z)), s(s(s(elem!1))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[143, 15113])).
% 2.74/3.01 tff(15360,plain,
% 2.74/3.01 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15082, 1960, 14749, 15359])).
% 2.74/3.01 tff(15361,plain,
% 2.74/3.01 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[3089, 15360, 1])).
% 2.74/3.01 tff(15362,plain,
% 2.74/3.01 (~r(s(s(s(z))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[6467, 1960, 15104, 15108])).
% 2.74/3.01 tff(15363,plain,
% 2.74/3.01 (b(s(s(s(z))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[402, 15362])).
% 2.74/3.01 tff(15364,plain,
% 2.74/3.01 (~r(z, s(s(s(z))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[14959, 1960, 2, 15108])).
% 2.74/3.01 tff(15365,plain,
% 2.74/3.01 (b(z, s(s(s(z))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1318, 15364])).
% 2.74/3.01 tff(15366,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(15367,plain,
% 2.74/3.01 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(15368,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[15367])).
% 2.74/3.01 tff(15369,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.74/3.01 inference(transitivity,[status(thm)],[15368, 15366])).
% 2.74/3.01 tff(15370,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.74/3.01 inference(quant_inst,[status(thm)],[])).
% 2.74/3.01 tff(15371,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[15370, 15369])).
% 2.74/3.01 tff(15372,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[15371, 97, 14660, 15365, 15363, 15361])).
% 2.74/3.01 tff(15373,plain,((~r(s(s(s(z))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(15374,plain,
% 2.74/3.01 (~r(s(s(s(z))), s(s(z)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15373, 2, 1])).
% 2.74/3.02 tff(15375,plain,
% 2.74/3.02 (b(s(s(s(z))), s(s(z)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[421, 15374])).
% 2.74/3.02 tff(15376,plain,
% 2.74/3.02 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1248, 15355, 15112])).
% 2.74/3.02 tff(15377,plain,
% 2.74/3.02 ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[5058, 14660])).
% 2.74/3.02 tff(15378,plain,
% 2.74/3.02 (~b(s(s(s(s(elem!1)))), z)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15377, 473, 372])).
% 2.74/3.02 tff(15379,plain,
% 2.74/3.02 (r(s(s(s(s(elem!1)))), z)),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[842, 15378])).
% 2.74/3.02 tff(15380,plain,
% 2.74/3.02 ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[3303, 14660])).
% 2.74/3.02 tff(15381,plain,
% 2.74/3.02 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15380, 473, 372])).
% 2.74/3.02 tff(15382,plain,
% 2.74/3.02 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[452, 15381])).
% 2.74/3.02 tff(15383,plain,
% 2.74/3.02 ($false),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[3278, 15382, 15379, 2, 15273, 226])).
% 2.74/3.02 tff(15384,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.02 tff(15385,plain,
% 2.74/3.02 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15384, 2, 15108, 15358, 14905, 15043])).
% 2.74/3.02 tff(15386,plain,
% 2.74/3.02 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[486, 15385, 15376])).
% 2.74/3.02 tff(15387,plain,
% 2.74/3.02 ((~r(s(s(z)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1003, 11419])).
% 2.74/3.02 tff(15388,plain,
% 2.74/3.02 ((~r(s(s(z)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15387, 14660])).
% 2.74/3.02 tff(15389,plain,
% 2.74/3.02 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15388, 15386, 15110, 15112, 15356, 15104])).
% 2.74/3.02 tff(15390,plain,
% 2.74/3.02 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[336, 15389])).
% 2.74/3.02 tff(15391,plain,
% 2.74/3.02 (~b(s(s(s(z))), s(z))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[11501, 15375, 14905, 15043, 1])).
% 2.74/3.02 tff(15392,plain,
% 2.74/3.02 (r(s(s(s(z))), s(z))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1358, 15391])).
% 2.74/3.02 tff(15393,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $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(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(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(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(15394,plain,
% 2.74/3.02 (((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(15395,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(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(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[15394])).
% 2.74/3.02 tff(15396,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(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(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.74/3.02 inference(transitivity,[status(thm)],[15395, 15393])).
% 2.74/3.02 tff(15397,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.74/3.02 inference(quant_inst,[status(thm)],[])).
% 2.74/3.02 tff(15398,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[15397, 15396])).
% 2.74/3.02 tff(15399,plain,
% 2.74/3.02 (~b(s(s(s(s(z)))), s(z))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15398, 97, 550, 372, 339, 535, 7084])).
% 2.74/3.02 tff(15400,plain,
% 2.74/3.02 (r(s(s(s(s(z)))), s(z))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[13335, 15399])).
% 2.74/3.02 tff(15401,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), 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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(15402,plain,
% 2.74/3.02 (((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(15403,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[15402])).
% 2.74/3.02 tff(15404,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.74/3.02 inference(transitivity,[status(thm)],[15403, 15401])).
% 2.74/3.02 tff(15405,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.74/3.02 inference(quant_inst,[status(thm)],[])).
% 2.74/3.02 tff(15406,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[15405, 15404])).
% 2.74/3.02 tff(15407,plain,
% 2.74/3.02 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15406, 97, 339, 1331, 7084])).
% 2.74/3.02 tff(15408,plain,
% 2.74/3.02 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[2829, 15407])).
% 2.74/3.02 tff(15409,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), 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(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(15410,plain,
% 2.74/3.02 (((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(15411,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), 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(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[15410])).
% 2.74/3.02 tff(15412,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), 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(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.74/3.02 inference(transitivity,[status(thm)],[15411, 15409])).
% 2.74/3.02 tff(15413,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.74/3.02 inference(quant_inst,[status(thm)],[])).
% 2.74/3.02 tff(15414,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[15413, 15412])).
% 2.74/3.02 tff(15415,plain,
% 2.74/3.02 (~b(s(z), s(s(s(s(z)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15414, 97, 339, 535, 7084])).
% 2.74/3.02 tff(15416,plain,
% 2.74/3.02 (b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[2844, 2833])).
% 2.74/3.02 tff(15417,plain,
% 2.74/3.02 (r(s(z), s(s(s(s(z)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15416, 15415])).
% 2.74/3.02 tff(15418,plain,
% 2.74/3.02 ($false),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[2851, 155, 2597, 15417, 15408, 15400])).
% 2.74/3.02 tff(15419,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.02 tff(15420,plain,
% 2.74/3.02 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15419, 15392, 15390, 15375, 14905, 15106, 15358])).
% 2.74/3.02 tff(15421,plain,
% 2.74/3.02 (r(s(s(s(s(z)))), s(s(z)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[13323, 15420])).
% 2.74/3.02 tff(15422,plain,
% 2.74/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(15423,plain,
% 2.74/3.02 (((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(15424,plain,
% 2.74/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[15423])).
% 2.74/3.02 tff(15425,plain,
% 2.74/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.74/3.02 inference(transitivity,[status(thm)],[15424, 15422])).
% 2.74/3.02 tff(15426,plain,
% 2.74/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 2.74/3.02 inference(quant_inst,[status(thm)],[])).
% 2.74/3.02 tff(15427,plain,
% 2.74/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[15426, 15425])).
% 2.74/3.02 tff(15428,plain,
% 2.74/3.02 (~r(z, s(s(s(s(z)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[15427, 155, 11419, 15108, 2, 15421])).
% 2.74/3.02 tff(15429,plain,
% 2.74/3.02 (b(z, s(s(s(s(z)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[7416, 15428])).
% 2.87/3.02 tff(15430,plain,
% 2.87/3.02 (((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.02 inference(rewrite,[status(thm)],[])).
% 2.87/3.02 tff(15431,plain,
% 2.87/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.87/3.02 inference(monotonicity,[status(thm)],[15430])).
% 2.87/3.02 tff(15432,plain,
% 2.87/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.02 inference(transitivity,[status(thm)],[15431, 2876])).
% 2.87/3.02 tff(15433,plain,
% 2.87/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.02 inference(quant_inst,[status(thm)],[])).
% 2.87/3.02 tff(15434,plain,
% 2.87/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.87/3.02 inference(modus_ponens,[status(thm)],[15433, 15432])).
% 2.87/3.02 tff(15435,plain,
% 2.87/3.02 (~r(s(s(s(s(z)))), z)),
% 2.87/3.02 inference(unit_resolution,[status(thm)],[15434, 155, 15108, 15104, 15421])).
% 2.87/3.02 tff(15436,plain,
% 2.87/3.02 (b(s(s(s(s(z)))), z)),
% 2.87/3.02 inference(unit_resolution,[status(thm)],[2860, 15435])).
% 2.87/3.02 tff(15437,plain,
% 2.87/3.02 (~r(z, s(s(s(z))))),
% 2.87/3.02 inference(unit_resolution,[status(thm)],[11471, 15392, 15108, 14905, 15375])).
% 2.87/3.02 tff(15438,plain,
% 2.87/3.02 (b(z, s(s(s(z))))),
% 2.87/3.02 inference(unit_resolution,[status(thm)],[1318, 15437])).
% 2.87/3.02 tff(15439,plain,
% 2.87/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.87/3.02 inference(rewrite,[status(thm)],[])).
% 2.87/3.02 tff(15440,plain,
% 2.87/3.02 (((~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(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.87/3.02 inference(rewrite,[status(thm)],[])).
% 2.87/3.02 tff(15441,plain,
% 2.87/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.87/3.02 inference(monotonicity,[status(thm)],[15440])).
% 2.87/3.02 tff(15442,plain,
% 2.87/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.87/3.03 inference(transitivity,[status(thm)],[15441, 15439])).
% 2.87/3.03 tff(15443,plain,
% 2.87/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.87/3.03 inference(quant_inst,[status(thm)],[])).
% 2.87/3.03 tff(15444,plain,
% 2.87/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.87/3.03 inference(modus_ponens,[status(thm)],[15443, 15442])).
% 2.87/3.03 tff(15445,plain,
% 2.87/3.03 ($false),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[15444, 97, 1331, 1330, 9019, 2796])).
% 2.87/3.03 tff(15446,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.03 tff(15447,plain,
% 2.87/3.03 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[15446, 15375, 15438, 15436])).
% 2.87/3.03 tff(15448,plain,
% 2.87/3.03 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[4169, 15447])).
% 2.87/3.03 tff(15449,plain,
% 2.87/3.03 (~b(s(z), s(s(s(z))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[7835, 15438, 15106, 15375])).
% 2.87/3.03 tff(15450,plain,
% 2.87/3.03 (r(s(z), s(s(s(z))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[253, 15449])).
% 2.87/3.03 tff(15451,plain,
% 2.87/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.03 inference(rewrite,[status(thm)],[])).
% 2.87/3.03 tff(15452,plain,
% 2.87/3.03 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.03 inference(rewrite,[status(thm)],[])).
% 2.87/3.03 tff(15453,plain,
% 2.87/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.87/3.03 inference(monotonicity,[status(thm)],[15452])).
% 2.87/3.03 tff(15454,plain,
% 2.87/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.03 inference(transitivity,[status(thm)],[15453, 15451])).
% 2.87/3.03 tff(15455,plain,
% 2.87/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.03 inference(quant_inst,[status(thm)],[])).
% 2.87/3.03 tff(15456,plain,
% 2.87/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.87/3.03 inference(modus_ponens,[status(thm)],[15455, 15454])).
% 2.87/3.03 tff(15457,plain,
% 2.87/3.03 (~r(s(s(s(s(z)))), s(z))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[15456, 155, 2, 15450, 15421, 15448])).
% 2.87/3.03 tff(15458,plain,
% 2.87/3.03 (b(s(s(s(s(z)))), s(z))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[13335, 15457])).
% 2.87/3.03 tff(15459,assumption,(b(z, s(s(s(s(z)))))), introduced(assumption)).
% 2.87/3.03 tff(15460,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 2.87/3.03 tff(15461,plain,
% 2.87/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $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(s(s(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(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.87/3.03 inference(rewrite,[status(thm)],[])).
% 2.87/3.03 tff(15462,plain,
% 2.87/3.03 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.87/3.03 inference(rewrite,[status(thm)],[])).
% 2.87/3.03 tff(15463,plain,
% 2.87/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 2.87/3.03 inference(monotonicity,[status(thm)],[15462])).
% 2.87/3.03 tff(15464,plain,
% 2.87/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.87/3.03 inference(transitivity,[status(thm)],[15463, 15461])).
% 2.87/3.03 tff(15465,plain,
% 2.87/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)))),
% 2.87/3.03 inference(quant_inst,[status(thm)],[])).
% 2.87/3.03 tff(15466,plain,
% 2.87/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 2.87/3.03 inference(modus_ponens,[status(thm)],[15465, 15464])).
% 2.87/3.03 tff(15467,plain,
% 2.87/3.03 ($false),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[15466, 97, 550, 15460, 10217, 15459])).
% 2.87/3.03 tff(15468,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.03 tff(15469,plain,
% 2.87/3.03 (~b(s(z), s(s(s(s(z)))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[15468, 15458, 15106, 15429])).
% 2.87/3.03 tff(15470,plain,
% 2.87/3.03 (r(s(z), s(s(s(s(z)))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[15416, 15469])).
% 2.87/3.03 tff(15471,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 2.87/3.03 tff(15472,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 2.87/3.03 tff(15473,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 2.87/3.03 tff(15474,plain,
% 2.87/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.87/3.03 inference(rewrite,[status(thm)],[])).
% 2.87/3.03 tff(15475,plain,
% 2.87/3.03 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.87/3.03 inference(rewrite,[status(thm)],[])).
% 2.87/3.03 tff(15476,plain,
% 2.87/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 2.87/3.03 inference(monotonicity,[status(thm)],[15475])).
% 2.87/3.03 tff(15477,plain,
% 2.87/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.87/3.03 inference(transitivity,[status(thm)],[15476, 15474])).
% 2.87/3.03 tff(15478,plain,
% 2.87/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 2.87/3.03 inference(quant_inst,[status(thm)],[])).
% 2.87/3.03 tff(15479,plain,
% 2.87/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 2.87/3.03 inference(modus_ponens,[status(thm)],[15478, 15477])).
% 2.87/3.03 tff(15480,plain,
% 2.87/3.03 ($false),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[15479, 155, 338, 15473, 15472, 15471])).
% 2.87/3.03 tff(15481,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.03 tff(15482,plain,
% 2.87/3.03 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[15481, 15450, 15470, 15448])).
% 2.87/3.03 tff(15483,plain,
% 2.87/3.03 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[2829, 15482])).
% 2.87/3.03 tff(15484,plain,
% 2.87/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.87/3.03 inference(rewrite,[status(thm)],[])).
% 2.87/3.03 tff(15485,plain,
% 2.87/3.03 (((~b(s(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(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.87/3.03 inference(rewrite,[status(thm)],[])).
% 2.87/3.03 tff(15486,plain,
% 2.87/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 2.87/3.03 inference(monotonicity,[status(thm)],[15485])).
% 2.87/3.03 tff(15487,plain,
% 2.87/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.87/3.03 inference(transitivity,[status(thm)],[15486, 15484])).
% 2.87/3.03 tff(15488,plain,
% 2.87/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 2.87/3.03 inference(quant_inst,[status(thm)],[])).
% 2.87/3.03 tff(15489,plain,
% 2.87/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 2.87/3.03 inference(modus_ponens,[status(thm)],[15488, 15487])).
% 2.87/3.03 tff(15490,plain,
% 2.87/3.03 ($false),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[15489, 97, 15438, 15483, 15458, 15429])).
% 2.87/3.03 tff(15491,plain,((~r(s(s(z)), s(z))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.03 tff(15492,plain,
% 2.87/3.03 (~r(s(s(z)), s(z))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[15491, 1])).
% 2.87/3.03 tff(15493,plain,
% 2.87/3.03 (b(s(s(z)), s(z))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[122, 15492])).
% 2.87/3.03 tff(15494,plain,
% 2.87/3.03 (~r(s(z), z)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[5665, 3, 15493])).
% 2.87/3.03 tff(15495,plain,
% 2.87/3.03 (b(s(z), z)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[568, 15494])).
% 2.87/3.03 tff(15496,plain,
% 2.87/3.03 (~r(s(z), z)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[5665, 3, 87])).
% 2.87/3.03 tff(15497,plain,
% 2.87/3.03 (b(s(z), z)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[568, 15496])).
% 2.87/3.03 tff(15498,plain,
% 2.87/3.03 (~b(s(s(z)), z)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[14200, 204, 550, 87])).
% 2.87/3.03 tff(15499,plain,
% 2.87/3.03 (r(s(s(z)), z)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[625, 15498])).
% 2.87/3.03 tff(15500,plain,
% 2.87/3.03 (~b(s(s(s(z))), z)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[11911, 1360, 550, 204])).
% 2.87/3.03 tff(15501,plain,
% 2.87/3.03 (r(s(s(s(z))), z)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[402, 15500])).
% 2.87/3.03 tff(15502,plain,
% 2.87/3.03 (~b(s(s(z)), s(s(s(z))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[7010, 1360, 87, 550])).
% 2.87/3.03 tff(15503,plain,
% 2.87/3.03 (r(s(s(z)), s(s(s(z))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[437, 15502])).
% 2.87/3.03 tff(15504,plain,
% 2.87/3.03 ($false),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[6410, 15503, 15501, 15499, 1300])).
% 2.87/3.03 tff(15505,plain,((~b(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.03 tff(15506,plain,
% 2.87/3.03 (~b(s(s(s(z))), s(z))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[15505, 204, 87, 15497, 1300])).
% 2.87/3.03 tff(15507,plain,
% 2.87/3.03 (r(s(s(s(z))), s(z))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1358, 15506])).
% 2.87/3.03 tff(15508,plain,
% 2.87/3.03 (~r(s(z), s(s(s(z))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[14376, 15507, 1300])).
% 2.87/3.03 tff(15509,plain,
% 2.87/3.03 (b(s(z), s(s(s(z))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[253, 15508])).
% 2.87/3.03 tff(15510,plain,
% 2.87/3.03 (~b(s(s(z)), z)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[14200, 204, 15497, 87])).
% 2.87/3.03 tff(15511,plain,
% 2.87/3.03 (r(s(s(z)), z)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[625, 15510])).
% 2.87/3.03 tff(15512,plain,
% 2.87/3.03 (~b(s(s(s(elem!1))), s(z))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[14666, 204, 15497])).
% 2.87/3.03 tff(15513,plain,
% 2.87/3.03 (r(s(s(s(elem!1))), s(z))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[493, 15512])).
% 2.87/3.03 tff(15514,plain,
% 2.87/3.03 (~b(s(z), s(s(s(elem!1))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[5838, 14151, 3008, 126])).
% 2.87/3.03 tff(15515,plain,
% 2.87/3.03 (r(s(z), s(s(s(elem!1))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[181, 15514])).
% 2.87/3.03 tff(15516,plain,
% 2.87/3.03 (~b(s(z), s(s(s(elem!1))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[5838, 14151, 124, 126])).
% 2.87/3.03 tff(15517,plain,
% 2.87/3.03 (r(s(z), s(s(s(elem!1))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[181, 15516])).
% 2.87/3.03 tff(15518,plain,
% 2.87/3.03 (~r(s(s(z)), s(s(s(z))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[14156, 1330, 2591, 3, 125, 137])).
% 2.87/3.03 tff(15519,plain,
% 2.87/3.03 (b(s(s(z)), s(s(s(z))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[437, 15518])).
% 2.87/3.03 tff(15520,plain,
% 2.87/3.03 (~b(s(s(s(z))), s(z))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[7010, 15519, 87, 14151])).
% 2.87/3.03 tff(15521,plain,
% 2.87/3.03 (r(s(s(s(z))), s(z))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1358, 15520])).
% 2.87/3.03 tff(15522,plain,
% 2.87/3.03 ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[4368, 155, 11419, 3, 2591])).
% 2.87/3.03 tff(15523,plain,
% 2.87/3.03 (~r(s(s(s(z))), z)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[15522, 15521])).
% 2.87/3.03 tff(15524,plain,
% 2.87/3.03 (b(s(s(s(z))), z)),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[402, 15523])).
% 2.87/3.03 tff(15525,plain,
% 2.87/3.03 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[5733, 97, 126, 124, 15524])).
% 2.87/3.03 tff(15526,plain,
% 2.87/3.03 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[5757, 15521, 125, 15517])).
% 2.87/3.03 tff(15527,plain,
% 2.87/3.03 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[1678, 53, 15526, 15525])).
% 2.87/3.03 tff(15528,plain,
% 2.87/3.03 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.87/3.03 inference(monotonicity,[status(thm)],[15527])).
% 2.87/3.03 tff(15529,plain,
% 2.87/3.03 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.87/3.03 inference(transitivity,[status(thm)],[15528, 1414])).
% 2.87/3.03 tff(15530,plain,
% 2.87/3.03 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.87/3.03 inference(transitivity,[status(thm)],[15529, 2507])).
% 2.87/3.03 tff(15531,plain,
% 2.87/3.03 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.87/3.03 inference(monotonicity,[status(thm)],[15530])).
% 2.87/3.03 tff(15532,plain,
% 2.87/3.03 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.87/3.03 inference(modus_ponens,[status(thm)],[286, 15531])).
% 2.87/3.03 tff(15533,plain,
% 2.87/3.03 (b(s(s(z)), s(s(s(elem!1))))),
% 2.87/3.03 inference(unit_resolution,[status(thm)],[143, 137])).
% 2.87/3.03 tff(15534,plain,
% 2.87/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.87/3.04 inference(rewrite,[status(thm)],[])).
% 2.87/3.04 tff(15535,plain,
% 2.87/3.04 (((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.87/3.04 inference(rewrite,[status(thm)],[])).
% 2.87/3.04 tff(15536,plain,
% 2.87/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~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(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15535])).
% 2.87/3.04 tff(15537,plain,
% 2.87/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~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(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.87/3.04 inference(transitivity,[status(thm)],[15536, 15534])).
% 2.87/3.04 tff(15538,plain,
% 2.87/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))))),
% 2.87/3.04 inference(quant_inst,[status(thm)],[])).
% 2.87/3.04 tff(15539,plain,
% 2.87/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[15538, 15537])).
% 2.87/3.04 tff(15540,plain,
% 2.87/3.04 (~b(z, s(s(z)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[15539, 97, 126, 15519, 15533, 1330, 15524])).
% 2.87/3.04 tff(15541,plain,
% 2.87/3.04 (r(z, s(s(z)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[222, 15540])).
% 2.87/3.04 tff(15542,plain,
% 2.87/3.04 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15529])).
% 2.87/3.04 tff(15543,plain,
% 2.87/3.04 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[286, 15542])).
% 2.87/3.04 tff(15544,plain,
% 2.87/3.04 (~b(s(s(s(s(elem!1)))), z)),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[7659, 15543, 125, 126, 124, 14151])).
% 2.87/3.04 tff(15545,plain,
% 2.87/3.04 (r(s(s(s(s(elem!1)))), z)),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[842, 15544])).
% 2.87/3.04 tff(15546,plain,
% 2.87/3.04 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[14125, 463, 3, 226])).
% 2.87/3.04 tff(15547,plain,
% 2.87/3.04 (b(s(s(s(s(elem!1)))), s(z))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[511, 15546])).
% 2.87/3.04 tff(15548,plain,
% 2.87/3.04 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[3326, 463, 645, 1393, 824])).
% 2.87/3.04 tff(15549,plain,
% 2.87/3.04 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[336, 15548])).
% 2.87/3.04 tff(15550,plain,
% 2.87/3.04 ($false),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[3240, 15549, 15547, 87, 550])).
% 2.87/3.04 tff(15551,plain,((~r(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~r(s(s(z)), z)) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.04 tff(15552,plain,
% 2.87/3.04 (~r(z, s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[15551, 15527, 14151, 645, 87, 15545, 3, 15541])).
% 2.87/3.04 tff(15553,plain,
% 2.87/3.04 (b(z, s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1093, 15552])).
% 2.87/3.04 tff(15554,plain,
% 2.87/3.04 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[914, 15553, 124, 126])).
% 2.87/3.04 tff(15555,plain,
% 2.87/3.04 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[821, 15554, 15532])).
% 2.87/3.04 tff(15556,plain,
% 2.87/3.04 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1136, 15555, 125, 15517])).
% 2.87/3.04 tff(15557,plain,
% 2.87/3.04 (b(s(s(s(s(elem!1)))), s(z))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[511, 15556])).
% 2.87/3.04 tff(15558,plain,
% 2.87/3.04 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[2677, 15527, 2590])).
% 2.87/3.04 tff(15559,plain,
% 2.87/3.04 (r(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[58, 15558])).
% 2.87/3.04 tff(15560,plain,
% 2.87/3.04 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15527])).
% 2.87/3.04 tff(15561,plain,
% 2.87/3.04 (s(s(z)) = s(s(elem!1))),
% 2.87/3.04 inference(transitivity,[status(thm)],[73, 15560, 19])).
% 2.87/3.04 tff(15562,plain,
% 2.87/3.04 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15561])).
% 2.87/3.04 tff(15563,plain,
% 2.87/3.04 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.87/3.04 inference(transitivity,[status(thm)],[15562, 1428])).
% 2.87/3.04 tff(15564,plain,
% 2.87/3.04 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15563])).
% 2.87/3.04 tff(15565,plain,
% 2.87/3.04 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[331, 15564])).
% 2.87/3.04 tff(15566,plain,
% 2.87/3.04 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15561])).
% 2.87/3.04 tff(15567,plain,
% 2.87/3.04 (r(z, s(s(elem!1)))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[15541, 15566])).
% 2.87/3.04 tff(15568,plain,
% 2.87/3.04 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15561])).
% 2.87/3.04 tff(15569,plain,
% 2.87/3.04 (r(s(s(elem!1)), z)),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[645, 15568])).
% 2.87/3.04 tff(15570,plain,
% 2.87/3.04 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[7685, 15545, 15569, 15567])).
% 2.87/3.04 tff(15571,plain,
% 2.87/3.04 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1484, 15570, 15565])).
% 2.87/3.04 tff(15572,plain,
% 2.87/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.87/3.04 inference(rewrite,[status(thm)],[])).
% 2.87/3.04 tff(15573,plain,
% 2.87/3.04 (((~b(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(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.87/3.04 inference(rewrite,[status(thm)],[])).
% 2.87/3.04 tff(15574,plain,
% 2.87/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15573])).
% 2.87/3.04 tff(15575,plain,
% 2.87/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.87/3.04 inference(transitivity,[status(thm)],[15574, 15572])).
% 2.87/3.04 tff(15576,plain,
% 2.87/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))),
% 2.87/3.04 inference(quant_inst,[status(thm)],[])).
% 2.87/3.04 tff(15577,plain,
% 2.87/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[15576, 15575])).
% 2.87/3.04 tff(15578,plain,
% 2.87/3.04 ($false),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[15577, 97, 1545, 124, 372, 473])).
% 2.87/3.04 tff(15579,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.04 tff(15580,plain,
% 2.87/3.04 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[15579, 15553, 124, 15571])).
% 2.87/3.04 tff(15581,plain,
% 2.87/3.04 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[486, 15580, 15543])).
% 2.87/3.04 tff(15582,plain,
% 2.87/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.87/3.04 inference(rewrite,[status(thm)],[])).
% 2.87/3.04 tff(15583,plain,
% 2.87/3.04 (((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~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)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.87/3.04 inference(rewrite,[status(thm)],[])).
% 2.87/3.04 tff(15584,plain,
% 2.87/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15583])).
% 2.87/3.04 tff(15585,plain,
% 2.87/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.87/3.04 inference(transitivity,[status(thm)],[15584, 15582])).
% 2.87/3.04 tff(15586,plain,
% 2.87/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.87/3.04 inference(quant_inst,[status(thm)],[])).
% 2.87/3.04 tff(15587,plain,
% 2.87/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[15586, 15585])).
% 2.87/3.04 tff(15588,plain,
% 2.87/3.04 ($false),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[15587, 155, 125, 488, 309, 3, 145])).
% 2.87/3.04 tff(15589,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.04 tff(15590,plain,
% 2.87/3.04 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[15589, 15581, 125, 3, 15559])).
% 2.87/3.04 tff(15591,plain,
% 2.87/3.04 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[336, 15590])).
% 2.87/3.04 tff(15592,plain,
% 2.87/3.04 ($false),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[3240, 15591, 15557, 87, 14151])).
% 2.87/3.04 tff(15593,plain,((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | b(s(s(s(z))), s(s(z))) | r(s(s(z)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.04 tff(15594,plain,
% 2.87/3.04 (~b(z, s(s(s(z))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[15593, 137, 125, 3, 3008, 126, 645, 2590, 87])).
% 2.87/3.04 tff(15595,plain,
% 2.87/3.04 (r(z, s(s(s(z))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1318, 15594])).
% 2.87/3.04 tff(15596,plain,
% 2.87/3.04 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[6652, 15595, 585])).
% 2.87/3.04 tff(15597,plain,
% 2.87/3.04 (~b(z, s(s(z)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[6347, 97, 126, 3008, 15533])).
% 2.87/3.04 tff(15598,plain,
% 2.87/3.04 (r(z, s(s(z)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[222, 15597])).
% 2.87/3.04 tff(15599,plain,
% 2.87/3.04 (~r(s(s(s(z))), s(z))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[6518, 15598, 125, 3, 2591, 15596])).
% 2.87/3.04 tff(15600,plain,
% 2.87/3.04 (b(s(s(s(z))), s(z))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1358, 15599])).
% 2.87/3.04 tff(15601,plain,
% 2.87/3.04 (~r(s(s(z)), s(s(s(z))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1969, 15598, 15595, 2591])).
% 2.87/3.04 tff(15602,plain,
% 2.87/3.04 (b(s(s(z)), s(s(s(z))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[437, 15601])).
% 2.87/3.04 tff(15603,plain,
% 2.87/3.04 ($false),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[7010, 15602, 15600, 87, 14151])).
% 2.87/3.04 tff(15604,plain,(r(s(s(z)), s(s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | r(z, s(s(s(elem!1)))) | (~r(s(s(z)), z)) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.04 tff(15605,plain,
% 2.87/3.04 (r(s(s(z)), s(s(s(elem!1))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[15604, 2590, 125, 3, 126, 585, 645, 87])).
% 2.87/3.04 tff(15606,plain,
% 2.87/3.04 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[5875, 15605, 3, 15515])).
% 2.87/3.04 tff(15607,plain,
% 2.87/3.04 (b(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[58, 15606])).
% 2.87/3.04 tff(15608,plain,
% 2.87/3.04 (~b(z, s(s(z)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[212, 15607, 87, 3008])).
% 2.87/3.04 tff(15609,plain,
% 2.87/3.04 (~r(z, s(s(z)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[3582, 15607, 3008, 125, 14151, 15515, 645, 2590])).
% 2.87/3.04 tff(15610,plain,
% 2.87/3.04 ($false),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[222, 15609, 15608])).
% 2.87/3.04 tff(15611,plain,(b(s(s(s(z))), s(s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.04 tff(15612,plain,
% 2.87/3.04 (b(s(s(s(z))), s(s(z)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[15611, 3, 645, 87, 125, 126, 585])).
% 2.87/3.04 tff(15613,plain,
% 2.87/3.04 (~b(s(s(s(z))), s(z))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[14035, 14151, 87, 15612])).
% 2.87/3.04 tff(15614,plain,
% 2.87/3.04 (r(s(s(s(z))), s(z))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1358, 15613])).
% 2.87/3.04 tff(15615,plain,
% 2.87/3.04 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[212, 204, 87, 124])).
% 2.87/3.04 tff(15616,plain,
% 2.87/3.04 (r(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[58, 15615])).
% 2.87/3.04 tff(15617,plain,
% 2.87/3.04 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1995, 15615, 1331])).
% 2.87/3.04 tff(15618,plain,
% 2.87/3.04 (~b(s(z), s(s(s(elem!1))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[5838, 550, 124, 126])).
% 2.87/3.04 tff(15619,plain,
% 2.87/3.04 (r(s(z), s(s(s(elem!1))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[181, 15618])).
% 2.87/3.04 tff(15620,plain,
% 2.87/3.04 (~r(s(s(z)), s(s(s(z))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[6410, 4719, 645, 4727])).
% 2.87/3.04 tff(15621,plain,
% 2.87/3.04 (b(s(s(z)), s(s(s(z))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[437, 15620])).
% 2.87/3.04 tff(15622,plain,
% 2.87/3.04 (~b(s(s(s(z))), s(z))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[7010, 15621, 87, 550])).
% 2.87/3.04 tff(15623,plain,
% 2.87/3.04 (r(s(s(s(z))), s(z))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1358, 15622])).
% 2.87/3.04 tff(15624,plain,
% 2.87/3.04 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[5757, 15623, 125, 15619])).
% 2.87/3.04 tff(15625,plain,
% 2.87/3.04 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[3089, 15624, 15617])).
% 2.87/3.04 tff(15626,plain,
% 2.87/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.87/3.04 inference(rewrite,[status(thm)],[])).
% 2.87/3.04 tff(15627,plain,
% 2.87/3.04 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~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(s(elem!1))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.87/3.04 inference(rewrite,[status(thm)],[])).
% 2.87/3.04 tff(15628,plain,
% 2.87/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z))), s(s(s(elem!1))))) | (~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(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15627])).
% 2.87/3.04 tff(15629,plain,
% 2.87/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z))), s(s(s(elem!1))))) | (~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(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.87/3.04 inference(transitivity,[status(thm)],[15628, 15626])).
% 2.87/3.04 tff(15630,plain,
% 2.87/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z))), s(s(s(elem!1))))) | (~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(z))))))),
% 2.87/3.04 inference(quant_inst,[status(thm)],[])).
% 2.87/3.04 tff(15631,plain,
% 2.87/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[15630, 15629])).
% 2.87/3.04 tff(15632,plain,
% 2.87/3.04 ($false),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[15631, 97, 126, 15621, 127, 15625])).
% 2.87/3.04 tff(15633,plain,((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.04 tff(15634,plain,
% 2.87/3.04 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[15633, 204, 126, 125, 87, 14151, 645, 1331, 124])).
% 2.87/3.04 tff(15635,plain,
% 2.87/3.04 (r(s(s(z)), s(s(s(elem!1))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[143, 15634])).
% 2.87/3.04 tff(15636,plain,
% 2.87/3.04 ($false),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[5875, 15635, 15616, 3, 15517])).
% 2.87/3.04 tff(15637,plain,((~b(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.04 tff(15638,plain,
% 2.87/3.04 (~b(z, s(s(z)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[15637, 3, 126, 125, 87, 645, 15612, 3008])).
% 2.87/3.04 tff(15639,plain,
% 2.87/3.04 (r(z, s(s(z)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[222, 15638])).
% 2.87/3.04 tff(15640,plain,
% 2.87/3.04 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[7847, 14049, 126, 1331])).
% 2.87/3.04 tff(15641,plain,
% 2.87/3.04 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[2687, 15640, 2466])).
% 2.87/3.04 tff(15642,plain,
% 2.87/3.04 (~b(s(z), s(s(s(z))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[7835, 14049, 1331, 14151])).
% 2.87/3.04 tff(15643,plain,
% 2.87/3.04 (r(s(z), s(s(s(z))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[253, 15642])).
% 2.87/3.04 tff(15644,plain,
% 2.87/3.04 ($false),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[2638, 15643, 15641, 125, 2597])).
% 2.87/3.04 tff(15645,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.04 tff(15646,plain,
% 2.87/3.04 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[15645, 15639, 125, 15612, 126, 15614, 3])).
% 2.87/3.04 tff(15647,plain,
% 2.87/3.04 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[2682, 15646])).
% 2.87/3.04 tff(15648,plain,
% 2.87/3.04 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15647])).
% 2.87/3.04 tff(15649,plain,
% 2.87/3.04 (s(s(z)) = s(s(elem!1))),
% 2.87/3.04 inference(transitivity,[status(thm)],[73, 15648, 19])).
% 2.87/3.04 tff(15650,plain,
% 2.87/3.04 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15649])).
% 2.87/3.04 tff(15651,plain,
% 2.87/3.04 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.87/3.04 inference(symmetry,[status(thm)],[15650])).
% 2.87/3.04 tff(15652,plain,
% 2.87/3.04 (s(elem!1) = s(z)),
% 2.87/3.04 inference(transitivity,[status(thm)],[30, 15651, 23])).
% 2.87/3.04 tff(15653,plain,
% 2.87/3.04 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15652])).
% 2.87/3.04 tff(15654,plain,
% 2.87/3.04 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(symmetry,[status(thm)],[15653])).
% 2.87/3.04 tff(15655,plain,
% 2.87/3.04 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15647])).
% 2.87/3.04 tff(15656,plain,
% 2.87/3.04 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(transitivity,[status(thm)],[15655, 1414])).
% 2.87/3.04 tff(15657,plain,
% 2.87/3.04 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.87/3.04 inference(transitivity,[status(thm)],[15656, 2507])).
% 2.87/3.04 tff(15658,plain,
% 2.87/3.04 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15657])).
% 2.87/3.04 tff(15659,plain,
% 2.87/3.04 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[286, 15658])).
% 2.87/3.04 tff(15660,plain,
% 2.87/3.04 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15656])).
% 2.87/3.04 tff(15661,plain,
% 2.87/3.04 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[286, 15660])).
% 2.87/3.04 tff(15662,plain,
% 2.87/3.04 (~b(s(s(s(s(elem!1)))), z)),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[7659, 15661, 125, 126, 3008, 14151])).
% 2.87/3.04 tff(15663,plain,
% 2.87/3.04 (r(s(s(s(s(elem!1)))), z)),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[842, 15662])).
% 2.87/3.04 tff(15664,plain,
% 2.87/3.04 (~r(z, s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[15551, 15663, 14151, 645, 87, 15647, 3, 15639])).
% 2.87/3.04 tff(15665,plain,
% 2.87/3.04 (b(z, s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1093, 15664])).
% 2.87/3.04 tff(15666,plain,
% 2.87/3.04 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[914, 15665, 3008, 126])).
% 2.87/3.04 tff(15667,plain,
% 2.87/3.04 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[821, 15666, 15659])).
% 2.87/3.04 tff(15668,plain,
% 2.87/3.04 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15649])).
% 2.87/3.04 tff(15669,plain,
% 2.87/3.04 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.87/3.04 inference(transitivity,[status(thm)],[15668, 1428])).
% 2.87/3.04 tff(15670,plain,
% 2.87/3.04 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15669])).
% 2.87/3.04 tff(15671,plain,
% 2.87/3.04 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[331, 15670])).
% 2.87/3.04 tff(15672,plain,
% 2.87/3.04 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15649])).
% 2.87/3.04 tff(15673,plain,
% 2.87/3.04 (r(z, s(s(elem!1)))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[15639, 15672])).
% 2.87/3.04 tff(15674,plain,
% 2.87/3.04 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15649])).
% 2.87/3.04 tff(15675,plain,
% 2.87/3.04 (r(s(s(elem!1)), z)),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[645, 15674])).
% 2.87/3.04 tff(15676,plain,
% 2.87/3.04 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[7685, 15663, 15675, 15673])).
% 2.87/3.04 tff(15677,plain,
% 2.87/3.04 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[1484, 15676, 15671])).
% 2.87/3.04 tff(15678,plain,
% 2.87/3.04 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[15579, 15665, 3008, 15677])).
% 2.87/3.04 tff(15679,plain,
% 2.87/3.04 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[486, 15678, 15661])).
% 2.87/3.04 tff(15680,plain,
% 2.87/3.04 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[924, 15679, 15515, 15667])).
% 2.87/3.04 tff(15681,plain,
% 2.87/3.04 (b(s(z), s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(unit_resolution,[status(thm)],[280, 15680])).
% 2.87/3.04 tff(15682,plain,
% 2.87/3.04 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.87/3.04 inference(modus_ponens,[status(thm)],[15681, 15654])).
% 2.87/3.04 tff(15683,plain,
% 2.87/3.04 (s(z) = s(elem!1)),
% 2.87/3.04 inference(transitivity,[status(thm)],[24, 15650, 29])).
% 2.87/3.04 tff(15684,plain,
% 2.87/3.04 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.87/3.04 inference(monotonicity,[status(thm)],[15683])).
% 2.87/3.04 tff(15685,plain,
% 2.87/3.04 (z = elem!1),
% 2.87/3.04 inference(transitivity,[status(thm)],[1443, 15684, 85])).
% 2.87/3.05 tff(15686,plain,
% 2.87/3.05 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 2.87/3.05 inference(monotonicity,[status(thm)],[15683, 15685])).
% 2.87/3.05 tff(15687,plain,
% 2.87/3.05 (b(s(elem!1), elem!1)),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[14151, 15686])).
% 2.87/3.05 tff(15688,plain,
% 2.87/3.05 (elem!1 = z),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1888, 15685])).
% 2.87/3.05 tff(15689,plain,
% 2.87/3.05 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[2407, 15665, 15688])).
% 2.87/3.05 tff(15690,plain,
% 2.87/3.05 (((~![X0: $i, X4: $i, X3: $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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(15691,plain,
% 2.87/3.05 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), 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(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(15692,plain,
% 2.87/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(elem!1)))), 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(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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), elem!1))))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[15691])).
% 2.87/3.05 tff(15693,plain,
% 2.87/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(elem!1)))), 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(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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 2.87/3.05 inference(transitivity,[status(thm)],[15692, 15690])).
% 2.87/3.05 tff(15694,plain,
% 2.87/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(elem!1)))), 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(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)))),
% 2.87/3.05 inference(quant_inst,[status(thm)],[])).
% 2.87/3.05 tff(15695,plain,
% 2.87/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), elem!1))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[15694, 15693])).
% 2.87/3.05 tff(15696,plain,
% 2.87/3.05 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15695, 97, 15677, 15689, 15687])).
% 2.87/3.05 tff(15697,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15696, 15682])).
% 2.87/3.05 tff(15698,plain,((~r(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(15699,plain,
% 2.87/3.05 ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | r(z, s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15698, 14660])).
% 2.87/3.05 tff(15700,plain,
% 2.87/3.05 (r(z, s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15699, 15513, 87, 3, 15511])).
% 2.87/3.05 tff(15701,plain,
% 2.87/3.05 (~r(s(s(s(z))), s(s(z)))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[14142, 15507, 3, 15513, 15700, 15497])).
% 2.87/3.05 tff(15702,plain,
% 2.87/3.05 (b(s(s(s(z))), s(s(z)))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[421, 15701])).
% 2.87/3.05 tff(15703,plain,
% 2.87/3.05 (~b(s(s(s(z))), z)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[4717, 97, 204, 87, 15702])).
% 2.87/3.05 tff(15704,plain,
% 2.87/3.05 (r(s(s(s(z))), z)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[402, 15703])).
% 2.87/3.05 tff(15705,plain,
% 2.87/3.05 (~r(s(s(z)), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[6410, 15704, 15511, 1300])).
% 2.87/3.05 tff(15706,plain,
% 2.87/3.05 (b(s(s(z)), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[437, 15705])).
% 2.87/3.05 tff(15707,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[14178, 97, 15497, 204, 87, 15706, 15702, 15509])).
% 2.87/3.05 tff(15708,plain,((~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(15709,plain,
% 2.87/3.05 (~b(z, s(s(z)))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15708, 3, 1300, 15493])).
% 2.87/3.05 tff(15710,plain,
% 2.87/3.05 (r(z, s(s(z)))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[222, 15709])).
% 2.87/3.05 tff(15711,plain,
% 2.87/3.05 (~r(s(s(z)), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1969, 2591, 1300, 15710])).
% 2.87/3.05 tff(15712,plain,
% 2.87/3.05 (b(s(s(z)), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[437, 15711])).
% 2.87/3.05 tff(15713,plain,
% 2.87/3.05 (~b(s(s(s(z))), s(z))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[7010, 15712, 15493, 15495])).
% 2.87/3.05 tff(15714,plain,
% 2.87/3.05 (r(s(s(s(z))), s(z))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1358, 15713])).
% 2.87/3.05 tff(15715,plain,
% 2.87/3.05 (~r(s(s(s(elem!1))), s(z))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[6518, 15714, 1, 2591, 15710, 3])).
% 2.87/3.05 tff(15716,plain,
% 2.87/3.05 (b(s(s(s(elem!1))), s(z))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[493, 15715])).
% 2.87/3.05 tff(15717,plain,
% 2.87/3.05 (~b(z, s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[14724, 15716, 15495])).
% 2.87/3.05 tff(15718,plain,
% 2.87/3.05 (r(z, s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[590, 15717])).
% 2.87/3.05 tff(15719,plain,
% 2.87/3.05 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[6945, 15718, 3, 2590, 15713, 15495])).
% 2.87/3.05 tff(15720,plain,
% 2.87/3.05 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[5184, 15718, 15493, 15716, 15710])).
% 2.87/3.05 tff(15721,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[280, 15720, 15719])).
% 2.87/3.05 tff(15722,plain,(b(s(s(s(z))), s(s(z))) | (~r(s(z), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(15723,plain,
% 2.87/3.05 (b(s(s(s(z))), s(s(z)))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15722, 3, 1, 1300])).
% 2.87/3.05 tff(15724,plain,
% 2.87/3.05 (~b(s(s(s(z))), s(z))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[14035, 15723, 15493, 15495])).
% 2.87/3.05 tff(15725,plain,
% 2.87/3.05 (r(s(s(s(z))), s(z))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1358, 15724])).
% 2.87/3.05 tff(15726,plain,
% 2.87/3.05 ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15645, 14660])).
% 2.87/3.05 tff(15727,plain,
% 2.87/3.05 (~r(s(s(s(elem!1))), s(z))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15726, 15725, 3, 4228, 15710, 15723])).
% 2.87/3.05 tff(15728,plain,
% 2.87/3.05 (b(s(s(s(elem!1))), s(z))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[493, 15727])).
% 2.87/3.05 tff(15729,plain,
% 2.87/3.05 (~b(z, s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[14724, 15728, 15495])).
% 2.87/3.05 tff(15730,plain,
% 2.87/3.05 (r(z, s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[590, 15729])).
% 2.87/3.05 tff(15731,plain,
% 2.87/3.05 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[13268, 15730, 1300, 15728, 15725])).
% 2.87/3.05 tff(15732,plain,
% 2.87/3.05 (~r(s(s(z)), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[11460, 15725, 1300, 15710])).
% 2.87/3.05 tff(15733,plain,
% 2.87/3.05 (b(s(s(z)), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[437, 15732])).
% 2.87/3.05 tff(15734,plain,
% 2.87/3.05 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[10541, 15730, 15710, 15723, 15733])).
% 2.87/3.05 tff(15735,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[5852, 15734, 15731, 1, 1300, 15730])).
% 2.87/3.05 tff(15736,plain,((~r(s(z), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(15737,plain,
% 2.87/3.05 (~r(s(z), s(s(z)))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15736, 1300, 1])).
% 2.87/3.05 tff(15738,plain,
% 2.87/3.05 (b(s(z), s(s(z)))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[548, 15737])).
% 2.87/3.05 tff(15739,plain,
% 2.87/3.05 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[14941, 14263, 204])).
% 2.87/3.05 tff(15740,plain,
% 2.87/3.05 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[4598, 97, 14660, 204, 14263])).
% 2.87/3.05 tff(15741,plain,
% 2.87/3.05 (~r(z, s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[5852, 15740, 1, 1300, 15739])).
% 2.87/3.05 tff(15742,plain,
% 2.87/3.05 (b(z, s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[590, 15741])).
% 2.87/3.05 tff(15743,plain,
% 2.87/3.05 (~r(s(z), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[14376, 2597, 1300])).
% 2.87/3.05 tff(15744,plain,
% 2.87/3.05 (b(s(z), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[253, 15743])).
% 2.87/3.05 tff(15745,plain,
% 2.87/3.05 (~b(s(s(z)), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[4270, 14263, 15738, 15744])).
% 2.87/3.05 tff(15746,plain,
% 2.87/3.05 (r(s(s(z)), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[437, 15745])).
% 2.87/3.05 tff(15747,plain,
% 2.87/3.05 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[2687, 15740, 4228])).
% 2.87/3.05 tff(15748,plain,
% 2.87/3.05 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[5794, 15747, 1960, 15746])).
% 2.87/3.05 tff(15749,plain,
% 2.87/3.05 (b(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[58, 15748])).
% 2.87/3.05 tff(15750,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[212, 15749, 15742, 15493, 204])).
% 2.87/3.05 tff(15751,plain,((~r(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(15752,plain,
% 2.87/3.05 (~r(s(s(s(z))), s(z))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15751, 204, 1960, 1, 1300, 81])).
% 2.87/3.05 tff(15753,plain,
% 2.87/3.05 (b(s(s(s(z))), s(z))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1358, 15752])).
% 2.87/3.05 tff(15754,plain,
% 2.87/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(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(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(15755,plain,
% 2.87/3.05 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(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), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(15756,plain,
% 2.87/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $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(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), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[15755])).
% 2.87/3.05 tff(15757,plain,
% 2.87/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $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(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), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.87/3.05 inference(transitivity,[status(thm)],[15756, 15754])).
% 2.87/3.05 tff(15758,plain,
% 2.87/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.87/3.05 inference(quant_inst,[status(thm)],[])).
% 2.87/3.05 tff(15759,plain,
% 2.87/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[15758, 15757])).
% 2.87/3.05 tff(15760,plain,
% 2.87/3.05 (~b(s(s(z)), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15759, 97, 15493, 15738, 15753])).
% 2.87/3.05 tff(15761,plain,
% 2.87/3.05 (r(s(s(z)), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[437, 15760])).
% 2.87/3.05 tff(15762,plain,
% 2.87/3.05 (~b(s(s(z)), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15759, 97, 15493, 15738, 1360])).
% 2.87/3.05 tff(15763,plain,
% 2.87/3.05 (r(s(s(z)), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[437, 15762])).
% 2.87/3.05 tff(15764,plain,
% 2.87/3.05 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[14661, 83, 204])).
% 2.87/3.05 tff(15765,plain,
% 2.87/3.05 (r(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[58, 15764])).
% 2.87/3.05 tff(15766,plain,
% 2.87/3.05 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[5794, 15765, 1960, 15763])).
% 2.87/3.05 tff(15767,plain,
% 2.87/3.05 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[2687, 15766, 4228])).
% 2.87/3.05 tff(15768,plain,
% 2.87/3.05 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15082, 15053, 1960, 15765])).
% 2.87/3.05 tff(15769,plain,
% 2.87/3.05 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[3089, 15768, 1])).
% 2.87/3.05 tff(15770,plain,
% 2.87/3.05 (~b(s(s(s(z))), z)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[14941, 15769, 204])).
% 2.87/3.05 tff(15771,plain,
% 2.87/3.05 (r(s(s(s(z))), z)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[402, 15770])).
% 2.87/3.05 tff(15772,plain,
% 2.87/3.05 (~r(s(z), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1308, 15771, 81, 1300])).
% 2.87/3.05 tff(15773,plain,
% 2.87/3.05 (b(s(z), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[253, 15772])).
% 2.87/3.05 tff(15774,plain,
% 2.87/3.05 (~b(s(z), s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[11923, 15773, 1360, 15767])).
% 2.87/3.05 tff(15775,plain,
% 2.87/3.05 (r(s(z), s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[181, 15774])).
% 2.87/3.05 tff(15776,plain,
% 2.87/3.05 (~r(z, s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[11807, 15775, 125])).
% 2.87/3.05 tff(15777,plain,
% 2.87/3.05 (b(z, s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[590, 15776])).
% 2.87/3.05 tff(15778,plain,
% 2.87/3.05 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[7701])).
% 2.87/3.05 tff(15779,plain,
% 2.87/3.05 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[15778])).
% 2.87/3.05 tff(15780,plain,
% 2.87/3.05 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[286, 15779])).
% 2.87/3.05 tff(15781,plain,
% 2.87/3.05 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[349, 15780])).
% 2.87/3.05 tff(15782,plain,
% 2.87/3.05 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 2.87/3.05 inference(symmetry,[status(thm)],[7700])).
% 2.87/3.05 tff(15783,plain,
% 2.87/3.05 (s(s(elem!1)) = s(s(s(z)))),
% 2.87/3.05 inference(transitivity,[status(thm)],[167, 15782, 63])).
% 2.87/3.05 tff(15784,plain,
% 2.87/3.05 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[15783])).
% 2.87/3.05 tff(15785,plain,
% 2.87/3.05 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.87/3.05 inference(symmetry,[status(thm)],[15784])).
% 2.87/3.05 tff(15786,plain,
% 2.87/3.05 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[1702, 15785])).
% 2.87/3.05 tff(15787,plain,
% 2.87/3.05 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[15783])).
% 2.87/3.05 tff(15788,plain,
% 2.87/3.05 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.87/3.05 inference(symmetry,[status(thm)],[15787])).
% 2.87/3.05 tff(15789,plain,
% 2.87/3.05 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[5941, 15788])).
% 2.87/3.05 tff(15790,plain,
% 2.87/3.05 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 2.87/3.05 inference(monotonicity,[status(thm)],[7701])).
% 2.87/3.05 tff(15791,plain,
% 2.87/3.05 (r(s(s(elem!1)), z)),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[15045, 15790])).
% 2.87/3.05 tff(15792,plain,
% 2.87/3.05 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[7701])).
% 2.87/3.05 tff(15793,plain,
% 2.87/3.05 (r(z, s(s(elem!1)))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[1300, 15792])).
% 2.87/3.05 tff(15794,plain,
% 2.87/3.05 ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[3290, 14660])).
% 2.87/3.05 tff(15795,plain,
% 2.87/3.05 (~b(s(s(s(s(elem!1)))), z)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15794, 473, 124])).
% 2.87/3.05 tff(15796,plain,
% 2.87/3.05 (r(s(s(s(s(elem!1)))), z)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[842, 15795])).
% 2.87/3.05 tff(15797,plain,
% 2.87/3.05 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[8941, 473, 1529, 2391])).
% 2.87/3.05 tff(15798,plain,
% 2.87/3.05 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1484, 15797, 347])).
% 2.87/3.05 tff(15799,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[7685, 15798, 15796, 7676, 7677])).
% 2.87/3.05 tff(15800,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(15801,plain,
% 2.87/3.05 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15800, 15793, 15791, 15780, 15789, 15786, 124])).
% 2.87/3.05 tff(15802,plain,
% 2.87/3.05 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[486, 15801, 15781])).
% 2.87/3.05 tff(15803,plain,
% 2.87/3.05 (~r(s(z), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1308, 15045, 81, 1300])).
% 2.87/3.05 tff(15804,plain,
% 2.87/3.05 (b(s(z), s(s(s(z))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[253, 15803])).
% 2.87/3.05 tff(15805,plain,
% 2.87/3.05 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[5279, 309, 145, 488])).
% 2.87/3.05 tff(15806,plain,
% 2.87/3.05 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[452, 15805])).
% 2.87/3.05 tff(15807,plain,
% 2.87/3.05 (~b(s(s(s(s(elem!1)))), z)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[4806, 15806, 87, 204])).
% 2.87/3.05 tff(15808,plain,
% 2.87/3.05 (r(s(s(s(s(elem!1)))), z)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[842, 15807])).
% 2.87/3.05 tff(15809,plain,
% 2.87/3.05 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[349, 347])).
% 2.87/3.05 tff(15810,plain,
% 2.87/3.05 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[523, 15809])).
% 2.87/3.05 tff(15811,plain,
% 2.87/3.05 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[12643, 309, 224, 488])).
% 2.87/3.05 tff(15812,plain,
% 2.87/3.05 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[821, 15811, 15810])).
% 2.87/3.05 tff(15813,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[8342, 97, 1545, 1529, 805, 2391])).
% 2.87/3.05 tff(15814,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(15815,plain,
% 2.87/3.05 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15814, 15812, 1529, 2391])).
% 2.87/3.05 tff(15816,plain,
% 2.87/3.05 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[1484, 15815, 347])).
% 2.87/3.05 tff(15817,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[7685, 15816, 15808, 7676, 7677])).
% 2.87/3.05 tff(15818,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~r(s(s(z)), 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(z))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(15819,plain,
% 2.87/3.05 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15818, 15802, 15791, 15780, 15789, 15786, 87, 204, 224, 15793, 145])).
% 2.87/3.05 tff(15820,plain,
% 2.87/3.05 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[336, 15819])).
% 2.87/3.05 tff(15821,plain,
% 2.87/3.05 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[5023, 15820, 87, 15804])).
% 2.87/3.05 tff(15822,plain,
% 2.87/3.05 (r(s(s(s(s(elem!1)))), s(z))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[511, 15821])).
% 2.87/3.05 tff(15823,plain,
% 2.87/3.05 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[5023, 339, 87, 86])).
% 2.87/3.05 tff(15824,plain,
% 2.87/3.05 (r(s(s(s(s(elem!1)))), s(z))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[511, 15823])).
% 2.87/3.05 tff(15825,plain,
% 2.87/3.05 (~b(s(s(s(s(elem!1)))), z)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[3812, 339, 535, 255])).
% 2.87/3.05 tff(15826,plain,
% 2.87/3.05 (r(s(s(s(s(elem!1)))), z)),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[842, 15825])).
% 2.87/3.05 tff(15827,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[11568, 15826, 15824, 81])).
% 2.87/3.05 tff(15828,plain,((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(15829,plain,
% 2.87/3.05 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15828, 15820, 535, 81, 87, 15804])).
% 2.87/3.05 tff(15830,plain,
% 2.87/3.05 (r(s(z), s(s(s(s(elem!1)))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[280, 15829])).
% 2.87/3.05 tff(15831,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[503, 15830, 15822, 125, 15802])).
% 2.87/3.05 tff(15832,plain,((~(s(s(s(s(z)))) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(15833,plain,
% 2.87/3.05 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15832, 15053, 15738, 81, 15493, 204, 125, 15765, 15777, 15767, 15769, 1300])).
% 2.87/3.05 tff(15834,plain,
% 2.87/3.05 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[7644, 155, 125, 225, 13308])).
% 2.87/3.05 tff(15835,plain,
% 2.87/3.05 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[7637, 53, 7634, 15834])).
% 2.87/3.05 tff(15836,plain,
% 2.87/3.05 (~r(z, s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[11807, 225, 125])).
% 2.87/3.05 tff(15837,plain,
% 2.87/3.05 (b(z, s(s(s(elem!1))))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[590, 15836])).
% 2.87/3.05 tff(15838,plain,
% 2.87/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(15839,plain,
% 2.87/3.05 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(15840,plain,
% 2.87/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 2.87/3.05 inference(monotonicity,[status(thm)],[15839])).
% 2.87/3.05 tff(15841,plain,
% 2.87/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.87/3.05 inference(transitivity,[status(thm)],[15840, 15838])).
% 2.87/3.05 tff(15842,plain,
% 2.87/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 2.87/3.05 inference(quant_inst,[status(thm)],[])).
% 2.87/3.05 tff(15843,plain,
% 2.87/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 2.87/3.05 inference(modus_ponens,[status(thm)],[15842, 15841])).
% 2.87/3.05 tff(15844,plain,
% 2.87/3.05 ($false),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15843, 97, 14660, 15837, 13316, 15835])).
% 2.87/3.05 tff(15845,plain,((~r(s(s(s(s(z)))), s(z))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.05 tff(15846,plain,
% 2.87/3.05 (~r(s(s(s(s(z)))), s(z))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[15845, 15833, 81, 125, 15775])).
% 2.87/3.05 tff(15847,plain,
% 2.87/3.05 (b(s(s(s(s(z)))), s(z))),
% 2.87/3.05 inference(unit_resolution,[status(thm)],[13335, 15846])).
% 2.87/3.05 tff(15848,plain,
% 2.87/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(15849,plain,
% 2.87/3.05 (((~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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.05 inference(rewrite,[status(thm)],[])).
% 2.87/3.05 tff(15850,plain,
% 2.87/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[15849])).
% 2.87/3.06 tff(15851,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.06 inference(transitivity,[status(thm)],[15850, 15848])).
% 2.87/3.06 tff(15852,plain,
% 2.87/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $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)))))))),
% 2.87/3.06 inference(quant_inst,[status(thm)],[])).
% 2.87/3.06 tff(15853,plain,
% 2.87/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[15852, 15851])).
% 2.87/3.06 tff(15854,plain,
% 2.87/3.06 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[15853, 97, 15493, 15738, 15847])).
% 2.87/3.06 tff(15855,plain,
% 2.87/3.06 (b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[4192, 2595])).
% 2.87/3.06 tff(15856,plain,
% 2.87/3.06 (r(s(s(z)), s(s(s(s(z)))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[15855, 15854])).
% 2.87/3.06 tff(15857,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $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(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(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(15858,plain,
% 2.87/3.06 (((~b(s(z), s(s(z)))) | (~b(s(z), 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(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(15859,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $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(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(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[15858])).
% 2.87/3.06 tff(15860,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $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(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(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.87/3.06 inference(transitivity,[status(thm)],[15859, 15857])).
% 2.87/3.06 tff(15861,plain,
% 2.87/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.87/3.06 inference(quant_inst,[status(thm)],[])).
% 2.87/3.06 tff(15862,plain,
% 2.87/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $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(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[15861, 15860])).
% 2.87/3.06 tff(15863,plain,
% 2.87/3.06 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[15862, 97, 15738, 1360, 15847])).
% 2.87/3.06 tff(15864,plain,
% 2.87/3.06 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[2829, 15863])).
% 2.87/3.06 tff(15865,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(15866,plain,
% 2.87/3.06 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(15867,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[15866])).
% 2.87/3.06 tff(15868,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.06 inference(transitivity,[status(thm)],[15867, 15865])).
% 2.87/3.06 tff(15869,plain,
% 2.87/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $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(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.06 inference(quant_inst,[status(thm)],[])).
% 2.87/3.06 tff(15870,plain,
% 2.87/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[15869, 15868])).
% 2.87/3.06 tff(15871,plain,
% 2.87/3.06 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[15870, 97, 204, 83, 15493, 15738, 15847])).
% 2.87/3.06 tff(15872,plain,
% 2.87/3.06 (r(s(s(s(s(z)))), s(s(z)))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[13323, 15871])).
% 2.87/3.06 tff(15873,plain,
% 2.87/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(15874,plain,
% 2.87/3.06 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(15875,plain,
% 2.87/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[15874])).
% 2.87/3.06 tff(15876,plain,
% 2.87/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.87/3.06 inference(transitivity,[status(thm)],[15875, 15873])).
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% 2.87/3.06 inference(quant_inst,[status(thm)],[])).
% 2.87/3.06 tff(15878,plain,
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% 2.87/3.06 inference(modus_ponens,[status(thm)],[15877, 15876])).
% 2.87/3.06 tff(15879,plain,
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% 2.87/3.06 inference(unit_resolution,[status(thm)],[15878, 155, 1960, 15872, 15864, 15856])).
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% 2.87/3.06 tff(15881,plain,
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% 2.87/3.06 inference(unit_resolution,[status(thm)],[625, 15881])).
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% 2.87/3.06 inference(unit_resolution,[status(thm)],[402, 15883])).
% 2.87/3.06 tff(15885,plain,
% 2.87/3.06 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[14941, 15884, 204])).
% 2.87/3.06 tff(15886,plain,
% 2.87/3.06 (~b(s(s(s(elem!1))), s(s(s(z))))),
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% 2.87/3.06 tff(15887,plain,
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% 2.87/3.06 tff(15888,plain,
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% 2.87/3.06 inference(unit_resolution,[status(thm)],[590, 15887])).
% 2.87/3.06 tff(15889,plain,
% 2.87/3.06 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[2687, 15886, 4228])).
% 2.87/3.06 tff(15890,plain,
% 2.87/3.06 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[5794, 15889, 1960, 15763])).
% 2.87/3.06 tff(15891,plain,
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% 2.87/3.06 inference(unit_resolution,[status(thm)],[58, 15890])).
% 2.87/3.06 tff(15892,plain,
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% 2.87/3.06 inference(unit_resolution,[status(thm)],[212, 15891, 15888, 15493, 204])).
% 2.87/3.06 tff(15893,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.06 tff(15894,plain,
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% 2.87/3.06 inference(unit_resolution,[status(thm)],[15893, 15753, 1960, 1, 1300, 81, 204])).
% 2.87/3.06 tff(15895,plain,
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% 2.87/3.06 inference(unit_resolution,[status(thm)],[493, 15894])).
% 2.87/3.06 tff(15896,plain,
% 2.87/3.06 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[11487, 97, 15895, 15738, 15753])).
% 2.87/3.06 tff(15897,plain,
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% 2.87/3.06 inference(unit_resolution,[status(thm)],[2687, 15896, 4228])).
% 2.87/3.06 tff(15898,plain,
% 2.87/3.06 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[14277, 97, 15895, 15493, 15738])).
% 2.87/3.06 tff(15899,plain,
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% 2.87/3.06 tff(15902,plain,
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% 2.87/3.06 inference(unit_resolution,[status(thm)],[1969, 15903, 1300, 1960])).
% 2.87/3.06 tff(15905,plain,
% 2.87/3.06 (b(s(s(z)), s(s(s(z))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[437, 15904])).
% 2.87/3.06 tff(15906,plain,
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% 2.87/3.06 tff(15907,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.06 tff(15908,plain,
% 2.87/3.06 (~b(s(s(s(z))), s(z))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[15907, 15905, 15738, 15493])).
% 2.87/3.06 tff(15909,plain,
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% 2.87/3.06 inference(unit_resolution,[status(thm)],[1358, 15908])).
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% 2.87/3.06 inference(unit_resolution,[status(thm)],[14376, 15909, 1300])).
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% 2.87/3.06 tff(15912,plain,
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% 2.87/3.06 tff(15917,plain,
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% 2.87/3.06 tff(15953,plain,
% 2.87/3.06 (r(s(z), s(s(s(elem!1))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[181, 15952])).
% 2.87/3.06 tff(15954,plain,
% 2.87/3.06 (~r(s(s(s(z))), s(z))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[13262, 15953, 1300, 570])).
% 2.87/3.06 tff(15955,plain,
% 2.87/3.06 (b(s(s(s(z))), s(z))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1358, 15954])).
% 2.87/3.06 tff(15956,plain,
% 2.87/3.06 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[14372, 15955, 15738, 1139])).
% 2.87/3.06 tff(15957,plain,
% 2.87/3.06 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[5852, 15956, 1, 1300, 570])).
% 2.87/3.06 tff(15958,plain,
% 2.87/3.06 ($false),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[11487, 97, 1139, 15738, 15955, 15957])).
% 2.87/3.06 tff(15959,plain,((~b(s(s(s(elem!1))), s(z))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.06 tff(15960,plain,
% 2.87/3.06 ($false),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[15959, 15951, 15946, 1300, 1, 15938])).
% 2.87/3.06 tff(15961,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.06 tff(15962,plain,
% 2.87/3.06 (~r(s(s(s(z))), s(z))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[15961, 1300, 1])).
% 2.87/3.06 tff(15963,plain,
% 2.87/3.06 (b(s(s(s(z))), s(z))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1358, 15962])).
% 2.87/3.06 tff(15964,plain,
% 2.87/3.06 (~b(s(s(s(z))), s(s(z)))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[14035, 15963, 15493, 15926])).
% 2.87/3.06 tff(15965,plain,
% 2.87/3.06 (r(s(s(s(z))), s(s(z)))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[421, 15964])).
% 2.87/3.06 tff(15966,plain,
% 2.87/3.06 (~b(s(s(z)), s(s(s(z))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[15907, 15963, 15738, 15493])).
% 2.87/3.06 tff(15967,plain,
% 2.87/3.06 (r(s(s(z)), s(s(s(z))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[437, 15966])).
% 2.87/3.06 tff(15968,plain,
% 2.87/3.06 ($false),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1969, 15967, 15965, 1300, 15928])).
% 2.87/3.06 tff(15969,plain,((~r(z, s(s(s(z))))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.06 tff(15970,plain,
% 2.87/3.06 (~r(z, s(s(s(z))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[15969, 1])).
% 2.87/3.06 tff(15971,plain,
% 2.87/3.06 (b(z, s(s(s(z))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[1318, 15970])).
% 2.87/3.06 tff(15972,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $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))), s(z))) | (~b(s(s(s(elem!1))), 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(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(15973,plain,
% 2.87/3.06 (((~b(z, s(s(s(z))))) | (~b(z, s(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(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))))),
% 2.87/3.06 inference(rewrite,[status(thm)],[])).
% 2.87/3.06 tff(15974,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z)))))))),
% 2.87/3.06 inference(monotonicity,[status(thm)],[15973])).
% 2.87/3.06 tff(15975,plain,
% 2.87/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z))))))),
% 2.87/3.06 inference(transitivity,[status(thm)],[15974, 15972])).
% 2.87/3.06 tff(15976,plain,
% 2.87/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.87/3.06 inference(quant_inst,[status(thm)],[])).
% 2.87/3.06 tff(15977,plain,
% 2.87/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(z)))))),
% 2.87/3.06 inference(modus_ponens,[status(thm)],[15976, 15975])).
% 2.87/3.06 tff(15978,plain,
% 2.87/3.06 ($false),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[15977, 97, 1139, 550, 14660, 1330])).
% 2.87/3.06 tff(15979,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.06 tff(15980,plain,
% 2.87/3.06 (~b(s(s(s(elem!1))), s(z))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[15979, 15497, 1330])).
% 2.87/3.06 tff(15981,plain,
% 2.87/3.06 (r(s(s(s(elem!1))), s(z))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[493, 15980])).
% 2.87/3.06 tff(15982,plain,
% 2.87/3.06 (~b(s(z), s(s(s(elem!1))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[5860, 97, 15497, 14660, 1330])).
% 2.87/3.06 tff(15983,plain,
% 2.87/3.06 (r(s(z), s(s(s(elem!1))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[181, 15982])).
% 2.87/3.06 tff(15984,plain,
% 2.87/3.06 ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[4316, 11419])).
% 2.87/3.06 tff(15985,plain,
% 2.87/3.06 ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[15984, 14660])).
% 2.87/3.06 tff(15986,plain,
% 2.87/3.06 (~b(s(s(z)), z)),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[15985, 15983, 3, 15981])).
% 2.87/3.06 tff(15987,plain,
% 2.87/3.06 (~r(z, s(s(s(elem!1))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[11807, 15983, 15981])).
% 2.87/3.06 tff(15988,plain,
% 2.87/3.06 (~r(s(s(z)), z)),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[15699, 15987, 87, 3, 15981])).
% 2.87/3.06 tff(15989,plain,
% 2.87/3.06 ($false),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[625, 15988, 15986])).
% 2.87/3.06 tff(15990,plain,((~r(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.06 tff(15991,plain,
% 2.87/3.06 (~r(s(z), s(s(z)))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[15990, 15493, 15971])).
% 2.87/3.06 tff(15992,plain,
% 2.87/3.06 (b(s(z), s(s(z)))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[548, 15991])).
% 2.87/3.06 tff(15993,plain,
% 2.87/3.06 (~b(s(s(z)), z)),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[2972, 550, 15971, 15992])).
% 2.87/3.06 tff(15994,plain,
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% 2.87/3.06 inference(unit_resolution,[status(thm)],[625, 15993])).
% 2.87/3.06 tff(15995,plain,
% 2.87/3.06 (~b(s(s(s(elem!1))), s(z))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[15979, 550, 15971])).
% 2.87/3.06 tff(15996,plain,
% 2.87/3.06 (~b(z, s(s(z)))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[3966, 550, 15493, 15992])).
% 2.87/3.06 tff(15997,plain,
% 2.87/3.06 (r(z, s(s(z)))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[222, 15996])).
% 2.87/3.06 tff(15998,plain,
% 2.87/3.06 (r(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[14025, 15997, 15493, 15992, 550, 15995, 15994])).
% 2.87/3.06 tff(15999,plain,
% 2.87/3.06 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[14981, 1331, 1330])).
% 2.87/3.06 tff(16000,plain,
% 2.87/3.06 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[2687, 15999, 2466])).
% 2.87/3.06 tff(16001,plain,
% 2.87/3.06 (~b(s(s(s(elem!1))), s(z))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[15979, 550, 1330])).
% 2.87/3.06 tff(16002,plain,
% 2.87/3.06 (r(s(s(s(elem!1))), s(z))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[493, 16001])).
% 2.87/3.06 tff(16003,plain,
% 2.87/3.06 (~b(s(s(s(z))), s(z))),
% 2.87/3.06 inference(unit_resolution,[status(thm)],[14035, 1331, 87, 550])).
% 2.87/3.07 tff(16004,plain,
% 2.87/3.07 (r(s(s(s(z))), s(z))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[1358, 16003])).
% 2.87/3.07 tff(16005,plain,
% 2.87/3.07 (~b(s(z), s(s(s(z))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[7835, 1331, 1330, 550])).
% 2.87/3.07 tff(16006,plain,
% 2.87/3.07 (r(s(z), s(s(s(z))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[253, 16005])).
% 2.87/3.07 tff(16007,plain,
% 2.87/3.07 ($false),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[2638, 16006, 16004, 16002, 16000])).
% 2.87/3.07 tff(16008,plain,((~b(s(s(s(z))), s(s(z)))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.07 tff(16009,plain,
% 2.87/3.07 (~b(s(s(s(z))), s(s(z)))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[16008, 550, 15971, 4228, 15493])).
% 2.87/3.07 tff(16010,plain,
% 2.87/3.07 (r(s(s(s(z))), s(s(z)))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[421, 16009])).
% 2.87/3.07 tff(16011,plain,
% 2.87/3.07 (r(s(s(s(elem!1))), s(z))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[493, 15995])).
% 2.87/3.07 tff(16012,plain,
% 2.87/3.07 (~r(s(s(s(z))), s(z))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[6049, 16010, 16011, 1, 15997, 15998])).
% 2.87/3.07 tff(16013,plain,
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% 2.87/3.07 inference(unit_resolution,[status(thm)],[1358, 16012])).
% 2.87/3.07 tff(16014,plain,
% 2.87/3.07 (~b(s(s(z)), s(s(s(z))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[15907, 16013, 15992, 15493])).
% 2.87/3.07 tff(16015,plain,
% 2.87/3.07 (r(s(s(z)), s(s(s(z))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[437, 16014])).
% 2.87/3.07 tff(16016,plain,
% 2.87/3.07 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[5794, 16015, 16010, 15998])).
% 2.87/3.07 tff(16017,plain,
% 2.87/3.07 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[2687, 16016, 4228])).
% 2.87/3.07 tff(16018,plain,
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% 2.87/3.07 inference(unit_resolution,[status(thm)],[6467, 16010, 15997, 15994])).
% 2.87/3.07 tff(16019,plain,
% 2.87/3.07 (b(s(s(s(z))), z)),
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% 2.87/3.07 tff(16020,plain,
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% 2.87/3.07 inference(unit_resolution,[status(thm)],[14974, 97, 14660, 15971, 16019, 16017])).
% 2.87/3.07 tff(16021,plain,((~b(s(z), z)) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.07 tff(16022,plain,
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% 2.87/3.07 inference(unit_resolution,[status(thm)],[16021, 1])).
% 2.87/3.07 tff(16023,plain,
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% 2.87/3.07 tff(16024,plain,
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% 2.87/3.07 inference(unit_resolution,[status(thm)],[4580, 155, 11419, 16023, 2597])).
% 2.87/3.07 tff(16025,plain,
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% 2.87/3.07 tff(16026,plain,
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% 2.87/3.07 inference(unit_resolution,[status(thm)],[15371, 97, 14660, 15971, 16025])).
% 2.87/3.07 tff(16027,plain,
% 2.87/3.07 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[3089, 16026, 1])).
% 2.87/3.07 tff(16028,plain,
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% 2.87/3.07 inference(unit_resolution,[status(thm)],[14974, 97, 14660, 15971, 16025])).
% 2.87/3.07 tff(16029,plain,
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% 2.87/3.07 inference(unit_resolution,[status(thm)],[2687, 16028, 4228])).
% 2.87/3.07 tff(16030,plain,
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% 2.87/3.07 inference(unit_resolution,[status(thm)],[15990, 87, 1330])).
% 2.87/3.07 tff(16031,plain,
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% 2.87/3.07 inference(unit_resolution,[status(thm)],[548, 16030])).
% 2.87/3.07 tff(16032,plain,
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% 2.87/3.07 inference(unit_resolution,[status(thm)],[14269, 97, 1139, 87, 16031])).
% 2.87/3.07 tff(16033,plain,
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% 2.87/3.07 inference(unit_resolution,[status(thm)],[143, 16032])).
% 2.87/3.07 tff(16034,plain,
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% 2.87/3.07 inference(unit_resolution,[status(thm)],[14277, 97, 1139, 87, 16031])).
% 2.87/3.07 tff(16035,plain,
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% 2.87/3.07 inference(unit_resolution,[status(thm)],[58, 16034])).
% 2.87/3.07 tff(16036,plain,
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% 2.87/3.07 inference(unit_resolution,[status(thm)],[15082, 16033, 4252, 16035])).
% 2.87/3.07 tff(16037,plain,
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% 2.87/3.07 inference(unit_resolution,[status(thm)],[421, 16036])).
% 2.87/3.07 tff(16038,plain,
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% 2.87/3.07 inference(unit_resolution,[status(thm)],[14286, 16037, 87, 81])).
% 2.87/3.07 tff(16039,plain,
% 2.87/3.07 (r(z, s(s(z)))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[222, 16038])).
% 2.87/3.07 tff(16040,plain,
% 2.87/3.07 (~r(z, s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[5182, 155, 16039, 16035, 16033])).
% 2.87/3.07 tff(16041,plain,
% 2.87/3.07 (b(z, s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[590, 16040])).
% 2.87/3.07 tff(16042,plain,
% 2.87/3.07 (~b(s(z), s(s(s(z))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[8990, 97, 87, 16031, 16037])).
% 2.87/3.07 tff(16043,plain,
% 2.87/3.07 (r(s(z), s(s(s(z))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[253, 16042])).
% 2.87/3.07 tff(16044,plain,
% 2.87/3.07 (~r(s(z), s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[10628, 155, 16043, 2630, 4252])).
% 2.87/3.07 tff(16045,plain,
% 2.87/3.07 (b(s(z), s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[181, 16044])).
% 2.87/3.07 tff(16046,plain,
% 2.87/3.07 (r(s(s(s(s(elem!1)))), z)),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[842, 834])).
% 2.87/3.07 tff(16047,plain,
% 2.87/3.07 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[11568, 16046, 81])).
% 2.87/3.07 tff(16048,plain,
% 2.87/3.07 (b(s(s(s(s(elem!1)))), s(z))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[511, 16047])).
% 2.87/3.07 tff(16049,plain,
% 2.87/3.07 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[2129, 16048, 535, 1139])).
% 2.87/3.07 tff(16050,plain,
% 2.87/3.07 ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[5614, 14660])).
% 2.87/3.07 tff(16051,plain,
% 2.87/3.07 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[16050, 16049, 87, 1139, 193, 16048])).
% 2.87/3.07 tff(16052,plain,
% 2.87/3.07 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.87/3.07 inference(monotonicity,[status(thm)],[16051])).
% 2.87/3.07 tff(16053,plain,
% 2.87/3.07 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(elem!1))), z)),
% 2.87/3.07 inference(symmetry,[status(thm)],[16052])).
% 2.87/3.07 tff(16054,plain,
% 2.87/3.07 ((~b(s(s(s(s(elem!1)))), z)) <=> (~b(s(s(s(elem!1))), z))),
% 2.87/3.07 inference(monotonicity,[status(thm)],[16053])).
% 2.87/3.07 tff(16055,plain,
% 2.87/3.07 (~b(s(s(s(elem!1))), z)),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[834, 16054])).
% 2.87/3.07 tff(16056,plain,
% 2.87/3.07 ($false),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[14660, 16055])).
% 2.87/3.07 tff(16057,plain,(b(s(s(s(s(elem!1)))), 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(z), s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.07 tff(16058,plain,
% 2.87/3.07 (b(s(s(s(s(elem!1)))), z)),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[16057, 1139, 87, 16045, 16031, 81])).
% 2.87/3.07 tff(16059,plain,
% 2.87/3.07 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[15794, 16058, 16041])).
% 2.87/3.07 tff(16060,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.87/3.07 inference(rewrite,[status(thm)],[])).
% 2.87/3.07 tff(16061,plain,
% 2.87/3.07 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.87/3.07 inference(rewrite,[status(thm)],[])).
% 2.87/3.07 tff(16062,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), 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(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.87/3.07 inference(monotonicity,[status(thm)],[16061])).
% 2.87/3.07 tff(16063,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), 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(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.87/3.07 inference(transitivity,[status(thm)],[16062, 16060])).
% 2.87/3.07 tff(16064,plain,
% 2.87/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.87/3.07 inference(quant_inst,[status(thm)],[])).
% 2.87/3.07 tff(16065,plain,
% 2.87/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[16064, 16063])).
% 2.87/3.07 tff(16066,plain,
% 2.87/3.07 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[16065, 97, 16041, 16058, 14263])).
% 2.87/3.07 tff(16067,plain,
% 2.87/3.07 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[2747, 16066])).
% 2.87/3.07 tff(16068,plain,
% 2.87/3.07 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[2703, 155, 16067, 16043, 2597])).
% 2.87/3.07 tff(16069,plain,
% 2.87/3.07 (b(s(s(s(s(elem!1)))), s(z))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[511, 16068])).
% 2.87/3.07 tff(16070,plain,
% 2.87/3.07 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[16050, 16069, 87, 1139, 16045, 16059])).
% 2.87/3.07 tff(16071,plain,
% 2.87/3.07 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[349, 16070])).
% 2.87/3.07 tff(16072,plain,
% 2.87/3.07 (s(s(s(s(elem!1)))) = elem!1),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[1734, 16071])).
% 2.87/3.07 tff(16073,plain,
% 2.87/3.07 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[12801, 97, 1139, 16045, 14660, 16041, 16058])).
% 2.87/3.07 tff(16074,plain,
% 2.87/3.07 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[14812, 155, 16067, 2630, 4252])).
% 2.87/3.07 tff(16075,plain,
% 2.87/3.07 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[821, 16074, 16073])).
% 2.87/3.07 tff(16076,plain,
% 2.87/3.07 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.87/3.07 inference(symmetry,[status(thm)],[16075])).
% 2.87/3.07 tff(16077,plain,
% 2.87/3.07 (s(s(s(elem!1))) = elem!1),
% 2.87/3.07 inference(transitivity,[status(thm)],[16076, 16072])).
% 2.87/3.07 tff(16078,plain,
% 2.87/3.07 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), elem!1)),
% 2.87/3.07 inference(monotonicity,[status(thm)],[16077])).
% 2.87/3.07 tff(16079,plain,
% 2.87/3.07 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.87/3.07 inference(symmetry,[status(thm)],[16078])).
% 2.87/3.07 tff(16080,plain,
% 2.87/3.07 (~(s(s(s(s(z)))) = elem!1)),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[2786, 16070])).
% 2.87/3.07 tff(16081,plain,
% 2.87/3.07 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), elem!1)),
% 2.87/3.07 inference(monotonicity,[status(thm)],[16077])).
% 2.87/3.07 tff(16082,plain,
% 2.87/3.07 ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 2.87/3.07 inference(monotonicity,[status(thm)],[16081])).
% 2.87/3.07 tff(16083,plain,
% 2.87/3.07 ($false),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[15446, 14439, 13316, 1330, 1331])).
% 2.87/3.07 tff(16084,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.07 tff(16085,plain,
% 2.87/3.07 (~r(s(s(s(s(z)))), s(z))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[16084, 16037, 1330, 16043, 2597, 81])).
% 2.87/3.07 tff(16086,plain,
% 2.87/3.07 (b(s(s(s(s(z)))), s(z))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[13335, 16085])).
% 2.87/3.07 tff(16087,plain,
% 2.87/3.07 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[10346, 97, 1139, 16045, 16086])).
% 2.87/3.07 tff(16088,plain,
% 2.87/3.07 (~b(s(s(s(s(z)))), elem!1)),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[16087, 16082])).
% 2.87/3.07 tff(16089,plain,
% 2.87/3.07 (r(s(s(s(s(z)))), elem!1)),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[2873, 16088, 16080])).
% 2.87/3.07 tff(16090,plain,
% 2.87/3.07 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[16089, 16079])).
% 2.87/3.07 tff(16091,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $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(s(z)), s(z))) | (~b(s(s(s(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(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.07 inference(rewrite,[status(thm)],[])).
% 2.87/3.07 tff(16092,plain,
% 2.87/3.07 (((~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(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.07 inference(rewrite,[status(thm)],[])).
% 2.87/3.07 tff(16093,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $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(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(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.87/3.07 inference(monotonicity,[status(thm)],[16092])).
% 2.87/3.07 tff(16094,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $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(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(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.07 inference(transitivity,[status(thm)],[16093, 16091])).
% 2.87/3.07 tff(16095,plain,
% 2.87/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.07 inference(quant_inst,[status(thm)],[])).
% 2.87/3.07 tff(16096,plain,
% 2.87/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[16095, 16094])).
% 2.87/3.07 tff(16097,plain,
% 2.87/3.07 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[16096, 97, 16045, 87, 16086])).
% 2.87/3.07 tff(16098,plain,
% 2.87/3.07 (r(s(s(s(s(z)))), s(s(z)))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[13323, 16097])).
% 2.87/3.07 tff(16099,plain,
% 2.87/3.07 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[10339, 155, 16035, 16033, 16098])).
% 2.87/3.07 tff(16100,plain,
% 2.87/3.07 ($false),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[16099, 16090])).
% 2.87/3.07 tff(16101,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.07 tff(16102,plain,
% 2.87/3.07 (~b(s(s(s(elem!1))), s(z))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[16101, 2597, 15971, 15493, 16023, 16029, 16027])).
% 2.87/3.07 tff(16103,plain,
% 2.87/3.07 (r(s(s(s(elem!1))), s(z))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[493, 16102])).
% 2.87/3.07 tff(16104,plain,
% 2.87/3.07 (~r(s(z), s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[5757, 16103, 2597, 16027])).
% 2.87/3.07 tff(16105,plain,
% 2.87/3.07 (b(s(z), s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[181, 16104])).
% 2.87/3.07 tff(16106,plain,
% 2.87/3.07 (~r(s(z), s(s(s(z))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[2638, 16103, 2597, 16029])).
% 2.87/3.07 tff(16107,plain,
% 2.87/3.07 (b(s(z), s(s(s(z))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[253, 16106])).
% 2.87/3.07 tff(16108,plain,
% 2.87/3.07 (~b(s(s(z)), s(s(s(z))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[4270, 16107, 15992, 16025])).
% 2.87/3.07 tff(16109,plain,
% 2.87/3.07 (r(s(s(z)), s(s(s(z))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[437, 16108])).
% 2.87/3.07 tff(16110,plain,
% 2.87/3.07 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[8834, 155, 16103, 16109, 2597, 16029])).
% 2.87/3.07 tff(16111,plain,
% 2.87/3.07 (b(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[58, 16110])).
% 2.87/3.07 tff(16112,plain,
% 2.87/3.07 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[5749, 155, 16109, 16029, 16027])).
% 2.87/3.07 tff(16113,plain,
% 2.87/3.07 (b(s(s(z)), s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[143, 16112])).
% 2.87/3.07 tff(16114,plain,
% 2.87/3.07 ($false),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[14693, 16113, 16111, 15992, 16105])).
% 2.87/3.07 tff(16115,plain,((~r(s(s(s(z))), s(z))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.07 tff(16116,plain,
% 2.87/3.07 (~r(s(s(s(z))), s(z))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[16115, 1])).
% 2.87/3.07 tff(16117,plain,
% 2.87/3.07 (b(s(s(s(z))), s(z))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[1358, 16116])).
% 2.87/3.07 tff(16118,plain,
% 2.87/3.07 (~b(s(s(z)), s(s(s(z))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[15907, 16117, 15992, 15493])).
% 2.87/3.07 tff(16119,plain,
% 2.87/3.07 (r(s(s(z)), s(s(s(z))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[437, 16118])).
% 2.87/3.07 tff(16120,plain,
% 2.87/3.07 (((~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(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.87/3.07 inference(rewrite,[status(thm)],[])).
% 2.87/3.07 tff(16121,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.87/3.07 inference(monotonicity,[status(thm)],[16120])).
% 2.87/3.07 tff(16122,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.87/3.07 inference(transitivity,[status(thm)],[16121, 3497])).
% 2.87/3.07 tff(16123,plain,
% 2.87/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $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)))))),
% 2.87/3.07 inference(quant_inst,[status(thm)],[])).
% 2.87/3.07 tff(16124,plain,
% 2.87/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[16123, 16122])).
% 2.87/3.07 tff(16125,plain,
% 2.87/3.07 (~b(s(s(s(z))), s(s(z)))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[16124, 97, 15493, 15992, 16117])).
% 2.87/3.07 tff(16126,plain,
% 2.87/3.07 (r(s(s(s(z))), s(s(z)))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[421, 16125])).
% 2.87/3.07 tff(16127,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.87/3.07 inference(rewrite,[status(thm)],[])).
% 2.87/3.07 tff(16128,plain,
% 2.87/3.07 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.87/3.07 inference(rewrite,[status(thm)],[])).
% 2.87/3.07 tff(16129,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), s(s(s(z))))) | (~b(z, s(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))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.87/3.07 inference(monotonicity,[status(thm)],[16128])).
% 2.87/3.07 tff(16130,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), s(s(s(z))))) | (~b(z, s(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))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.87/3.07 inference(transitivity,[status(thm)],[16129, 16127])).
% 2.87/3.07 tff(16131,plain,
% 2.87/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z)))),
% 2.87/3.07 inference(quant_inst,[status(thm)],[])).
% 2.87/3.07 tff(16132,plain,
% 2.87/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[16131, 16130])).
% 2.87/3.07 tff(16133,plain,
% 2.87/3.07 ($false),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[16132, 97, 14660, 1360, 1330, 5941])).
% 2.87/3.07 tff(16134,plain,((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.07 tff(16135,plain,
% 2.87/3.07 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[16134, 16117, 15971])).
% 2.87/3.07 tff(16136,plain,
% 2.87/3.07 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[2687, 16135, 4228])).
% 2.87/3.07 tff(16137,plain,
% 2.87/3.07 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[5794, 16136, 16126, 16119])).
% 2.87/3.07 tff(16138,plain,
% 2.87/3.07 (b(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[58, 16137])).
% 2.87/3.07 tff(16139,plain,
% 2.87/3.07 (((~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(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.87/3.07 inference(rewrite,[status(thm)],[])).
% 2.87/3.07 tff(16140,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 2.87/3.07 inference(monotonicity,[status(thm)],[16139])).
% 2.87/3.07 tff(16141,plain,
% 2.87/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.87/3.07 inference(transitivity,[status(thm)],[16140, 14272])).
% 2.87/3.07 tff(16142,plain,
% 2.87/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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))))),
% 2.87/3.07 inference(quant_inst,[status(thm)],[])).
% 2.87/3.07 tff(16143,plain,
% 2.87/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 2.87/3.07 inference(modus_ponens,[status(thm)],[16142, 16141])).
% 2.87/3.07 tff(16144,plain,
% 2.87/3.07 (~b(s(s(s(elem!1))), s(z))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[16143, 97, 16138, 15493, 15992])).
% 2.87/3.07 tff(16145,plain,
% 2.87/3.07 (r(s(s(s(elem!1))), s(z))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[493, 16144])).
% 2.87/3.07 tff(16146,plain,
% 2.87/3.07 (~b(s(z), s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[5699, 97, 60, 15493, 15992])).
% 2.87/3.07 tff(16147,plain,
% 2.87/3.07 (r(s(z), s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[181, 16146])).
% 2.87/3.07 tff(16148,plain,
% 2.87/3.07 (~r(z, s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[11807, 16147, 125])).
% 2.87/3.07 tff(16149,plain,
% 2.87/3.07 (b(z, s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[590, 16148])).
% 2.87/3.07 tff(16150,plain,
% 2.87/3.07 ($false),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[4312, 97, 14660, 124, 60, 83])).
% 2.87/3.07 tff(16151,plain,((~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.07 tff(16152,plain,
% 2.87/3.07 (~b(s(s(z)), z)),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[16151, 16149, 60])).
% 2.87/3.07 tff(16153,plain,
% 2.87/3.07 (r(s(s(z)), z)),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[625, 16152])).
% 2.87/3.07 tff(16154,plain,
% 2.87/3.07 (~r(s(s(s(z))), z)),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[6467, 16153, 16126, 226])).
% 2.87/3.07 tff(16155,plain,
% 2.87/3.07 (b(s(s(s(z))), z)),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[402, 16154])).
% 2.87/3.07 tff(16156,plain,
% 2.87/3.07 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[5733, 97, 14660, 16149, 16155])).
% 2.87/3.07 tff(16157,plain,
% 2.87/3.07 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.87/3.07 inference(unit_resolution,[status(thm)],[3089, 16156, 1])).
% 2.87/3.07 tff(16158,plain,
% 2.87/3.07 ($false),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[5741, 97, 126, 124, 1216, 5941])).
% 2.87/3.08 tff(16159,plain,((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.08 tff(16160,plain,
% 2.87/3.08 ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[16159, 14660])).
% 2.87/3.08 tff(16161,plain,
% 2.87/3.08 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[16160, 16155, 16149])).
% 2.87/3.08 tff(16162,plain,
% 2.87/3.08 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[2687, 16161, 4228])).
% 2.87/3.08 tff(16163,plain,
% 2.87/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.87/3.08 inference(rewrite,[status(thm)],[])).
% 2.87/3.08 tff(16164,plain,
% 2.87/3.08 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.87/3.08 inference(rewrite,[status(thm)],[])).
% 2.87/3.08 tff(16165,plain,
% 2.87/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), 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(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[16164])).
% 2.87/3.08 tff(16166,plain,
% 2.87/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), 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(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.87/3.08 inference(transitivity,[status(thm)],[16165, 16163])).
% 2.87/3.08 tff(16167,plain,
% 2.87/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.87/3.08 inference(quant_inst,[status(thm)],[])).
% 2.87/3.08 tff(16168,plain,
% 2.87/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[16167, 16166])).
% 2.87/3.08 tff(16169,plain,
% 2.87/3.08 ($false),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[16168, 97, 14660, 60, 83, 87, 86, 1330])).
% 2.87/3.08 tff(16170,plain,((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.08 tff(16171,plain,
% 2.87/3.08 (~b(s(s(z)), z)),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[16170, 86, 15493, 60, 15971])).
% 2.87/3.08 tff(16172,plain,
% 2.87/3.08 (r(s(s(z)), z)),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[625, 16171])).
% 2.87/3.08 tff(16173,plain,
% 2.87/3.08 (~r(s(s(s(z))), z)),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[6467, 16172, 16126, 226])).
% 2.87/3.08 tff(16174,plain,
% 2.87/3.08 (b(s(s(s(z))), z)),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[402, 16173])).
% 2.87/3.08 tff(16175,plain,
% 2.87/3.08 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[15371, 97, 14660, 15971, 16174])).
% 2.87/3.08 tff(16176,plain,
% 2.87/3.08 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[3089, 16175, 1])).
% 2.87/3.08 tff(16177,plain,
% 2.87/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.87/3.08 inference(rewrite,[status(thm)],[])).
% 2.87/3.08 tff(16178,plain,
% 2.87/3.08 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.87/3.08 inference(rewrite,[status(thm)],[])).
% 2.87/3.08 tff(16179,plain,
% 2.87/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[16178])).
% 2.87/3.08 tff(16180,plain,
% 2.87/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.87/3.08 inference(transitivity,[status(thm)],[16179, 16177])).
% 2.87/3.08 tff(16181,plain,
% 2.87/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.87/3.08 inference(quant_inst,[status(thm)],[])).
% 2.87/3.08 tff(16182,plain,
% 2.87/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[16181, 16180])).
% 2.87/3.08 tff(16183,plain,
% 2.87/3.08 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[16182, 97, 14660, 16117, 86, 15971, 16174])).
% 2.87/3.08 tff(16184,plain,
% 2.87/3.08 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[2687, 16183, 4228])).
% 2.87/3.08 tff(16185,plain,
% 2.87/3.08 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[5749, 155, 16119, 16184, 16176])).
% 2.87/3.08 tff(16186,plain,
% 2.87/3.08 (b(s(s(z)), s(s(s(elem!1))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[143, 16185])).
% 2.87/3.08 tff(16187,plain,
% 2.87/3.08 (~b(s(z), s(s(s(elem!1))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[14693, 16186, 15992, 60])).
% 2.87/3.08 tff(16188,plain,
% 2.87/3.08 (r(s(z), s(s(s(elem!1))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[181, 16187])).
% 2.87/3.08 tff(16189,plain,
% 2.87/3.08 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[15853, 97, 87, 535, 10217])).
% 2.87/3.08 tff(16190,plain,
% 2.87/3.08 (r(s(s(z)), s(s(s(s(z)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[15855, 16189])).
% 2.87/3.08 tff(16191,plain,
% 2.87/3.08 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[15862, 97, 535, 1360, 10217])).
% 2.87/3.08 tff(16192,plain,
% 2.87/3.08 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[2829, 16191])).
% 2.87/3.08 tff(16193,plain,
% 2.87/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(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(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.08 inference(rewrite,[status(thm)],[])).
% 2.87/3.08 tff(16194,plain,
% 2.87/3.08 (((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.08 inference(rewrite,[status(thm)],[])).
% 2.87/3.08 tff(16195,plain,
% 2.87/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $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(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~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(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[16194])).
% 2.87/3.08 tff(16196,plain,
% 2.87/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $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(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~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(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.08 inference(transitivity,[status(thm)],[16195, 16193])).
% 2.87/3.08 tff(16197,plain,
% 2.87/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.08 inference(quant_inst,[status(thm)],[])).
% 2.87/3.08 tff(16198,plain,
% 2.87/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[16197, 16196])).
% 2.87/3.08 tff(16199,plain,
% 2.87/3.08 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[16198, 97, 60, 87, 535, 127, 10217])).
% 2.87/3.08 tff(16200,plain,
% 2.87/3.08 (r(s(s(s(s(z)))), s(s(z)))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[13323, 16199])).
% 2.87/3.08 tff(16201,plain,
% 2.87/3.08 (~b(s(s(s(z))), s(s(z)))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[16124, 97, 87, 535, 1360])).
% 2.87/3.08 tff(16202,plain,
% 2.87/3.08 (r(s(s(s(z))), s(s(z)))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[421, 16201])).
% 2.87/3.08 tff(16203,plain,
% 2.87/3.08 ($false),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[15878, 155, 16202, 16200, 16192, 16190])).
% 2.87/3.08 tff(16204,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.08 tff(16205,plain,
% 2.87/3.08 (~b(s(s(s(s(z)))), s(z))),
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% 2.87/3.08 tff(16206,plain,
% 2.87/3.08 (r(s(s(s(s(z)))), s(z))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[13335, 16205])).
% 2.87/3.08 tff(16207,plain,
% 2.87/3.08 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[15845, 16206, 16023, 125, 16188])).
% 2.87/3.08 tff(16208,plain,
% 2.87/3.08 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[16207])).
% 2.87/3.08 tff(16209,plain,
% 2.87/3.08 (s(s(s(z))) = s(s(elem!1))),
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% 2.87/3.08 tff(16210,plain,
% 2.87/3.08 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[16209])).
% 2.87/3.08 tff(16211,plain,
% 2.87/3.08 (s(s(z)) = s(elem!1)),
% 2.87/3.08 inference(transitivity,[status(thm)],[73, 16210, 29])).
% 2.87/3.08 tff(16212,plain,
% 2.87/3.08 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[16211, 16209])).
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% 2.87/3.08 (r(s(elem!1), s(s(elem!1)))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[16119, 16212])).
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% 2.87/3.08 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[16211])).
% 2.87/3.08 tff(16215,plain,
% 2.87/3.08 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[16209])).
% 2.87/3.08 tff(16216,plain,
% 2.87/3.08 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[16215])).
% 2.87/3.08 tff(16217,plain,
% 2.87/3.08 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[286, 16216])).
% 2.87/3.08 tff(16218,plain,
% 2.87/3.08 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[349, 16217])).
% 2.87/3.08 tff(16219,plain,
% 2.87/3.08 (~r(z, s(s(s(elem!1))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[11807, 16188, 125])).
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% 2.87/3.08 (b(z, s(s(s(elem!1))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[590, 16219])).
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% 2.87/3.08 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 2.87/3.08 inference(monotonicity,[status(thm)],[16211])).
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% 2.87/3.08 inference(modus_ponens,[status(thm)],[16172, 16221])).
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% 2.87/3.08 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 2.87/3.08 inference(symmetry,[status(thm)],[16208])).
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% 2.87/3.08 inference(transitivity,[status(thm)],[167, 16223, 63])).
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% 2.87/3.08 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[16224])).
% 2.87/3.08 tff(16226,plain,
% 2.87/3.08 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.87/3.08 inference(symmetry,[status(thm)],[16225])).
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% 2.87/3.08 inference(modus_ponens,[status(thm)],[16184, 16226])).
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% 2.87/3.08 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[16224])).
% 2.87/3.08 tff(16229,plain,
% 2.87/3.08 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
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% 2.87/3.08 tff(16230,plain,
% 2.87/3.08 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[16176, 16229])).
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% 2.87/3.08 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[523, 15781])).
% 2.87/3.08 tff(16232,plain,
% 2.87/3.08 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[10668])).
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% 2.87/3.08 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[5023, 11585, 87, 86])).
% 2.87/3.08 tff(16234,plain,
% 2.87/3.08 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[336, 16233])).
% 2.87/3.08 tff(16235,plain,
% 2.87/3.08 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[16234, 16232])).
% 2.87/3.08 tff(16236,plain,
% 2.87/3.08 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[4887, 463, 81, 824])).
% 2.87/3.08 tff(16237,plain,
% 2.87/3.08 (b(s(z), s(s(s(s(elem!1)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[280, 16236])).
% 2.87/3.08 tff(16238,plain,
% 2.87/3.08 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[10998, 16237, 1360, 11585])).
% 2.87/3.08 tff(16239,plain,
% 2.87/3.08 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[2747, 16238])).
% 2.87/3.08 tff(16240,plain,
% 2.87/3.08 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[7707, 16239, 7699])).
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% 2.87/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)))),
% 2.87/3.08 inference(rewrite,[status(thm)],[])).
% 2.87/3.08 tff(16242,plain,
% 2.87/3.08 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)))),
% 2.87/3.08 inference(rewrite,[status(thm)],[])).
% 2.87/3.08 tff(16243,plain,
% 2.87/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), z))))),
% 2.87/3.08 inference(monotonicity,[status(thm)],[16242])).
% 2.87/3.08 tff(16244,plain,
% 2.87/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)))),
% 2.87/3.08 inference(transitivity,[status(thm)],[16243, 16241])).
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% 2.87/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)))),
% 2.87/3.08 inference(quant_inst,[status(thm)],[])).
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% 2.87/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), z))),
% 2.87/3.08 inference(modus_ponens,[status(thm)],[16245, 16244])).
% 2.87/3.08 tff(16247,plain,
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% 2.87/3.08 inference(unit_resolution,[status(thm)],[16246, 155, 16240, 463, 15159, 1912, 8103])).
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% 2.87/3.08 tff(16249,plain,
% 2.87/3.08 (~r(z, s(s(s(s(elem!1)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[16248, 16235, 15159, 8103, 7699, 1360, 81, 824])).
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% 2.87/3.08 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[914, 14660])).
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% 2.87/3.08 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
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% 2.87/3.08 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
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% 2.87/3.08 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
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% 2.87/3.08 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
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% 2.87/3.08 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
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% 2.87/3.08 tff(16259,plain,
% 2.87/3.08 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
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% 2.87/3.08 tff(16260,plain,
% 2.87/3.08 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
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% 2.87/3.08 tff(16261,plain,
% 2.87/3.08 ($false),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[4688, 155, 16260, 4497, 6277, 823])).
% 2.87/3.08 tff(16262,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(s(s(s(s(z)))) = s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.08 tff(16263,plain,
% 2.87/3.08 ($false),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[16262, 16255, 16253, 6277, 7699, 1360, 11585, 225, 4497])).
% 2.87/3.08 tff(16264,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(s(s(s(s(z)))) = s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.08 tff(16265,plain,
% 2.87/3.08 (~r(s(s(s(s(elem!1)))), z)),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[16264, 16230, 16207, 16117, 16188, 16227, 16220, 16222, 16213, 16023, 15493, 86])).
% 2.87/3.08 tff(16266,plain,
% 2.87/3.08 (b(s(s(s(s(elem!1)))), z)),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[842, 16265])).
% 2.87/3.08 tff(16267,plain,
% 2.87/3.08 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[15794, 16266, 16220])).
% 2.87/3.08 tff(16268,plain,
% 2.87/3.08 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[486, 16267, 16218])).
% 2.87/3.08 tff(16269,plain,
% 2.87/3.08 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[523, 16218])).
% 2.87/3.08 tff(16270,plain,
% 2.87/3.08 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[821, 3295, 802])).
% 2.87/3.08 tff(16271,plain,
% 2.87/3.08 (~b(z, s(s(s(s(elem!1)))))),
% 2.87/3.08 inference(unit_resolution,[status(thm)],[16251, 16270, 15837])).
% 2.87/3.08 tff(16272,plain,
% 2.87/3.08 (r(z, s(s(s(s(elem!1)))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1093, 16271])).
% 2.87/3.09 tff(16273,plain,
% 2.87/3.09 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[15828, 3025, 535, 81, 87, 86])).
% 2.87/3.09 tff(16274,plain,
% 2.87/3.09 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[336, 16273])).
% 2.87/3.09 tff(16275,plain,
% 2.87/3.09 ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[12838, 11419])).
% 2.87/3.09 tff(16276,plain,
% 2.87/3.09 ($false),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[16275, 16274, 16272, 226, 495])).
% 2.87/3.09 tff(16277,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.09 tff(16278,plain,
% 2.87/3.09 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[16277, 86, 15992, 16023, 15493, 226, 16269, 125, 16268, 16188])).
% 2.87/3.09 tff(16279,plain,
% 2.87/3.09 (b(s(s(s(s(elem!1)))), s(z))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[511, 16278])).
% 2.87/3.09 tff(16280,plain,
% 2.87/3.09 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[5023, 16279, 15493, 86])).
% 2.87/3.09 tff(16281,plain,
% 2.87/3.09 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[336, 16280])).
% 2.87/3.09 tff(16282,plain,
% 2.87/3.09 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[16281, 16214])).
% 2.87/3.09 tff(16283,plain,
% 2.87/3.09 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[16262, 16279, 16230, 16207, 16117, 16268, 16188, 16227])).
% 2.87/3.09 tff(16284,plain,
% 2.87/3.09 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[821, 16283, 16269])).
% 2.87/3.09 tff(16285,plain,
% 2.87/3.09 (~b(z, s(s(s(s(elem!1)))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[16251, 16284, 16220])).
% 2.87/3.09 tff(16286,plain,
% 2.87/3.09 (r(z, s(s(s(s(elem!1)))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1093, 16285])).
% 2.87/3.09 tff(16287,plain,
% 2.87/3.09 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[16209])).
% 2.87/3.09 tff(16288,plain,
% 2.87/3.09 (b(z, s(s(elem!1)))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[15971, 16287])).
% 2.87/3.09 tff(16289,plain,
% 2.87/3.09 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[16211])).
% 2.87/3.09 tff(16290,plain,
% 2.87/3.09 (s(z) = elem!1),
% 2.87/3.09 inference(transitivity,[status(thm)],[24, 16289, 85])).
% 2.87/3.09 tff(16291,plain,
% 2.87/3.09 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 2.87/3.09 inference(monotonicity,[status(thm)],[16209, 16290])).
% 2.87/3.09 tff(16292,plain,
% 2.87/3.09 (b(s(s(elem!1)), elem!1)),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[16117, 16291])).
% 2.87/3.09 tff(16293,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 2.87/3.09 tff(16294,plain,
% 2.87/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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)))), z)) | (~b(z, s(s(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(s(s(elem!1)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.87/3.09 inference(rewrite,[status(thm)],[])).
% 2.87/3.09 tff(16295,plain,
% 2.87/3.09 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), 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(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.87/3.09 inference(rewrite,[status(thm)],[])).
% 2.87/3.09 tff(16296,plain,
% 2.87/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(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(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[16295])).
% 2.87/3.09 tff(16297,plain,
% 2.87/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(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(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.87/3.09 inference(transitivity,[status(thm)],[16296, 16294])).
% 2.87/3.09 tff(16298,plain,
% 2.87/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(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)))),
% 2.87/3.09 inference(quant_inst,[status(thm)],[])).
% 2.87/3.09 tff(16299,plain,
% 2.87/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[16298, 16297])).
% 2.87/3.09 tff(16300,plain,
% 2.87/3.09 ($false),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[16299, 97, 1545, 1915, 876, 16293])).
% 2.87/3.09 tff(16301,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.09 tff(16302,plain,
% 2.87/3.09 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[16301, 16292, 16266, 16288])).
% 2.87/3.09 tff(16303,plain,
% 2.87/3.09 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[1484, 16302, 16217])).
% 2.87/3.09 tff(16304,plain,
% 2.87/3.09 ($false),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[16246, 155, 16303, 16286, 16222, 16282, 16213])).
% 2.87/3.09 tff(16305,plain,((~b(s(z), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.09 tff(16306,plain,
% 2.87/3.09 (~b(s(z), s(s(s(z))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[16305, 60, 125, 226, 1])).
% 2.87/3.09 tff(16307,plain,
% 2.87/3.09 (r(s(z), s(s(s(z))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[253, 16306])).
% 2.87/3.09 tff(16308,plain,
% 2.87/3.09 ($false),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[10628, 155, 16307, 16147, 16162, 16157])).
% 2.87/3.09 tff(16309,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.09 tff(16310,plain,
% 2.87/3.09 (~r(z, s(s(z)))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[16309, 16145, 1, 16138])).
% 2.87/3.09 tff(16311,plain,
% 2.87/3.09 (b(z, s(s(z)))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[222, 16310])).
% 2.87/3.09 tff(16312,plain,
% 2.87/3.09 (~b(s(z), s(s(s(elem!1))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[5699, 97, 16138, 15493, 15992])).
% 2.87/3.09 tff(16313,plain,
% 2.87/3.09 (r(s(z), s(s(s(elem!1))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[181, 16312])).
% 2.87/3.09 tff(16314,plain,
% 2.87/3.09 (~r(z, s(s(s(elem!1))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[11807, 16313, 16145])).
% 2.87/3.09 tff(16315,plain,
% 2.87/3.09 (b(z, s(s(s(elem!1))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[590, 16314])).
% 2.87/3.09 tff(16316,plain,
% 2.87/3.09 ($false),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[212, 16315, 16311, 15493, 16138])).
% 2.87/3.09 tff(16317,plain,(s(s(s(z))) = s(s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.09 tff(16318,plain,
% 2.87/3.09 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 2.87/3.09 inference(monotonicity,[status(thm)],[16317])).
% 2.87/3.09 tff(16319,plain,
% 2.87/3.09 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 2.87/3.09 inference(symmetry,[status(thm)],[16318])).
% 2.87/3.09 tff(16320,plain,
% 2.87/3.09 (b(s(s(s(z))), z)),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[14660, 16319])).
% 2.87/3.09 tff(16321,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
% 2.87/3.09 tff(16322,plain,
% 2.87/3.09 ($false),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[16321, 16320])).
% 2.87/3.09 tff(16323,plain,(b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 2.87/3.09 tff(16324,plain,
% 2.87/3.09 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[11529, 16317])).
% 2.87/3.09 tff(16325,plain,
% 2.87/3.09 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[16324])).
% 2.87/3.09 tff(16326,plain,
% 2.87/3.09 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.87/3.09 inference(symmetry,[status(thm)],[16325])).
% 2.87/3.09 tff(16327,plain,
% 2.87/3.09 (s(s(z)) = s(s(elem!1))),
% 2.87/3.09 inference(transitivity,[status(thm)],[73, 16326, 19])).
% 2.87/3.09 tff(16328,plain,
% 2.87/3.09 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[16324])).
% 2.87/3.09 tff(16329,plain,
% 2.87/3.09 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[16328])).
% 2.87/3.09 tff(16330,plain,
% 2.87/3.09 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 2.87/3.09 inference(symmetry,[status(thm)],[16329])).
% 2.87/3.09 tff(16331,plain,
% 2.87/3.09 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[16330, 16327])).
% 2.87/3.09 tff(16332,plain,
% 2.87/3.09 (b(s(s(s(s(s(elem!1))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 2.87/3.09 inference(symmetry,[status(thm)],[16331])).
% 2.87/3.09 tff(16333,plain,
% 2.87/3.09 ((s(s(z)) = s(s(s(s(s(elem!1)))))) <=> (s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[16327])).
% 2.87/3.09 tff(16334,plain,
% 2.87/3.09 ((s(s(z)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.87/3.09 inference(transitivity,[status(thm)],[16333, 11819])).
% 2.87/3.09 tff(16335,plain,
% 2.87/3.09 ((~(s(s(z)) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[16334])).
% 2.87/3.09 tff(16336,plain,
% 2.87/3.09 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[13386, 16335])).
% 2.87/3.09 tff(16337,plain,
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% 2.87/3.09 inference(monotonicity,[status(thm)],[16330, 16327])).
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% 2.87/3.09 inference(monotonicity,[status(thm)],[16337])).
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% 2.87/3.09 inference(monotonicity,[status(thm)],[16330])).
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% 2.87/3.09 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
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% 2.87/3.09 inference(unit_resolution,[status(thm)],[6222, 16317])).
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% 2.87/3.09 inference(monotonicity,[status(thm)],[16330])).
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% 2.87/3.09 tff(16347,plain,
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% 2.87/3.09 tff(16353,plain,
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% 2.87/3.09 tff(16363,plain,
% 2.87/3.09 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | r(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)))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[5608, 11419])).
% 2.87/3.09 tff(16364,plain,
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% 2.87/3.09 tff(16365,plain,
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% 2.87/3.09 inference(unit_resolution,[status(thm)],[6197, 16364, 16317])).
% 2.87/3.09 tff(16366,plain,
% 2.87/3.09 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[7544, 16365])).
% 2.87/3.09 tff(16367,plain,
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% 2.87/3.09 inference(unit_resolution,[status(thm)],[1995, 14882, 16317])).
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% 2.87/3.09 (~b(s(s(s(s(z)))), s(s(s(z))))),
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% 2.87/3.09 tff(16370,plain,
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% 2.87/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $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(elem!1)))))) | (~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(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.87/3.09 inference(rewrite,[status(thm)],[])).
% 2.87/3.09 tff(16372,plain,
% 2.87/3.09 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.87/3.09 inference(rewrite,[status(thm)],[])).
% 2.87/3.09 tff(16373,plain,
% 2.87/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $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(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[16372])).
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% 2.87/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $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(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.87/3.09 inference(transitivity,[status(thm)],[16373, 16371])).
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% 2.87/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $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(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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)))))))),
% 2.87/3.09 inference(quant_inst,[status(thm)],[])).
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% 2.87/3.09 inference(modus_ponens,[status(thm)],[16375, 16374])).
% 2.87/3.09 tff(16377,plain,
% 2.87/3.09 (~b(s(s(s(z))), s(s(s(s(z)))))),
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% 2.87/3.09 tff(16378,plain,
% 2.87/3.09 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[2829, 16377])).
% 2.87/3.09 tff(16379,plain,
% 2.87/3.09 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[16330])).
% 2.87/3.09 tff(16380,plain,
% 2.87/3.09 (r(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.87/3.09 inference(symmetry,[status(thm)],[16379])).
% 2.87/3.09 tff(16381,plain,
% 2.87/3.09 (~(s(s(s(s(s(elem!1))))) = s(s(s(z))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[7491, 16317])).
% 2.87/3.09 tff(16382,plain,
% 2.87/3.09 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[16330])).
% 2.87/3.09 tff(16383,plain,
% 2.87/3.09 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[16382])).
% 2.87/3.09 tff(16384,assumption,(b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
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% 2.87/3.09 inference(rewrite,[status(thm)],[])).
% 2.87/3.09 tff(16386,plain,
% 2.87/3.09 (((~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(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.87/3.09 inference(rewrite,[status(thm)],[])).
% 2.87/3.09 tff(16387,plain,
% 2.87/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $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(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[16386])).
% 2.87/3.09 tff(16388,plain,
% 2.87/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $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(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.87/3.09 inference(transitivity,[status(thm)],[16387, 16385])).
% 2.87/3.09 tff(16389,plain,
% 2.87/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.87/3.09 inference(quant_inst,[status(thm)],[])).
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% 2.87/3.09 inference(modus_ponens,[status(thm)],[16389, 16388])).
% 2.87/3.09 tff(16391,plain,
% 2.87/3.09 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[16390, 97, 1360, 86])).
% 2.87/3.09 tff(16392,plain,
% 2.87/3.09 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
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% 2.87/3.09 tff(16393,plain,
% 2.87/3.09 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[16392, 16383])).
% 2.87/3.09 tff(16394,plain,
% 2.87/3.09 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.87/3.09 inference(unit_resolution,[status(thm)],[6289, 16393, 16381])).
% 2.87/3.09 tff(16395,plain,
% 2.87/3.09 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.87/3.09 inference(modus_ponens,[status(thm)],[16394, 16380])).
% 2.87/3.09 tff(16396,plain,
% 2.87/3.09 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.87/3.09 inference(symmetry,[status(thm)],[16328])).
% 2.87/3.09 tff(16397,plain,
% 2.87/3.09 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[16330, 16396])).
% 2.87/3.09 tff(16398,plain,
% 2.87/3.09 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.87/3.09 inference(symmetry,[status(thm)],[16397])).
% 2.87/3.09 tff(16399,plain,
% 2.87/3.09 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[16330, 16396])).
% 2.87/3.09 tff(16400,plain,
% 2.87/3.09 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.87/3.09 inference(monotonicity,[status(thm)],[16399])).
% 2.87/3.09 tff(16401,plain,
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% 2.87/3.09 inference(rewrite,[status(thm)],[])).
% 2.87/3.09 tff(16402,plain,
% 2.87/3.09 (((~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(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.87/3.09 inference(rewrite,[status(thm)],[])).
% 2.87/3.09 tff(16403,plain,
% 2.87/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $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(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16402])).
% 2.87/3.10 tff(16404,plain,
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% 2.87/3.10 inference(transitivity,[status(thm)],[16403, 16401])).
% 2.87/3.10 tff(16405,plain,
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% 2.87/3.10 inference(quant_inst,[status(thm)],[])).
% 2.87/3.10 tff(16406,plain,
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% 2.87/3.10 inference(modus_ponens,[status(thm)],[16405, 16404])).
% 2.87/3.10 tff(16407,plain,
% 2.87/3.10 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[16406, 97, 86, 10217])).
% 2.87/3.10 tff(16408,plain,
% 2.87/3.10 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[16407, 16384])).
% 2.87/3.10 tff(16409,plain,
% 2.87/3.10 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[16408, 16400])).
% 2.87/3.10 tff(16410,plain,
% 2.87/3.10 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[6254, 16409, 6243])).
% 2.87/3.10 tff(16411,plain,
% 2.87/3.10 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[16410, 16398])).
% 2.87/3.10 tff(16412,plain,
% 2.87/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(16413,plain,
% 2.87/3.10 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(16414,plain,
% 2.87/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16413])).
% 2.87/3.10 tff(16415,plain,
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% 2.87/3.10 inference(transitivity,[status(thm)],[16414, 16412])).
% 2.87/3.10 tff(16416,plain,
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% 2.87/3.10 inference(quant_inst,[status(thm)],[])).
% 2.87/3.10 tff(16417,plain,
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% 2.87/3.10 inference(modus_ponens,[status(thm)],[16416, 16415])).
% 2.87/3.10 tff(16418,plain,
% 2.87/3.10 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[16417, 155, 15472, 15471])).
% 2.87/3.10 tff(16419,plain,
% 2.87/3.10 ($false),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[16418, 16411, 16395])).
% 2.87/3.10 tff(16420,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (s(s(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(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.10 tff(16421,plain,
% 2.87/3.10 (~b(s(s(s(s(s(z))))), s(z))),
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% 2.87/3.10 tff(16422,plain,
% 2.87/3.10 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[16421, 16343])).
% 2.87/3.10 tff(16423,plain,
% 2.87/3.10 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[6239, 16422, 16341])).
% 2.87/3.10 tff(16424,plain,
% 2.87/3.10 (r(s(s(s(s(s(z))))), s(z))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[16423, 16340])).
% 2.87/3.10 tff(16425,plain,
% 2.87/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(16426,plain,
% 2.87/3.10 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(16427,plain,
% 2.87/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16426])).
% 2.87/3.10 tff(16428,plain,
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% 2.87/3.10 inference(transitivity,[status(thm)],[16427, 16425])).
% 2.87/3.10 tff(16429,plain,
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% 2.87/3.10 inference(quant_inst,[status(thm)],[])).
% 2.87/3.10 tff(16430,plain,
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% 2.87/3.10 inference(modus_ponens,[status(thm)],[16429, 16428])).
% 2.87/3.10 tff(16431,plain,
% 2.87/3.10 ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[16430, 155, 2, 3])).
% 2.87/3.10 tff(16432,plain,
% 2.87/3.10 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[16431, 16424])).
% 2.87/3.10 tff(16433,plain,
% 2.87/3.10 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[16432, 16338])).
% 2.87/3.10 tff(16434,plain,
% 2.87/3.10 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[6269, 16433, 16336])).
% 2.87/3.10 tff(16435,plain,
% 2.87/3.10 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[16434, 16332])).
% 2.87/3.10 tff(16436,plain,
% 2.87/3.10 (s(s(elem!1)) = s(s(z))),
% 2.87/3.10 inference(transitivity,[status(thm)],[167, 16325, 72])).
% 2.87/3.10 tff(16437,plain,
% 2.87/3.10 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16436])).
% 2.87/3.10 tff(16438,plain,
% 2.87/3.10 (s(elem!1) = s(z)),
% 2.87/3.10 inference(transitivity,[status(thm)],[30, 16437, 23])).
% 2.87/3.10 tff(16439,plain,
% 2.87/3.10 (inj_0(s(elem!1)) = inj_0(s(z))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16438])).
% 2.87/3.10 tff(16440,plain,
% 2.87/3.10 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.87/3.10 inference(symmetry,[status(thm)],[16439])).
% 2.87/3.10 tff(16441,plain,
% 2.87/3.10 (z = elem!1),
% 2.87/3.10 inference(transitivity,[status(thm)],[1443, 16440, 85])).
% 2.87/3.10 tff(16442,plain,
% 2.87/3.10 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16330, 16441])).
% 2.87/3.10 tff(16443,plain,
% 2.87/3.10 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(z))))), z)),
% 2.87/3.10 inference(symmetry,[status(thm)],[16442])).
% 2.87/3.10 tff(16444,plain,
% 2.87/3.10 ((z = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = z)),
% 2.87/3.10 inference(commutativity,[status(thm)],[])).
% 2.87/3.10 tff(16445,plain,
% 2.87/3.10 (elem!1 = z),
% 2.87/3.10 inference(transitivity,[status(thm)],[1450, 16439, 17])).
% 2.87/3.10 tff(16446,plain,
% 2.87/3.10 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (z = s(s(s(s(s(z))))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16445, 16329])).
% 2.87/3.10 tff(16447,plain,
% 2.87/3.10 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(z))))) = z)),
% 2.87/3.10 inference(transitivity,[status(thm)],[16446, 16444])).
% 2.87/3.10 tff(16448,plain,
% 2.87/3.10 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 2.87/3.10 inference(symmetry,[status(thm)],[16447])).
% 2.87/3.10 tff(16449,plain,
% 2.87/3.10 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.87/3.10 inference(transitivity,[status(thm)],[16448, 6293])).
% 2.87/3.10 tff(16450,plain,
% 2.87/3.10 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16449])).
% 2.87/3.10 tff(16451,plain,
% 2.87/3.10 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 2.87/3.10 inference(quant_inst,[status(thm)],[])).
% 2.87/3.10 tff(16452,plain,
% 2.87/3.10 (~(s(s(s(s(s(z))))) = z)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[16451, 38])).
% 2.87/3.10 tff(16453,plain,
% 2.87/3.10 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[16452, 16450])).
% 2.87/3.10 tff(16454,plain,
% 2.87/3.10 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16330, 16441])).
% 2.87/3.10 tff(16455,plain,
% 2.87/3.10 ((~r(s(s(s(s(s(z))))), z)) <=> (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16454])).
% 2.87/3.10 tff(16456,plain,
% 2.87/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(16457,plain,
% 2.87/3.10 (((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(16458,plain,
% 2.87/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16457])).
% 2.87/3.10 tff(16459,plain,
% 2.87/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.87/3.10 inference(transitivity,[status(thm)],[16458, 16456])).
% 2.87/3.10 tff(16460,plain,
% 2.87/3.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.87/3.10 inference(quant_inst,[status(thm)],[])).
% 2.87/3.10 tff(16461,plain,
% 2.87/3.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[16460, 16459])).
% 2.87/3.10 tff(16462,plain,
% 2.87/3.10 ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[16461, 155, 11419, 16351])).
% 2.87/3.10 tff(16463,plain,
% 2.87/3.10 (~r(s(s(s(s(s(z))))), z)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[16462, 16424])).
% 2.87/3.10 tff(16464,plain,
% 2.87/3.10 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[16463, 16455])).
% 2.87/3.10 tff(16465,plain,
% 2.87/3.10 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[6313, 16464, 16453])).
% 2.87/3.10 tff(16466,plain,
% 2.87/3.10 (b(s(s(s(s(s(z))))), z)),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[16465, 16443])).
% 2.87/3.10 tff(16467,plain,
% 2.87/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), 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(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(16468,plain,
% 2.87/3.10 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.87/3.10 inference(rewrite,[status(thm)],[])).
% 2.87/3.10 tff(16469,plain,
% 2.87/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16468])).
% 2.87/3.10 tff(16470,plain,
% 2.87/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.87/3.10 inference(transitivity,[status(thm)],[16469, 16467])).
% 2.87/3.10 tff(16471,plain,
% 2.87/3.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.87/3.10 inference(quant_inst,[status(thm)],[])).
% 2.87/3.10 tff(16472,plain,
% 2.87/3.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[16471, 16470])).
% 2.87/3.10 tff(16473,plain,
% 2.87/3.10 ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[16472, 97, 11429, 16355])).
% 2.87/3.10 tff(16474,plain,
% 2.87/3.10 ($false),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[16473, 16466, 16435])).
% 2.87/3.10 tff(16475,plain,((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.10 tff(16476,plain,
% 2.87/3.10 (~r(s(z), s(s(z)))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[16475, 2])).
% 2.87/3.10 tff(16477,plain,
% 2.87/3.10 (b(s(z), s(s(z)))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[548, 16476])).
% 2.87/3.10 tff(16478,plain,
% 2.87/3.10 (~b(z, s(s(z)))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[13733, 550, 2, 16477])).
% 2.87/3.10 tff(16479,plain,
% 2.87/3.10 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16396])).
% 2.87/3.10 tff(16480,plain,
% 2.87/3.10 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.87/3.10 inference(symmetry,[status(thm)],[16479])).
% 2.87/3.10 tff(16481,plain,
% 2.87/3.10 (~b(s(s(s(elem!1))), s(z))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1846, 1843, 16317])).
% 2.87/3.10 tff(16482,plain,
% 2.87/3.10 (r(z, s(s(z)))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[222, 16478])).
% 2.87/3.10 tff(16483,plain,
% 2.87/3.10 (r(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[14716, 16482, 2, 82])).
% 2.87/3.10 tff(16484,plain,
% 2.87/3.10 (r(s(s(s(z))), s(s(z)))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[8734, 16483, 16317])).
% 2.87/3.10 tff(16485,plain,
% 2.87/3.10 (~r(z, s(s(s(z))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[14959, 16484, 2, 16482])).
% 2.87/3.10 tff(16486,plain,
% 2.87/3.10 (~r(z, s(s(s(elem!1))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[6374, 16485, 16324])).
% 2.87/3.10 tff(16487,plain,
% 2.87/3.10 (b(z, s(s(s(elem!1))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[590, 16486])).
% 2.87/3.10 tff(16488,plain,
% 2.87/3.10 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16324])).
% 2.87/3.10 tff(16489,plain,
% 2.87/3.10 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 2.87/3.10 inference(transitivity,[status(thm)],[16488, 4295])).
% 2.87/3.10 tff(16490,plain,
% 2.87/3.10 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(symmetry,[status(thm)],[16489])).
% 2.87/3.10 tff(16491,plain,
% 2.87/3.10 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16490])).
% 2.87/3.10 tff(16492,plain,
% 2.87/3.10 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(modus_ponens,[status(thm)],[286, 16491])).
% 2.87/3.10 tff(16493,plain,
% 2.87/3.10 ((~b(s(s(s(s(elem!1)))), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1)))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[7659, 14660])).
% 2.87/3.10 tff(16494,plain,
% 2.87/3.10 (~b(s(s(s(s(elem!1)))), z)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[16493, 16492, 550, 494, 16487])).
% 2.87/3.10 tff(16495,plain,
% 2.87/3.10 (r(s(s(s(s(elem!1)))), z)),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[842, 16494])).
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% 2.87/3.10 inference(unit_resolution,[status(thm)],[15072, 16482, 2, 16477, 550])).
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% 2.87/3.10 inference(unit_resolution,[status(thm)],[625, 16496])).
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% 2.87/3.10 inference(unit_resolution,[status(thm)],[402, 16498])).
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% 2.87/3.10 ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | b(s(s(s(elem!1))), s(z)) | (~b(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[8657, 14660])).
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% 2.87/3.10 inference(unit_resolution,[status(thm)],[486, 16492, 16504])).
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% 2.87/3.10 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(elem!1)))) = s(s(z)))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16436])).
% 2.87/3.10 tff(16507,plain,
% 2.87/3.10 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(transitivity,[status(thm)],[16506, 319])).
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% 2.87/3.10 inference(symmetry,[status(thm)],[16507])).
% 2.87/3.10 tff(16509,plain,
% 2.87/3.10 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16508])).
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% 2.87/3.10 inference(modus_ponens,[status(thm)],[331, 16509])).
% 2.87/3.10 tff(16511,plain,
% 2.87/3.10 (r(s(s(elem!1)), z) <=> r(s(s(z)), z)),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16436])).
% 2.87/3.10 tff(16512,plain,
% 2.87/3.10 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 2.87/3.10 inference(symmetry,[status(thm)],[16511])).
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% 2.87/3.10 inference(modus_ponens,[status(thm)],[16497, 16512])).
% 2.87/3.10 tff(16514,plain,
% 2.87/3.10 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16436])).
% 2.87/3.10 tff(16515,plain,
% 2.87/3.10 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 2.87/3.10 inference(symmetry,[status(thm)],[16514])).
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% 2.87/3.10 inference(modus_ponens,[status(thm)],[16482, 16515])).
% 2.87/3.10 tff(16517,plain,
% 2.87/3.10 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[7685, 16495, 16516, 16513])).
% 2.87/3.10 tff(16518,plain,
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% 2.87/3.10 inference(unit_resolution,[status(thm)],[1484, 16517, 16510])).
% 2.87/3.10 tff(16519,plain,
% 2.87/3.10 (~b(z, s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[15579, 16518, 16487, 16505])).
% 2.87/3.10 tff(16520,plain,
% 2.87/3.10 (r(z, s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1093, 16519])).
% 2.87/3.10 tff(16521,plain,
% 2.87/3.10 (r(s(z), s(s(s(elem!1))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[13916, 16502, 16324])).
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% 2.87/3.10 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1273, 16521, 2, 494])).
% 2.87/3.10 tff(16523,plain,
% 2.87/3.10 (b(s(s(z)), s(s(s(elem!1))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[143, 16522])).
% 2.87/3.10 tff(16524,plain,
% 2.87/3.10 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[2574, 16518, 16523, 16505])).
% 2.87/3.10 tff(16525,plain,
% 2.87/3.10 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[336, 16524])).
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% 2.87/3.10 ($false),
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% 2.87/3.10 tff(16527,plain,((~b(s(z), z)) | (~r(s(s(z)), s(z))) | b(s(s(s(elem!1))), s(z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.10 tff(16528,plain,
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% 2.87/3.10 inference(unit_resolution,[status(thm)],[16527, 16481, 2, 6691])).
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% 2.87/3.10 (b(s(s(s(z))), z)),
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% 2.87/3.10 inference(unit_resolution,[status(thm)],[493, 16481])).
% 2.87/3.10 tff(16533,plain,
% 2.87/3.10 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16396])).
% 2.87/3.10 tff(16534,plain,
% 2.87/3.10 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 2.87/3.10 inference(symmetry,[status(thm)],[16533])).
% 2.87/3.10 tff(16535,plain,
% 2.87/3.10 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.87/3.10 inference(monotonicity,[status(thm)],[16324])).
% 2.87/3.10 tff(16536,plain,
% 2.87/3.10 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 2.87/3.10 inference(transitivity,[status(thm)],[16535, 16534])).
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% 2.87/3.10 inference(unit_resolution,[status(thm)],[625, 16537])).
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% 2.87/3.10 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[1273, 225, 2, 125])).
% 2.87/3.10 tff(16540,plain,
% 2.87/3.10 (b(s(s(z)), s(s(s(elem!1))))),
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% 2.87/3.10 inference(unit_resolution,[status(thm)],[14698, 16540, 15837, 83])).
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% 2.87/3.10 inference(unit_resolution,[status(thm)],[16542, 16538, 2, 125])).
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% 2.87/3.10 (~r(s(z), s(s(s(z))))),
% 2.87/3.10 inference(unit_resolution,[status(thm)],[13916, 16543, 16324])).
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% 2.87/3.10 inference(unit_resolution,[status(thm)],[253, 16544])).
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% 2.87/3.10 inference(unit_resolution,[status(thm)],[10091, 16547, 16317])).
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% 2.87/3.10 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.87/3.10 inference(symmetry,[status(thm)],[16551])).
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% 2.87/3.11 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
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% 2.87/3.11 tff(16567,plain,
% 2.87/3.11 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
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% 2.87/3.11 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
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% 2.87/3.11 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[3812, 16590, 535, 13879])).
% 2.87/3.11 tff(16592,plain,
% 2.87/3.11 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[336, 16591])).
% 2.87/3.11 tff(16593,plain,
% 2.87/3.11 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[5279, 16592, 145, 16569])).
% 2.87/3.11 tff(16594,plain,
% 2.87/3.11 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[486, 16593, 16492])).
% 2.87/3.11 tff(16595,plain,
% 2.87/3.11 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[16594, 16567])).
% 2.87/3.11 tff(16596,plain,
% 2.87/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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))), 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(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.87/3.11 inference(rewrite,[status(thm)],[])).
% 2.87/3.11 tff(16597,plain,
% 2.87/3.11 (((~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(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.87/3.11 inference(rewrite,[status(thm)],[])).
% 2.87/3.11 tff(16598,plain,
% 2.87/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[16597])).
% 2.87/3.11 tff(16599,plain,
% 2.87/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.87/3.11 inference(transitivity,[status(thm)],[16598, 16596])).
% 2.87/3.11 tff(16600,plain,
% 2.87/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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)))))))),
% 2.87/3.11 inference(quant_inst,[status(thm)],[])).
% 2.87/3.11 tff(16601,plain,
% 2.87/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[16600, 16599])).
% 2.87/3.11 tff(16602,plain,
% 2.87/3.11 ($false),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[16601, 97, 204, 1216, 16595, 16563])).
% 2.87/3.11 tff(16603,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.11 tff(16604,plain,
% 2.87/3.11 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[16603, 16550, 14263, 16558, 16477, 16548, 16538, 81])).
% 2.87/3.11 tff(16605,plain,
% 2.87/3.11 (b(s(s(s(s(elem!1)))), s(z))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[511, 16604])).
% 2.87/3.11 tff(16606,plain,
% 2.87/3.11 (b(s(s(s(s(z)))), s(z))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[13104, 16605, 16324])).
% 2.87/3.11 tff(16607,plain,
% 2.87/3.11 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[473, 16567])).
% 2.87/3.11 tff(16608,plain,
% 2.87/3.11 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[16328])).
% 2.87/3.11 tff(16609,plain,
% 2.87/3.11 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(z)))), z)),
% 2.87/3.11 inference(monotonicity,[status(thm)],[16328])).
% 2.87/3.11 tff(16610,plain,
% 2.87/3.11 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 2.87/3.11 inference(symmetry,[status(thm)],[16609])).
% 2.87/3.11 tff(16611,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 2.87/3.11 tff(16612,plain,
% 2.87/3.11 ($false),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[16601, 97, 204, 1216, 16611, 2796])).
% 2.87/3.11 tff(16613,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.11 tff(16614,plain,
% 2.87/3.11 (~b(s(s(s(s(z)))), z)),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[16613, 16607, 1216, 204])).
% 2.87/3.11 tff(16615,plain,
% 2.87/3.11 (r(s(s(s(s(z)))), z)),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[2860, 16614])).
% 2.87/3.11 tff(16616,plain,
% 2.87/3.11 (r(s(s(s(s(elem!1)))), z)),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[16615, 16610])).
% 2.87/3.11 tff(16617,plain,
% 2.87/3.11 (r(s(z), elem!1) <=> r(s(z), z)),
% 2.87/3.11 inference(monotonicity,[status(thm)],[16445])).
% 2.87/3.11 tff(16618,plain,
% 2.87/3.11 (r(s(z), z) <=> r(s(z), elem!1)),
% 2.87/3.11 inference(symmetry,[status(thm)],[16617])).
% 2.87/3.11 tff(16619,plain,
% 2.87/3.11 (r(s(z), elem!1)),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[81, 16618])).
% 2.87/3.11 tff(16620,plain,
% 2.87/3.11 (~b(s(s(s(s(elem!1)))), z)),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[5058, 126, 372, 473])).
% 2.87/3.11 tff(16621,plain,
% 2.87/3.11 (r(s(s(s(s(elem!1)))), z)),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[840, 53, 837, 16620])).
% 2.87/3.11 tff(16622,plain,
% 2.87/3.11 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[12166, 155, 570, 1813, 4497])).
% 2.87/3.11 tff(16623,plain,
% 2.87/3.11 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[16622, 16621])).
% 2.87/3.11 tff(16624,plain,
% 2.87/3.11 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[821, 16623, 802])).
% 2.87/3.11 tff(16625,plain,
% 2.87/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.87/3.11 inference(rewrite,[status(thm)],[])).
% 2.87/3.11 tff(16626,plain,
% 2.87/3.11 (((~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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.87/3.11 inference(rewrite,[status(thm)],[])).
% 2.87/3.11 tff(16627,plain,
% 2.87/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[16626])).
% 2.87/3.11 tff(16628,plain,
% 2.87/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.87/3.11 inference(transitivity,[status(thm)],[16627, 16625])).
% 2.87/3.11 tff(16629,plain,
% 2.87/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))),
% 2.87/3.11 inference(quant_inst,[status(thm)],[])).
% 2.87/3.11 tff(16630,plain,
% 2.87/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[16629, 16628])).
% 2.87/3.11 tff(16631,plain,
% 2.87/3.11 ($false),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[16630, 97, 126, 372, 473, 16624])).
% 2.87/3.11 tff(16632,plain,((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.11 tff(16633,plain,
% 2.87/3.11 ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[16632, 14660])).
% 2.87/3.11 tff(16634,plain,
% 2.87/3.11 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[16633, 372, 570, 16572, 4497, 473])).
% 2.87/3.11 tff(16635,plain,
% 2.87/3.11 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(z)))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[16324, 16436])).
% 2.87/3.11 tff(16636,plain,
% 2.87/3.11 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(z))))),
% 2.87/3.11 inference(transitivity,[status(thm)],[16635, 430])).
% 2.87/3.11 tff(16637,plain,
% 2.87/3.11 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.87/3.11 inference(symmetry,[status(thm)],[16636])).
% 2.87/3.11 tff(16638,plain,
% 2.87/3.11 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[16637])).
% 2.87/3.11 tff(16639,plain,
% 2.87/3.11 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[432, 16638])).
% 2.87/3.11 tff(16640,plain,
% 2.87/3.11 (r(elem!1, s(s(z))) <=> r(z, s(s(z)))),
% 2.87/3.11 inference(symmetry,[status(thm)],[11243])).
% 2.87/3.11 tff(16641,plain,
% 2.87/3.11 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(z)))),
% 2.87/3.11 inference(transitivity,[status(thm)],[11241, 16640])).
% 2.87/3.11 tff(16642,plain,
% 2.87/3.11 ((~r(elem!1, s(s(elem!1)))) <=> (~r(z, s(s(z))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[16641])).
% 2.87/3.11 tff(16643,plain,
% 2.87/3.11 (s(elem!1) = s(z)),
% 2.87/3.11 inference(symmetry,[status(thm)],[1535])).
% 2.87/3.11 tff(16644,plain,
% 2.87/3.11 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 2.87/3.11 inference(monotonicity,[status(thm)],[16643])).
% 2.87/3.11 tff(16645,plain,
% 2.87/3.11 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 2.87/3.11 inference(symmetry,[status(thm)],[16644])).
% 2.87/3.11 tff(16646,plain,
% 2.87/3.11 (r(s(elem!1), elem!1)),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[13452, 16645])).
% 2.87/3.11 tff(16647,plain,
% 2.87/3.11 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 2.87/3.11 inference(monotonicity,[status(thm)],[1540])).
% 2.87/3.11 tff(16648,plain,
% 2.87/3.11 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 2.87/3.11 inference(symmetry,[status(thm)],[16647])).
% 2.87/3.11 tff(16649,plain,
% 2.87/3.11 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.87/3.11 inference(monotonicity,[status(thm)],[1534])).
% 2.87/3.11 tff(16650,plain,
% 2.87/3.11 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 2.87/3.11 inference(symmetry,[status(thm)],[16649])).
% 2.87/3.11 tff(16651,plain,
% 2.87/3.11 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(s(s(elem!1))), z))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[16650])).
% 2.87/3.11 tff(16652,plain,
% 2.87/3.11 (b(elem!1, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(elem!1)))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[1540])).
% 2.87/3.11 tff(16653,plain,
% 2.87/3.11 (b(z, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 2.87/3.11 inference(symmetry,[status(thm)],[16652])).
% 2.87/3.11 tff(16654,plain,
% 2.87/3.11 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[372, 16653])).
% 2.87/3.11 tff(16655,plain,
% 2.87/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.87/3.11 inference(rewrite,[status(thm)],[])).
% 2.87/3.11 tff(16656,plain,
% 2.87/3.11 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), 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(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(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.87/3.11 inference(rewrite,[status(thm)],[])).
% 2.87/3.11 tff(16657,plain,
% 2.87/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(elem!1)))), 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(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(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[16656])).
% 2.87/3.11 tff(16658,plain,
% 2.87/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(elem!1)))), 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(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(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.87/3.11 inference(transitivity,[status(thm)],[16657, 16655])).
% 2.87/3.11 tff(16659,plain,
% 2.87/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(elem!1)))), 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(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.87/3.11 inference(quant_inst,[status(thm)],[])).
% 2.87/3.11 tff(16660,plain,
% 2.87/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[16659, 16658])).
% 2.87/3.11 tff(16661,plain,
% 2.87/3.11 ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[16660, 97, 1545, 473])).
% 2.87/3.11 tff(16662,plain,
% 2.87/3.11 (~b(s(s(s(elem!1))), elem!1)),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[16661, 16654])).
% 2.87/3.11 tff(16663,plain,
% 2.87/3.11 (~b(s(s(s(elem!1))), z)),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[16662, 16651])).
% 2.87/3.11 tff(16664,plain,
% 2.87/3.11 (r(s(s(s(elem!1))), z)),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[246, 16663])).
% 2.87/3.11 tff(16665,plain,
% 2.87/3.11 (r(s(s(s(elem!1))), elem!1)),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[16664, 16648])).
% 2.87/3.11 tff(16666,plain,
% 2.87/3.11 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[1540])).
% 2.87/3.11 tff(16667,plain,
% 2.87/3.11 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.87/3.11 inference(symmetry,[status(thm)],[16666])).
% 2.87/3.11 tff(16668,plain,
% 2.87/3.11 (r(elem!1, s(s(s(elem!1))))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[570, 16667])).
% 2.87/3.11 tff(16669,plain,
% 2.87/3.11 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[1586, 1545, 473, 352, 16665, 16668, 1534])).
% 2.87/3.11 tff(16670,plain,
% 2.87/3.11 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[11287, 16669, 352])).
% 2.87/3.11 tff(16671,plain,
% 2.87/3.11 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[2507])).
% 2.87/3.11 tff(16672,plain,
% 2.87/3.11 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[472, 16671])).
% 2.87/3.11 tff(16673,plain,
% 2.87/3.11 ((s(s(s(s(elem!1)))) = elem!1) <=> (s(s(s(s(elem!1)))) = z)),
% 2.87/3.11 inference(monotonicity,[status(thm)],[1540])).
% 2.87/3.11 tff(16674,plain,
% 2.87/3.11 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.87/3.11 inference(symmetry,[status(thm)],[16673])).
% 2.87/3.11 tff(16675,plain,
% 2.87/3.11 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[16674])).
% 2.87/3.11 tff(16676,plain,
% 2.87/3.11 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[837, 16675])).
% 2.87/3.11 tff(16677,plain,
% 2.87/3.11 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(z)), elem!1))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[1538])).
% 2.87/3.11 tff(16678,plain,
% 2.87/3.11 (~r(s(s(elem!1)), elem!1)),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[11262, 16670, 16665, 1534, 1545, 16654, 352, 16668])).
% 2.87/3.11 tff(16679,plain,
% 2.87/3.11 (~r(s(s(z)), elem!1)),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[16678, 16677])).
% 2.87/3.11 tff(16680,plain,
% 2.87/3.11 (b(s(s(z)), elem!1)),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[1563, 16679, 1544])).
% 2.87/3.11 tff(16681,plain,
% 2.87/3.11 (b(s(s(elem!1)), elem!1)),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[16680, 1547])).
% 2.87/3.11 tff(16682,plain,
% 2.87/3.11 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[7787, 1545, 16654, 16681])).
% 2.87/3.11 tff(16683,plain,
% 2.87/3.11 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[1471, 16682, 16676])).
% 2.87/3.11 tff(16684,plain,
% 2.87/3.11 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[7302, 155, 16683, 16665, 16668])).
% 2.87/3.11 tff(16685,plain,
% 2.87/3.11 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[819, 53, 16684])).
% 2.87/3.11 tff(16686,plain,
% 2.87/3.11 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[16685, 16672])).
% 2.87/3.11 tff(16687,plain,
% 2.87/3.11 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[16643])).
% 2.87/3.11 tff(16688,plain,
% 2.87/3.11 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.87/3.11 inference(symmetry,[status(thm)],[16687])).
% 2.87/3.11 tff(16689,plain,
% 2.87/3.11 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[16643])).
% 2.87/3.11 tff(16690,plain,
% 2.87/3.11 ((~r(s(s(s(elem!1))), s(elem!1))) <=> (~r(s(s(s(elem!1))), s(z)))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[16689])).
% 2.87/3.11 tff(16691,plain,
% 2.87/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.87/3.11 inference(rewrite,[status(thm)],[])).
% 2.87/3.11 tff(16692,plain,
% 2.87/3.11 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.87/3.11 inference(rewrite,[status(thm)],[])).
% 2.87/3.11 tff(16693,plain,
% 2.87/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))))),
% 2.87/3.11 inference(monotonicity,[status(thm)],[16692])).
% 2.87/3.11 tff(16694,plain,
% 2.87/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.87/3.11 inference(transitivity,[status(thm)],[16693, 16691])).
% 2.87/3.11 tff(16695,plain,
% 2.87/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.87/3.11 inference(quant_inst,[status(thm)],[])).
% 2.87/3.11 tff(16696,plain,
% 2.87/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[16695, 16694])).
% 2.87/3.11 tff(16697,plain,
% 2.87/3.11 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[16696, 155, 4497, 1528, 1932, 6301])).
% 2.87/3.11 tff(16698,plain,
% 2.87/3.11 (~r(s(s(s(elem!1))), s(z))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[16697, 16690])).
% 2.87/3.11 tff(16699,plain,
% 2.87/3.11 (b(s(s(s(elem!1))), s(z))),
% 2.87/3.11 inference(unit_resolution,[status(thm)],[492, 16698, 172])).
% 2.87/3.11 tff(16700,plain,
% 2.87/3.11 (b(s(s(s(elem!1))), s(elem!1))),
% 2.87/3.11 inference(modus_ponens,[status(thm)],[16699, 16688])).
% 2.87/3.12 tff(16701,plain,
% 2.87/3.12 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[2431, 16700, 805, 1545])).
% 2.87/3.12 tff(16702,plain,
% 2.87/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(16703,plain,
% 2.87/3.12 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(16704,plain,
% 2.87/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.87/3.12 inference(monotonicity,[status(thm)],[16703])).
% 2.87/3.12 tff(16705,plain,
% 2.87/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.87/3.12 inference(transitivity,[status(thm)],[16704, 16702])).
% 2.87/3.12 tff(16706,plain,
% 2.87/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 2.87/3.12 inference(quant_inst,[status(thm)],[])).
% 2.87/3.12 tff(16707,plain,
% 2.87/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[16706, 16705])).
% 2.87/3.12 tff(16708,plain,
% 2.87/3.12 ($false),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[16707, 155, 4497, 1523, 6277, 6301])).
% 2.87/3.12 tff(16709,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.12 tff(16710,plain,
% 2.87/3.12 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[16709, 6301, 1523, 4497])).
% 2.87/3.12 tff(16711,plain,
% 2.87/3.12 ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[1576, 53, 16710])).
% 2.87/3.12 tff(16712,plain,
% 2.87/3.12 ($false),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[16711, 16701, 1533])).
% 2.87/3.12 tff(16713,plain,((~r(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~(z = elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.12 tff(16714,plain,
% 2.87/3.12 (~r(elem!1, s(s(elem!1)))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[16713, 16686, 1545, 352, 1534, 16668, 16670, 16665, 16646])).
% 2.87/3.12 tff(16715,plain,
% 2.87/3.12 (~r(z, s(s(z)))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[16714, 16642])).
% 2.87/3.12 tff(16716,plain,
% 2.87/3.12 (b(z, s(s(z)))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[222, 16715])).
% 2.87/3.12 tff(16717,plain,
% 2.87/3.12 (b(elem!1, s(s(z)))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[204, 11244])).
% 2.87/3.12 tff(16718,assumption,(~b(elem!1, s(s(z)))), introduced(assumption)).
% 2.87/3.12 tff(16719,plain,
% 2.87/3.12 ($false),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[16718, 16717])).
% 2.87/3.12 tff(16720,plain,((~b(z, s(s(z)))) | b(elem!1, s(s(z))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.12 tff(16721,plain,
% 2.87/3.12 (b(elem!1, s(s(z)))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[16720, 16716, 1534])).
% 2.87/3.12 tff(16722,plain,
% 2.87/3.12 (b(elem!1, s(s(elem!1)))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[16721, 2388])).
% 2.87/3.12 tff(16723,plain,
% 2.87/3.12 ($false),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[1921, 97, 1545, 16654, 16681, 16722])).
% 2.87/3.12 tff(16724,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~(z = elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.12 tff(16725,plain,
% 2.87/3.12 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[16724, 372, 570, 16492, 13452, 16639, 16441, 473])).
% 2.87/3.12 tff(16726,plain,
% 2.87/3.12 ($false),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[1484, 16725, 16634, 16510])).
% 2.87/3.12 tff(16727,plain,((~b(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.12 tff(16728,plain,
% 2.87/3.12 (~b(z, s(s(s(s(elem!1)))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[16727, 473, 16619, 570, 4497])).
% 2.87/3.12 tff(16729,plain,
% 2.87/3.12 (r(z, s(s(s(s(elem!1)))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[1093, 16728])).
% 2.87/3.12 tff(16730,plain,
% 2.87/3.12 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[4887, 16729, 81, 16616])).
% 2.87/3.12 tff(16731,plain,
% 2.87/3.12 (b(s(z), s(s(s(s(elem!1)))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[280, 16730])).
% 2.87/3.12 tff(16732,plain,
% 2.87/3.12 (b(s(z), s(s(s(s(z)))))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[16731, 16608])).
% 2.87/3.12 tff(16733,plain,
% 2.87/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $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(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(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(16734,plain,
% 2.87/3.12 (((~b(s(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(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(16735,plain,
% 2.87/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(s(z)))))) | (~b(s(s(s(z))), s(s(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(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.87/3.12 inference(monotonicity,[status(thm)],[16734])).
% 2.87/3.12 tff(16736,plain,
% 2.87/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(s(z)))))) | (~b(s(s(s(z))), s(s(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(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.87/3.12 inference(transitivity,[status(thm)],[16735, 16733])).
% 2.87/3.12 tff(16737,plain,
% 2.87/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 2.87/3.12 inference(quant_inst,[status(thm)],[])).
% 2.87/3.12 tff(16738,plain,
% 2.87/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[16737, 16736])).
% 2.87/3.12 tff(16739,plain,
% 2.87/3.12 ($false),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[16738, 97, 86, 16732, 16607, 10217])).
% 2.87/3.12 tff(16740,plain,((~b(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(z))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.12 tff(16741,plain,
% 2.87/3.12 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[16740, 16606, 16545, 81, 570, 16556, 14263, 16550])).
% 2.87/3.12 tff(16742,plain,
% 2.87/3.12 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[486, 16741, 16492])).
% 2.87/3.12 tff(16743,plain,
% 2.87/3.12 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[16742, 16536])).
% 2.87/3.12 tff(16744,plain,
% 2.87/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), z)) | (~b(s(s(s(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(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(16745,plain,
% 2.87/3.12 (((~b(s(s(z)), z)) | (~b(s(s(z)), 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(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(16746,plain,
% 2.87/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.87/3.12 inference(monotonicity,[status(thm)],[16745])).
% 2.87/3.12 tff(16747,plain,
% 2.87/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(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(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.12 inference(transitivity,[status(thm)],[16746, 16744])).
% 2.87/3.12 tff(16748,plain,
% 2.87/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.87/3.12 inference(quant_inst,[status(thm)],[])).
% 2.87/3.12 tff(16749,plain,
% 2.87/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[16748, 16747])).
% 2.87/3.12 tff(16750,plain,
% 2.87/3.12 ($false),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[16749, 97, 83, 535, 7084, 10217])).
% 2.87/3.12 tff(16751,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.12 tff(16752,plain,
% 2.87/3.12 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[16751, 16606, 16477, 16538])).
% 2.87/3.12 tff(16753,plain,
% 2.87/3.12 (r(s(s(s(s(z)))), s(s(z)))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[13323, 16752])).
% 2.87/3.12 tff(16754,plain,
% 2.87/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(16755,plain,
% 2.87/3.12 (((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~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(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(16756,plain,
% 2.87/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.87/3.12 inference(monotonicity,[status(thm)],[16755])).
% 2.87/3.12 tff(16757,plain,
% 2.87/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.12 inference(transitivity,[status(thm)],[16756, 16754])).
% 2.87/3.12 tff(16758,plain,
% 2.87/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~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(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.87/3.12 inference(quant_inst,[status(thm)],[])).
% 2.87/3.12 tff(16759,plain,
% 2.87/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.87/3.12 inference(modus_ponens,[status(thm)],[16758, 16757])).
% 2.87/3.12 tff(16760,plain,
% 2.87/3.12 ($false),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[16759, 155, 2, 2597, 16555, 16753, 16743])).
% 2.87/3.12 tff(16761,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.87/3.12 tff(16762,plain,
% 2.87/3.12 (~r(z, s(s(s(elem!1))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[16761, 6691, 2, 16529, 16532])).
% 2.87/3.12 tff(16763,plain,
% 2.87/3.12 (~r(z, s(s(s(z))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[6652, 16762, 16317])).
% 2.87/3.12 tff(16764,plain,
% 2.87/3.12 (b(z, s(s(s(z))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[1318, 16763])).
% 2.87/3.12 tff(16765,plain,
% 2.87/3.12 (~r(s(s(z)), z)),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[14963, 16529, 2])).
% 2.87/3.12 tff(16766,plain,
% 2.87/3.12 (b(s(s(z)), z)),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[625, 16765])).
% 2.87/3.12 tff(16767,plain,
% 2.87/3.12 (b(z, s(s(s(elem!1))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[590, 16762])).
% 2.87/3.12 tff(16768,plain,
% 2.87/3.12 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[16151, 16767, 16766])).
% 2.87/3.12 tff(16769,plain,
% 2.87/3.12 (r(s(s(s(elem!1))), s(s(z)))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[58, 16768])).
% 2.87/3.12 tff(16770,plain,
% 2.87/3.12 (r(s(s(s(z))), s(s(z)))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[8734, 16769, 16317])).
% 2.87/3.12 tff(16771,plain,
% 2.87/3.12 (~b(s(s(s(s(elem!1)))), z)),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[11562, 16770, 16766, 16764, 16531])).
% 2.87/3.12 tff(16772,plain,
% 2.87/3.12 (r(s(s(s(s(elem!1)))), z)),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[842, 16771])).
% 2.87/3.12 tff(16773,plain,
% 2.87/3.12 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[11568, 16772, 16529])).
% 2.87/3.12 tff(16774,plain,
% 2.87/3.12 (b(s(s(s(s(elem!1)))), s(z))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[511, 16773])).
% 2.87/3.12 tff(16775,plain,
% 2.87/3.12 (b(s(s(s(s(z)))), s(z))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[13104, 16774, 16324])).
% 2.87/3.12 tff(16776,plain,
% 2.87/3.12 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[16751, 16775, 16477, 16766])).
% 2.87/3.12 tff(16777,plain,
% 2.87/3.12 (r(s(s(s(s(z)))), s(s(z)))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[13323, 16776])).
% 2.87/3.12 tff(16778,plain,
% 2.87/3.12 (~r(s(z), s(s(s(elem!1))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[16542, 16766, 2, 16532])).
% 2.87/3.12 tff(16779,plain,
% 2.87/3.12 (~r(s(z), s(s(s(z))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[13916, 16778, 16324])).
% 2.87/3.12 tff(16780,plain,
% 2.87/3.12 (b(s(z), s(s(s(z))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[253, 16779])).
% 2.87/3.12 tff(16781,plain,
% 2.87/3.12 (~b(s(s(z)), s(s(s(z))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[4270, 16780, 16477, 16531])).
% 2.87/3.12 tff(16782,plain,
% 2.87/3.12 (r(s(s(z)), s(s(s(z))))),
% 2.87/3.12 inference(unit_resolution,[status(thm)],[437, 16781])).
% 2.87/3.12 tff(16783,plain,
% 2.87/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(16784,plain,
% 2.87/3.12 (((~r(s(s(s(z))), 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(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.12 inference(rewrite,[status(thm)],[])).
% 2.87/3.12 tff(16785,plain,
% 2.87/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.87/3.12 inference(monotonicity,[status(thm)],[16784])).
% 2.87/3.12 tff(16786,plain,
% 2.87/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.12 inference(transitivity,[status(thm)],[16785, 16783])).
% 2.87/3.12 tff(16787,plain,
% 2.87/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.87/3.12 inference(quant_inst,[status(thm)],[])).
% 2.87/3.12 tff(16788,plain,
% 2.87/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[16787, 16786])).
% 2.97/3.13 tff(16789,plain,
% 2.97/3.13 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16788, 155, 16782, 16770, 16777])).
% 2.97/3.13 tff(16790,plain,
% 2.97/3.13 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[4169, 16789])).
% 2.97/3.13 tff(16791,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(16792,plain,
% 2.97/3.13 (((~b(s(s(s(z))), z)) | (~b(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(z)))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(16793,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[16792])).
% 2.97/3.13 tff(16794,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, 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)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.97/3.13 inference(transitivity,[status(thm)],[16793, 16791])).
% 2.97/3.13 tff(16795,plain,
% 2.97/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.97/3.13 inference(quant_inst,[status(thm)],[])).
% 2.97/3.13 tff(16796,plain,
% 2.97/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[16795, 16794])).
% 2.97/3.13 tff(16797,plain,
% 2.97/3.13 ($false),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16796, 97, 16766, 16477, 16780, 16531, 16790, 16775])).
% 2.97/3.13 tff(16798,plain,(b(s(s(s(z))), s(z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.13 tff(16799,plain,
% 2.97/3.13 (b(s(s(s(z))), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16798, 2])).
% 2.97/3.13 tff(16800,plain,
% 2.97/3.13 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[16324])).
% 2.97/3.13 tff(16801,plain,
% 2.97/3.13 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.97/3.13 inference(symmetry,[status(thm)],[16800])).
% 2.97/3.13 tff(16802,plain,
% 2.97/3.13 (b(s(s(s(elem!1))), s(z))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[1360, 16801])).
% 2.97/3.13 tff(16803,plain,
% 2.97/3.13 ($false),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[82, 16802])).
% 2.97/3.13 tff(16804,plain,(b(s(s(s(elem!1))), s(z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.13 tff(16805,plain,
% 2.97/3.13 (b(s(s(s(elem!1))), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16804, 16799])).
% 2.97/3.13 tff(16806,plain,
% 2.97/3.13 (~b(z, s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13733, 14965, 2, 16477])).
% 2.97/3.13 tff(16807,plain,
% 2.97/3.13 (r(z, s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[222, 16806])).
% 2.97/3.13 tff(16808,plain,
% 2.97/3.13 (~b(z, s(s(s(elem!1))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[14724, 14965, 16805])).
% 2.97/3.13 tff(16809,plain,
% 2.97/3.13 (r(z, s(s(s(elem!1))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[590, 16808])).
% 2.97/3.13 tff(16810,plain,
% 2.97/3.13 (~r(s(z), s(s(s(elem!1))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[14728, 16809, 2, 16807])).
% 2.97/3.13 tff(16811,plain,
% 2.97/3.13 (b(s(z), s(s(s(elem!1))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[181, 16810])).
% 2.97/3.13 tff(16812,plain,
% 2.97/3.13 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[11339, 16811, 16477, 16805])).
% 2.97/3.13 tff(16813,plain,
% 2.97/3.13 (r(s(s(z)), s(s(s(elem!1))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[143, 16812])).
% 2.97/3.13 tff(16814,plain,
% 2.97/3.13 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[15354, 16812, 16477, 14965, 16809])).
% 2.97/3.13 tff(16815,plain,
% 2.97/3.13 (r(s(z), s(s(s(s(elem!1)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[280, 16814])).
% 2.97/3.13 tff(16816,plain,
% 2.97/3.13 (~r(z, s(s(s(s(elem!1)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[11787, 16815, 2, 16807])).
% 2.97/3.13 tff(16817,plain,
% 2.97/3.13 (b(z, s(s(s(s(elem!1)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[1093, 16816])).
% 2.97/3.13 tff(16818,plain,
% 2.97/3.13 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[15384, 16817, 2, 16805, 16477, 16807])).
% 2.97/3.13 tff(16819,plain,
% 2.97/3.13 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[486, 16818, 16492])).
% 2.97/3.13 tff(16820,plain,
% 2.97/3.13 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[15145, 16819, 645, 16809, 16813])).
% 2.97/3.13 tff(16821,plain,
% 2.97/3.13 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[336, 16820])).
% 2.97/3.13 tff(16822,plain,
% 2.97/3.13 (b(s(s(z)), s(s(s(s(z)))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[16821, 16480])).
% 2.97/3.13 tff(16823,plain,
% 2.97/3.13 (~b(z, s(s(s(z))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[15979, 14965, 16805])).
% 2.97/3.13 tff(16824,plain,
% 2.97/3.13 (r(z, s(s(s(z))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[1318, 16823])).
% 2.97/3.13 tff(16825,plain,
% 2.97/3.13 (~r(s(s(s(z))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[14959, 16824, 2, 16807])).
% 2.97/3.13 tff(16826,plain,
% 2.97/3.13 (b(s(s(s(z))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[421, 16825])).
% 2.97/3.13 tff(16827,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z))), s(z))) | (~b(s(s(s(z))), 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(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(16828,plain,
% 2.97/3.13 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(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(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(16829,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(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(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[16828])).
% 2.97/3.13 tff(16830,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(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(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.97/3.13 inference(transitivity,[status(thm)],[16829, 16827])).
% 2.97/3.13 tff(16831,plain,
% 2.97/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(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))))),
% 2.97/3.13 inference(quant_inst,[status(thm)],[])).
% 2.97/3.13 tff(16832,plain,
% 2.97/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[16831, 16830])).
% 2.97/3.13 tff(16833,plain,
% 2.97/3.13 ($false),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16832, 97, 16477, 16799, 16826, 16822])).
% 2.97/3.13 tff(16834,plain,((~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.13 tff(16835,plain,
% 2.97/3.13 (~r(s(s(z)), z)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16834, 2])).
% 2.97/3.13 tff(16836,plain,
% 2.97/3.13 (b(s(s(z)), z)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[625, 16835])).
% 2.97/3.13 tff(16837,plain,
% 2.97/3.13 (~r(z, s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[15072, 550, 2, 16477, 16836])).
% 2.97/3.13 tff(16838,plain,
% 2.97/3.13 ($false),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[222, 16837, 16478])).
% 2.97/3.13 tff(16839,plain,((~b(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.13 tff(16840,plain,
% 2.97/3.13 (~b(s(z), z)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16839, 2])).
% 2.97/3.13 tff(16841,plain,
% 2.97/3.13 (r(s(z), z)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[568, 16840])).
% 2.97/3.13 tff(16842,plain,
% 2.97/3.13 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[11644, 16836, 16805, 16477])).
% 2.97/3.13 tff(16843,plain,
% 2.97/3.13 (r(s(s(s(elem!1))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[58, 16842])).
% 2.97/3.13 tff(16844,plain,
% 2.97/3.13 (r(s(s(s(z))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[8734, 16843, 16317])).
% 2.97/3.13 tff(16845,plain,
% 2.97/3.13 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 2.97/3.13 inference(monotonicity,[status(thm)],[16324])).
% 2.97/3.13 tff(16846,plain,
% 2.97/3.13 (b(s(s(s(z))), z)),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[14660, 16845])).
% 2.97/3.13 tff(16847,plain,
% 2.97/3.13 (b(s(s(s(elem!1))), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16804, 1360])).
% 2.97/3.13 tff(16848,plain,
% 2.97/3.13 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[11644, 83, 16847, 535])).
% 2.97/3.13 tff(16849,plain,
% 2.97/3.13 (r(s(s(s(elem!1))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[58, 16848])).
% 2.97/3.13 tff(16850,plain,
% 2.97/3.13 (r(s(s(s(z))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[8734, 16849, 16317])).
% 2.97/3.13 tff(16851,plain,
% 2.97/3.13 (~b(s(s(s(s(elem!1)))), z)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[11562, 6362, 83, 16850, 16846])).
% 2.97/3.13 tff(16852,plain,
% 2.97/3.13 (r(s(s(s(s(elem!1)))), z)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[842, 16851])).
% 2.97/3.13 tff(16853,plain,
% 2.97/3.13 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[11568, 16852, 81])).
% 2.97/3.13 tff(16854,plain,
% 2.97/3.13 (b(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[511, 16853])).
% 2.97/3.13 tff(16855,plain,
% 2.97/3.13 (b(s(s(s(s(z)))), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13104, 16854, 16324])).
% 2.97/3.13 tff(16856,plain,
% 2.97/3.13 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16751, 16855, 535, 83])).
% 2.97/3.13 tff(16857,plain,
% 2.97/3.13 (r(s(s(s(s(z)))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13323, 16856])).
% 2.97/3.13 tff(16858,plain,
% 2.97/3.13 (~r(z, s(s(s(elem!1))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[6374, 6361, 16324])).
% 2.97/3.13 tff(16859,plain,
% 2.97/3.13 (b(z, s(s(s(elem!1))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[590, 16858])).
% 2.97/3.13 tff(16860,plain,
% 2.97/3.13 (~b(s(s(z)), s(s(s(z))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[1369, 16859, 16847, 83, 1360, 6362])).
% 2.97/3.13 tff(16861,plain,
% 2.97/3.13 (r(s(s(z)), s(s(s(z))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[437, 16860])).
% 2.97/3.13 tff(16862,plain,
% 2.97/3.13 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16788, 155, 16861, 16850, 16857])).
% 2.97/3.13 tff(16863,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $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(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(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(16864,plain,
% 2.97/3.13 (((~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(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(16865,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[16864])).
% 2.97/3.13 tff(16866,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.97/3.13 inference(transitivity,[status(thm)],[16865, 16863])).
% 2.97/3.13 tff(16867,plain,
% 2.97/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $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))))))),
% 2.97/3.13 inference(quant_inst,[status(thm)],[])).
% 2.97/3.13 tff(16868,plain,
% 2.97/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[16867, 16866])).
% 2.97/3.13 tff(16869,plain,
% 2.97/3.13 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16868, 97, 535, 1360, 16855])).
% 2.97/3.13 tff(16870,plain,
% 2.97/3.13 ($false),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[4169, 16869, 16862])).
% 2.97/3.13 tff(16871,plain,(r(z, s(s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.13 tff(16872,plain,
% 2.97/3.13 (r(z, s(s(s(z))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16871, 16477, 16799, 16836, 16841])).
% 2.97/3.13 tff(16873,plain,
% 2.97/3.13 (~r(z, s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[14959, 16872, 2, 16844])).
% 2.97/3.13 tff(16874,plain,
% 2.97/3.13 (b(z, s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[222, 16873])).
% 2.97/3.13 tff(16875,plain,
% 2.97/3.13 (~b(s(s(z)), s(s(s(z))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[5211, 97, 16874, 16836, 16846])).
% 2.97/3.13 tff(16876,plain,
% 2.97/3.13 (r(s(s(z)), s(s(s(z))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[437, 16875])).
% 2.97/3.13 tff(16877,plain,
% 2.97/3.13 (r(s(s(z)), s(s(s(elem!1))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[10091, 16876, 16317])).
% 2.97/3.13 tff(16878,plain,
% 2.97/3.13 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16603, 16877, 16846, 16843, 16477, 16874, 16836, 16841])).
% 2.97/3.13 tff(16879,plain,
% 2.97/3.13 (b(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[511, 16878])).
% 2.97/3.13 tff(16880,plain,
% 2.97/3.13 (b(s(s(s(s(z)))), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13104, 16879, 16324])).
% 2.97/3.13 tff(16881,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(16882,plain,
% 2.97/3.13 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.97/3.13 inference(rewrite,[status(thm)],[])).
% 2.97/3.13 tff(16883,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[16882])).
% 2.97/3.13 tff(16884,plain,
% 2.97/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $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(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $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(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.97/3.13 inference(transitivity,[status(thm)],[16883, 16881])).
% 2.97/3.13 tff(16885,plain,
% 2.97/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $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(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.97/3.13 inference(quant_inst,[status(thm)],[])).
% 2.97/3.13 tff(16886,plain,
% 2.97/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[16885, 16884])).
% 2.97/3.13 tff(16887,plain,
% 2.97/3.13 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16886, 97, 16874, 16477, 16799, 16846, 16880])).
% 2.97/3.13 tff(16888,plain,
% 2.97/3.13 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16751, 16880, 16477, 16836])).
% 2.97/3.13 tff(16889,plain,
% 2.97/3.13 (r(s(s(s(s(z)))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13323, 16888])).
% 2.97/3.13 tff(16890,plain,
% 2.97/3.13 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16788, 155, 16876, 16844, 16889])).
% 2.97/3.13 tff(16891,plain,
% 2.97/3.13 ($false),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[4169, 16890, 16887])).
% 2.97/3.13 tff(16892,plain,(~r(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.13 tff(16893,plain,
% 2.97/3.13 (b(s(s(z)), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[122, 16892])).
% 2.97/3.13 tff(16894,plain,
% 2.97/3.13 (~b(z, s(s(s(z))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[15990, 3, 16893])).
% 2.97/3.13 tff(16895,plain,
% 2.97/3.13 (r(z, s(s(s(z))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[1318, 16894])).
% 2.97/3.13 tff(16896,plain,
% 2.97/3.13 (~b(z, s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[15708, 16895, 16893, 3])).
% 2.97/3.13 tff(16897,plain,
% 2.97/3.13 (r(z, s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[222, 16896])).
% 2.97/3.13 tff(16898,plain,
% 2.97/3.13 (~r(s(z), z)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[5665, 3, 16893])).
% 2.97/3.13 tff(16899,plain,
% 2.97/3.13 (b(s(z), z)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[568, 16898])).
% 2.97/3.13 tff(16900,plain,
% 2.97/3.13 (r(z, s(s(s(elem!1))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[6652, 16895, 16317])).
% 2.97/3.13 tff(16901,plain,
% 2.97/3.13 (~r(s(s(s(elem!1))), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[14085, 16897, 3, 16900])).
% 2.97/3.13 tff(16902,plain,
% 2.97/3.13 (b(s(s(s(elem!1))), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[493, 16901])).
% 2.97/3.13 tff(16903,plain,
% 2.97/3.13 (b(s(s(s(z))), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[1846, 16902, 16317])).
% 2.97/3.13 tff(16904,plain,
% 2.97/3.13 (~b(s(s(z)), s(s(s(z))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[7010, 16903, 16893, 16899])).
% 2.97/3.13 tff(16905,plain,
% 2.97/3.13 (r(s(s(z)), s(s(s(z))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[437, 16904])).
% 2.97/3.13 tff(16906,plain,
% 2.97/3.13 (~b(s(s(s(z))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[14035, 16903, 16893, 16899])).
% 2.97/3.13 tff(16907,plain,
% 2.97/3.13 (r(s(s(s(z))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[421, 16906])).
% 2.97/3.13 tff(16908,plain,
% 2.97/3.13 ($false),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[1969, 16907, 16905, 16897, 16895])).
% 2.97/3.13 tff(16909,plain,(~r(s(z), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.13 tff(16910,plain,
% 2.97/3.13 (b(s(z), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[548, 16909])).
% 2.97/3.13 tff(16911,plain,
% 2.97/3.13 (~b(s(s(s(z))), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16804, 82])).
% 2.97/3.13 tff(16912,plain,
% 2.97/3.13 (r(s(s(s(z))), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[1358, 16911])).
% 2.97/3.13 tff(16913,plain,
% 2.97/3.13 (~b(z, s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[3966, 550, 16893, 16910])).
% 2.97/3.13 tff(16914,plain,
% 2.97/3.13 (r(z, s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[222, 16913])).
% 2.97/3.13 tff(16915,plain,
% 2.97/3.13 (r(s(s(s(elem!1))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[14025, 645, 16893, 16910, 550, 16914, 82])).
% 2.97/3.13 tff(16916,plain,
% 2.97/3.13 (r(s(s(s(z))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[8734, 16915, 16317])).
% 2.97/3.13 tff(16917,plain,
% 2.97/3.13 (~r(s(s(s(z))), z)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[6467, 16916, 645, 16914])).
% 2.97/3.13 tff(16918,plain,
% 2.97/3.13 (b(s(s(s(z))), z)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[402, 16917])).
% 2.97/3.13 tff(16919,plain,
% 2.97/3.13 (~b(s(z), s(s(s(elem!1))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[14677, 124, 550])).
% 2.97/3.13 tff(16920,plain,
% 2.97/3.13 (~b(s(z), s(s(s(z))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[6628, 16919, 16317])).
% 2.97/3.13 tff(16921,plain,
% 2.97/3.13 (r(s(z), s(s(s(z))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[253, 16920])).
% 2.97/3.13 tff(16922,plain,
% 2.97/3.13 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16503, 16921, 16910, 550, 16317, 2597, 16914, 82, 16324, 645, 124])).
% 2.97/3.13 tff(16923,plain,
% 2.97/3.13 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[16317])).
% 2.97/3.13 tff(16924,plain,
% 2.97/3.13 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.97/3.13 inference(transitivity,[status(thm)],[16923, 1414])).
% 2.97/3.13 tff(16925,plain,
% 2.97/3.13 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[16924])).
% 2.97/3.13 tff(16926,plain,
% 2.97/3.13 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[286, 16925])).
% 2.97/3.13 tff(16927,plain,
% 2.97/3.13 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[486, 16926, 16922])).
% 2.97/3.13 tff(16928,plain,
% 2.97/3.13 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[16317])).
% 2.97/3.13 tff(16929,plain,
% 2.97/3.13 (s(s(z)) = s(s(elem!1))),
% 2.97/3.13 inference(transitivity,[status(thm)],[73, 16928, 19])).
% 2.97/3.13 tff(16930,plain,
% 2.97/3.13 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[16929])).
% 2.97/3.13 tff(16931,plain,
% 2.97/3.13 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.97/3.13 inference(transitivity,[status(thm)],[16930, 1428])).
% 2.97/3.13 tff(16932,plain,
% 2.97/3.13 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[16931])).
% 2.97/3.13 tff(16933,plain,
% 2.97/3.13 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[331, 16932])).
% 2.97/3.13 tff(16934,plain,
% 2.97/3.13 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 2.97/3.13 inference(monotonicity,[status(thm)],[16929])).
% 2.97/3.13 tff(16935,plain,
% 2.97/3.13 (r(z, s(s(elem!1)))),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[16914, 16934])).
% 2.97/3.13 tff(16936,plain,
% 2.97/3.13 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 2.97/3.13 inference(monotonicity,[status(thm)],[16929])).
% 2.97/3.13 tff(16937,plain,
% 2.97/3.13 (r(s(s(elem!1)), z)),
% 2.97/3.13 inference(modus_ponens,[status(thm)],[645, 16936])).
% 2.97/3.13 tff(16938,plain,
% 2.97/3.13 (~b(s(s(s(s(elem!1)))), z)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16493, 16926, 494, 550, 124])).
% 2.97/3.13 tff(16939,plain,
% 2.97/3.13 (r(s(s(s(s(elem!1)))), z)),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[842, 16938])).
% 2.97/3.13 tff(16940,plain,
% 2.97/3.13 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[7685, 16939, 16937, 16935])).
% 2.97/3.13 tff(16941,plain,
% 2.97/3.13 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[1484, 16940, 16933])).
% 2.97/3.13 tff(16942,plain,
% 2.97/3.13 (~b(z, s(s(s(s(elem!1)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[15579, 16941, 124, 16927])).
% 2.97/3.13 tff(16943,plain,
% 2.97/3.13 (r(z, s(s(s(s(elem!1)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[1093, 16942])).
% 2.97/3.13 tff(16944,plain,
% 2.97/3.13 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[3326, 16943, 16317, 645, 16939])).
% 2.97/3.13 tff(16945,plain,
% 2.97/3.13 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[336, 16944])).
% 2.97/3.13 tff(16946,plain,
% 2.97/3.13 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[3240, 16945, 16893, 550])).
% 2.97/3.13 tff(16947,plain,
% 2.97/3.13 (r(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[511, 16946])).
% 2.97/3.13 tff(16948,plain,
% 2.97/3.13 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[1822, 16940, 16317])).
% 2.97/3.13 tff(16949,plain,
% 2.97/3.13 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[452, 16948])).
% 2.97/3.13 tff(16950,plain,
% 2.97/3.13 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[3267, 16945, 16910, 16949])).
% 2.97/3.13 tff(16951,plain,
% 2.97/3.13 (r(s(z), s(s(s(s(elem!1)))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[280, 16950])).
% 2.97/3.13 tff(16952,plain,
% 2.97/3.13 ($false),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[13894, 16951, 16947, 16943])).
% 2.97/3.13 tff(16953,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(z))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.13 tff(16954,plain,
% 2.97/3.13 (~b(z, s(s(s(elem!1))))),
% 2.97/3.13 inference(unit_resolution,[status(thm)],[16953, 645, 550, 2597, 82])).
% 2.97/3.14 tff(16955,plain,
% 2.97/3.14 (r(z, s(s(s(elem!1))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[590, 16954])).
% 2.97/3.14 tff(16956,plain,
% 2.97/3.14 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[15944, 16955, 16893, 16910, 550])).
% 2.97/3.14 tff(16957,plain,
% 2.97/3.14 (~r(s(s(z)), s(s(s(z))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[10091, 16956, 16317])).
% 2.97/3.14 tff(16958,plain,
% 2.97/3.14 (b(s(s(z)), s(s(s(z))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[437, 16957])).
% 2.97/3.14 tff(16959,plain,
% 2.97/3.14 (r(z, s(s(s(z))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[6374, 16955, 16324])).
% 2.97/3.14 tff(16960,plain,
% 2.97/3.14 (~r(s(z), s(s(s(z))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[14376, 16959, 2597])).
% 2.97/3.14 tff(16961,plain,
% 2.97/3.14 (b(s(z), s(s(s(z))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[253, 16960])).
% 2.97/3.14 tff(16962,plain,
% 2.97/3.14 ($false),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[4270, 16961, 16958, 16910, 16918])).
% 2.97/3.14 tff(16963,plain,((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.14 tff(16964,plain,
% 2.97/3.14 (~r(s(s(z)), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[16963, 550, 16912, 82])).
% 2.97/3.14 tff(16965,plain,
% 2.97/3.14 (b(s(s(z)), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[625, 16964])).
% 2.97/3.14 tff(16966,plain,
% 2.97/3.14 (~b(s(s(s(z))), s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[14208, 16965, 16910, 550])).
% 2.97/3.14 tff(16967,plain,
% 2.97/3.14 (r(s(s(s(z))), s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[421, 16966])).
% 2.97/3.14 tff(16968,plain,
% 2.97/3.14 (~b(z, s(s(s(elem!1))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[14190, 16965, 16893, 550])).
% 2.97/3.14 tff(16969,plain,
% 2.97/3.14 (r(z, s(s(s(elem!1))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[590, 16968])).
% 2.97/3.14 tff(16970,plain,
% 2.97/3.14 ((~r(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1)))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[4549, 11419])).
% 2.97/3.14 tff(16971,plain,
% 2.97/3.14 ((~r(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1)))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[16970, 14660])).
% 2.97/3.14 tff(16972,plain,
% 2.97/3.14 (~r(s(s(z)), s(s(s(z))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[16971, 16969, 16914, 494, 16965, 16967])).
% 2.97/3.14 tff(16973,plain,
% 2.97/3.14 (b(s(s(z)), s(s(s(z))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[437, 16972])).
% 2.97/3.14 tff(16974,plain,
% 2.97/3.14 (~b(z, s(s(s(z))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2972, 16965, 550, 16910])).
% 2.97/3.14 tff(16975,plain,
% 2.97/3.14 (r(z, s(s(s(z))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[1318, 16974])).
% 2.97/3.14 tff(16976,plain,
% 2.97/3.14 (~r(s(z), s(s(s(z))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[14376, 16975, 16912])).
% 2.97/3.14 tff(16977,plain,
% 2.97/3.14 (b(s(z), s(s(s(z))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[253, 16976])).
% 2.97/3.14 tff(16978,plain,
% 2.97/3.14 ($false),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[4270, 16977, 16973, 16910, 16323])).
% 2.97/3.14 tff(16979,plain,((~b(s(z), z)) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.14 tff(16980,plain,
% 2.97/3.14 (~b(s(z), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[16979, 82])).
% 2.97/3.14 tff(16981,plain,
% 2.97/3.14 (r(s(z), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[568, 16980])).
% 2.97/3.14 tff(16982,plain,
% 2.97/3.14 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16929])).
% 2.97/3.14 tff(16983,plain,
% 2.97/3.14 (s(z) = s(elem!1)),
% 2.97/3.14 inference(transitivity,[status(thm)],[24, 16982, 29])).
% 2.97/3.14 tff(16984,plain,
% 2.97/3.14 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16983])).
% 2.97/3.14 tff(16985,plain,
% 2.97/3.14 (z = elem!1),
% 2.97/3.14 inference(transitivity,[status(thm)],[1443, 16984, 85])).
% 2.97/3.14 tff(16986,plain,
% 2.97/3.14 (b(z, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16985])).
% 2.97/3.14 tff(16987,plain,
% 2.97/3.14 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16317])).
% 2.97/3.14 tff(16988,plain,
% 2.97/3.14 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(s(elem!1)))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16987])).
% 2.97/3.14 tff(16989,plain,
% 2.97/3.14 (~b(z, s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[14286, 1331, 16893, 81])).
% 2.97/3.14 tff(16990,plain,
% 2.97/3.14 (r(z, s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[222, 16989])).
% 2.97/3.14 tff(16991,plain,
% 2.97/3.14 (~r(z, s(s(s(z))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[11471, 16990, 2597, 16910, 1331])).
% 2.97/3.14 tff(16992,plain,
% 2.97/3.14 (b(z, s(s(s(z))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[1318, 16991])).
% 2.97/3.14 tff(16993,plain,
% 2.97/3.14 (b(s(s(s(elem!1))), s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[1995, 1331, 16317])).
% 2.97/3.14 tff(16994,plain,
% 2.97/3.14 (~r(z, s(s(s(elem!1))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[6374, 16991, 16324])).
% 2.97/3.14 tff(16995,plain,
% 2.97/3.14 (b(z, s(s(s(elem!1))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[590, 16994])).
% 2.97/3.14 tff(16996,plain,
% 2.97/3.14 (~b(s(s(z)), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[16151, 16995, 16993])).
% 2.97/3.14 tff(16997,plain,
% 2.97/3.14 (r(s(s(z)), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[625, 16996])).
% 2.97/3.14 tff(16998,plain,
% 2.97/3.14 (~b(s(z), s(s(s(elem!1))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[9797, 16997, 16317, 2597, 81, 1331, 16910])).
% 2.97/3.14 tff(16999,plain,
% 2.97/3.14 (~b(s(z), s(s(s(z))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[6628, 16998, 16317])).
% 2.97/3.14 tff(17000,plain,
% 2.97/3.14 (r(s(z), s(s(s(z))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[253, 16999])).
% 2.97/3.14 tff(17001,plain,
% 2.97/3.14 (~r(s(s(s(s(z)))), s(z))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[16084, 17000, 1331, 16992, 2597, 81])).
% 2.97/3.14 tff(17002,plain,
% 2.97/3.14 (b(s(s(s(s(z)))), s(z))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13335, 17001])).
% 2.97/3.14 tff(17003,plain,
% 2.97/3.14 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[15853, 97, 16893, 16910, 17002])).
% 2.97/3.14 tff(17004,plain,
% 2.97/3.14 (r(s(s(z)), s(s(s(s(z)))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[15855, 17003])).
% 2.97/3.14 tff(17005,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(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(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(17006,plain,
% 2.97/3.14 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~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(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(17007,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $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(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(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[17006])).
% 2.97/3.14 tff(17008,plain,
% 2.97/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $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(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(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.97/3.14 inference(transitivity,[status(thm)],[17007, 17005])).
% 2.97/3.14 tff(17009,plain,
% 2.97/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $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(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.97/3.14 inference(quant_inst,[status(thm)],[])).
% 2.97/3.14 tff(17010,plain,
% 2.97/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[17009, 17008])).
% 2.97/3.14 tff(17011,plain,
% 2.97/3.14 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[17010, 97, 16893, 16910, 17002])).
% 2.97/3.14 tff(17012,plain,
% 2.97/3.14 (r(s(s(s(s(z)))), s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13323, 17011])).
% 2.97/3.14 tff(17013,plain,
% 2.97/3.14 (~r(z, s(s(s(s(z)))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[9056, 155, 16990, 17012, 17004])).
% 2.97/3.14 tff(17014,plain,
% 2.97/3.14 (b(z, s(s(s(s(z)))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[7416, 17013])).
% 2.97/3.14 tff(17015,plain,
% 2.97/3.14 (b(z, s(s(s(s(elem!1)))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[17014, 16988])).
% 2.97/3.14 tff(17016,plain,
% 2.97/3.14 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[17015, 16986])).
% 2.97/3.14 tff(17017,plain,
% 2.97/3.14 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16987, 16929])).
% 2.97/3.14 tff(17018,plain,
% 2.97/3.14 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[17012, 17017])).
% 2.97/3.14 tff(17019,plain,
% 2.97/3.14 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16985])).
% 2.97/3.14 tff(17020,plain,
% 2.97/3.14 (r(z, s(s(elem!1)))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[16990, 16934])).
% 2.97/3.14 tff(17021,plain,
% 2.97/3.14 (r(elem!1, s(s(elem!1)))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[17020, 17019])).
% 2.97/3.14 tff(17022,plain,
% 2.97/3.14 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16985])).
% 2.97/3.14 tff(17023,plain,
% 2.97/3.14 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16987])).
% 2.97/3.14 tff(17024,plain,
% 2.97/3.14 (~r(s(s(s(s(z)))), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[15434, 155, 16990, 16997, 17012])).
% 2.97/3.14 tff(17025,plain,
% 2.97/3.14 (b(s(s(s(s(z)))), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2860, 17024])).
% 2.97/3.14 tff(17026,plain,
% 2.97/3.14 (b(s(s(s(s(elem!1)))), z)),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[17025, 17023])).
% 2.97/3.14 tff(17027,plain,
% 2.97/3.14 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[17026, 17022])).
% 2.97/3.14 tff(17028,plain,
% 2.97/3.14 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16929, 16987])).
% 2.97/3.14 tff(17029,plain,
% 2.97/3.14 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[17004, 17028])).
% 2.97/3.14 tff(17030,plain,
% 2.97/3.14 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16985])).
% 2.97/3.14 tff(17031,plain,
% 2.97/3.14 ((s(s(s(s(s(elem!1))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 2.97/3.14 inference(transitivity,[status(thm)],[17030, 6292])).
% 2.97/3.14 tff(17032,plain,
% 2.97/3.14 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.97/3.14 inference(transitivity,[status(thm)],[17031, 6293])).
% 2.97/3.14 tff(17033,plain,
% 2.97/3.14 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[17032])).
% 2.97/3.14 tff(17034,plain,
% 2.97/3.14 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[6299, 17033])).
% 2.97/3.14 tff(17035,plain,
% 2.97/3.14 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16985])).
% 2.97/3.14 tff(17036,plain,
% 2.97/3.14 (r(s(s(elem!1)), z)),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[16997, 16936])).
% 2.97/3.14 tff(17037,plain,
% 2.97/3.14 (r(s(s(elem!1)), elem!1)),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[17036, 17035])).
% 2.97/3.14 tff(17038,plain,
% 2.97/3.14 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[6197, 16926, 16317])).
% 2.97/3.14 tff(17039,plain,
% 2.97/3.14 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[7544, 17038])).
% 2.97/3.14 tff(17040,plain,
% 2.97/3.14 ((s(s(z)) = s(s(s(s(s(elem!1)))))) <=> (s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16929])).
% 2.97/3.14 tff(17041,plain,
% 2.97/3.14 ((s(s(z)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.97/3.14 inference(transitivity,[status(thm)],[17040, 11819])).
% 2.97/3.14 tff(17042,plain,
% 2.97/3.14 ((~(s(s(z)) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[17041])).
% 2.97/3.14 tff(17043,plain,
% 2.97/3.14 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[13386, 17042])).
% 2.97/3.14 tff(17044,plain,
% 2.97/3.14 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.97/3.14 inference(symmetry,[status(thm)],[16982])).
% 2.97/3.14 tff(17045,plain,
% 2.97/3.14 (s(elem!1) = s(z)),
% 2.97/3.14 inference(transitivity,[status(thm)],[30, 17044, 23])).
% 2.97/3.14 tff(17046,plain,
% 2.97/3.14 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[17045])).
% 2.97/3.14 tff(17047,plain,
% 2.97/3.14 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.97/3.14 inference(symmetry,[status(thm)],[17046])).
% 2.97/3.14 tff(17048,plain,
% 2.97/3.14 (r(s(s(s(elem!1))), s(elem!1))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[125, 17047])).
% 2.97/3.14 tff(17049,plain,
% 2.97/3.14 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16985])).
% 2.97/3.14 tff(17050,plain,
% 2.97/3.14 (b(s(s(s(elem!1))), elem!1)),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[14660, 17049])).
% 2.97/3.14 tff(17051,plain,
% 2.97/3.14 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16985])).
% 2.97/3.14 tff(17052,plain,
% 2.97/3.14 (b(elem!1, s(s(s(elem!1))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[16995, 17051])).
% 2.97/3.14 tff(17053,plain,
% 2.97/3.14 (r(s(z), s(s(s(elem!1))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[181, 16998])).
% 2.97/3.14 tff(17054,plain,
% 2.97/3.14 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16983, 16929])).
% 2.97/3.14 tff(17055,plain,
% 2.97/3.14 (b(s(elem!1), s(s(elem!1)))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[16910, 17054])).
% 2.97/3.14 tff(17056,plain,
% 2.97/3.14 (b(s(s(elem!1)), s(elem!1))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[9687, 16893, 16317])).
% 2.97/3.14 tff(17057,plain,
% 2.97/3.14 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16985])).
% 2.97/3.14 tff(17058,plain,
% 2.97/3.14 (r(s(z), z) <=> r(s(elem!1), z)),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16983])).
% 2.97/3.14 tff(17059,plain,
% 2.97/3.14 (r(s(elem!1), z)),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[81, 17058])).
% 2.97/3.14 tff(17060,plain,
% 2.97/3.14 (r(s(elem!1), elem!1)),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[17059, 17057])).
% 2.97/3.14 tff(17061,plain,
% 2.97/3.14 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[9681, 17060, 17056, 17055, 16317, 17053, 17052, 17050, 17048])).
% 2.97/3.14 tff(17062,plain,
% 2.97/3.14 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[6269, 17061, 17043])).
% 2.97/3.14 tff(17063,plain,
% 2.97/3.14 ($false),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[9205, 17062, 17039, 17037, 17034, 17029, 17027, 17021, 17018, 17016])).
% 2.97/3.14 tff(17064,plain,((~b(s(s(s(z))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.14 tff(17065,plain,
% 2.97/3.14 (~b(s(s(s(z))), s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[17064, 16981, 494, 16912])).
% 2.97/3.14 tff(17066,plain,
% 2.97/3.14 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[2677, 17065, 16317])).
% 2.97/3.14 tff(17067,plain,
% 2.97/3.14 (r(s(s(s(elem!1))), s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[58, 17066])).
% 2.97/3.14 tff(17068,plain,
% 2.97/3.14 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16985])).
% 2.97/3.14 tff(17069,plain,
% 2.97/3.14 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16929])).
% 2.97/3.14 tff(17070,plain,
% 2.97/3.14 (b(z, s(s(elem!1)))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[204, 17069])).
% 2.97/3.14 tff(17071,plain,
% 2.97/3.14 (b(elem!1, s(s(elem!1)))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[17070, 17068])).
% 2.97/3.14 tff(17072,plain,
% 2.97/3.14 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.97/3.14 inference(transitivity,[status(thm)],[16924, 2507])).
% 2.97/3.14 tff(17073,plain,
% 2.97/3.14 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[17072])).
% 2.97/3.14 tff(17074,plain,
% 2.97/3.14 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[286, 17073])).
% 2.97/3.14 tff(17075,plain,
% 2.97/3.14 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.97/3.14 inference(symmetry,[status(thm)],[11819])).
% 2.97/3.14 tff(17076,plain,
% 2.97/3.14 ((s(s(z)) = s(s(s(s(s(elem!1)))))) <=> (s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.97/3.14 inference(transitivity,[status(thm)],[17041, 17075])).
% 2.97/3.14 tff(17077,plain,
% 2.97/3.14 ((~(s(s(z)) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(elem!1)))))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[17076])).
% 2.97/3.14 tff(17078,plain,
% 2.97/3.14 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[13386, 17077])).
% 2.97/3.14 tff(17079,plain,
% 2.97/3.14 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[16983])).
% 2.97/3.14 tff(17080,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))), introduced(assumption)).
% 2.97/3.14 tff(17081,plain,
% 2.97/3.14 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(elem!1))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[17080])).
% 2.97/3.14 tff(17082,plain,
% 2.97/3.14 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.97/3.14 inference(transitivity,[status(thm)],[6168, 17081, 19])).
% 2.97/3.14 tff(17083,plain,
% 2.97/3.14 ($false),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[347, 17082])).
% 2.97/3.14 tff(17084,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,[]))).
% 2.97/3.14 tff(17085,plain,
% 2.97/3.14 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[17084, 16933])).
% 2.97/3.14 tff(17086,plain,
% 2.97/3.14 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[2508])).
% 2.97/3.14 tff(17087,plain,
% 2.97/3.14 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 2.97/3.14 inference(transitivity,[status(thm)],[17086, 4295])).
% 2.97/3.14 tff(17088,plain,
% 2.97/3.14 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.97/3.14 inference(symmetry,[status(thm)],[17087])).
% 2.97/3.14 tff(17089,plain,
% 2.97/3.14 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[17088])).
% 2.97/3.14 tff(17090,plain,
% 2.97/3.14 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[286, 17089])).
% 2.97/3.14 tff(17091,plain,
% 2.97/3.14 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[2526, 2508])).
% 2.97/3.14 tff(17092,plain,
% 2.97/3.14 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.97/3.14 inference(symmetry,[status(thm)],[17091])).
% 2.97/3.14 tff(17093,plain,
% 2.97/3.14 (~r(s(z), s(s(s(z))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[13916, 175, 2508])).
% 2.97/3.14 tff(17094,plain,
% 2.97/3.14 (b(s(z), s(s(s(z))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[253, 17093])).
% 2.97/3.14 tff(17095,plain,
% 2.97/3.14 (b(s(elem!1), s(s(s(elem!1))))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[17094, 17092])).
% 2.97/3.14 tff(17096,plain,
% 2.97/3.14 ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), z))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[4442, 11419])).
% 2.97/3.14 tff(17097,plain,
% 2.97/3.14 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[17096, 17095, 81, 126, 124, 12052])).
% 2.97/3.14 tff(17098,plain,
% 2.97/3.14 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[486, 17097, 17090])).
% 2.97/3.14 tff(17099,plain,
% 2.97/3.14 (b(s(z), s(s(s(elem!1))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[181, 175])).
% 2.97/3.14 tff(17100,plain,
% 2.97/3.14 ((~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(z), z))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[4465, 11419])).
% 2.97/3.14 tff(17101,plain,
% 2.97/3.14 (~r(s(s(s(s(elem!1)))), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[17100, 17098, 87, 17099, 12052, 81, 126])).
% 2.97/3.14 tff(17102,plain,
% 2.97/3.14 (b(s(s(s(s(elem!1)))), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[842, 17101])).
% 2.97/3.14 tff(17103,plain,
% 2.97/3.14 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[4806, 17102, 87, 204])).
% 2.97/3.14 tff(17104,plain,
% 2.97/3.14 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[452, 17103])).
% 2.97/3.14 tff(17105,plain,
% 2.97/3.14 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[5279, 17104, 15616, 17098])).
% 2.97/3.14 tff(17106,plain,
% 2.97/3.14 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[336, 17105])).
% 2.97/3.14 tff(17107,plain,
% 2.97/3.14 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[4824, 17106, 17099, 87, 126, 17102])).
% 2.97/3.14 tff(17108,plain,
% 2.97/3.14 (r(s(z), s(s(s(s(elem!1)))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[280, 17107])).
% 2.97/3.14 tff(17109,plain,
% 2.97/3.14 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[5023, 17106, 87, 17094])).
% 2.97/3.14 tff(17110,plain,
% 2.97/3.14 (r(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[511, 17109])).
% 2.97/3.14 tff(17111,plain,
% 2.97/3.14 ($false),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[503, 17110, 17108, 125, 17098])).
% 2.97/3.14 tff(17112,plain,(r(s(z), s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~(s(s(s(elem!1))) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.14 tff(17113,plain,
% 2.97/3.14 (r(s(z), s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[17112, 14660])).
% 2.97/3.14 tff(17114,plain,
% 2.97/3.14 (r(s(z), s(s(s(elem!1))))),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[17113, 3008, 16324, 16893, 81, 204, 125])).
% 2.97/3.14 tff(17115,assumption,(r(s(s(s(s(s(elem!1))))), s(z))), introduced(assumption)).
% 2.97/3.14 tff(17116,plain,
% 2.97/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(17117,plain,
% 2.97/3.14 (((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(17118,plain,
% 2.97/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), z))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[17117])).
% 2.97/3.14 tff(17119,plain,
% 2.97/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 2.97/3.14 inference(transitivity,[status(thm)],[17118, 17116])).
% 2.97/3.14 tff(17120,plain,
% 2.97/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.97/3.14 inference(quant_inst,[status(thm)],[])).
% 2.97/3.14 tff(17121,plain,
% 2.97/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), z))),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[17120, 17119])).
% 2.97/3.14 tff(17122,plain,
% 2.97/3.14 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[17121, 155, 11419, 81, 17115])).
% 2.97/3.14 tff(17123,plain,
% 2.97/3.14 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = z) | b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = z) | b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(17124,plain,
% 2.97/3.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = z) | b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z))),
% 2.97/3.14 inference(quant_inst,[status(thm)],[])).
% 2.97/3.14 tff(17125,plain,
% 2.97/3.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = z) | b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z)),
% 2.97/3.14 inference(modus_ponens,[status(thm)],[17124, 17123])).
% 2.97/3.14 tff(17126,plain,
% 2.97/3.14 (b(s(s(s(s(s(elem!1))))), z)),
% 2.97/3.14 inference(unit_resolution,[status(thm)],[17125, 53, 6299, 17122])).
% 2.97/3.14 tff(17127,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))), introduced(assumption)).
% 2.97/3.14 tff(17128,plain,
% 2.97/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(17129,plain,
% 2.97/3.14 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.97/3.14 inference(rewrite,[status(thm)],[])).
% 2.97/3.14 tff(17130,plain,
% 2.97/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))))),
% 2.97/3.14 inference(monotonicity,[status(thm)],[17129])).
% 2.97/3.14 tff(17131,plain,
% 2.97/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.97/3.14 inference(transitivity,[status(thm)],[17130, 17128])).
% 2.97/3.14 tff(17132,plain,
% 2.97/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.97/3.15 inference(quant_inst,[status(thm)],[])).
% 2.97/3.15 tff(17133,plain,
% 2.97/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[17132, 17131])).
% 2.97/3.15 tff(17134,plain,
% 2.97/3.15 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[17133, 155, 125, 225, 17115])).
% 2.97/3.15 tff(17135,plain,
% 2.97/3.15 (((~![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)))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(17136,plain,
% 2.97/3.15 ((~![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)))))),
% 2.97/3.15 inference(quant_inst,[status(thm)],[])).
% 2.97/3.15 tff(17137,plain,
% 2.97/3.15 ((~![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))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[17136, 17135])).
% 2.97/3.15 tff(17138,plain,
% 2.97/3.15 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[17137, 53, 17134, 17127])).
% 2.97/3.15 tff(17139,plain,
% 2.97/3.15 (((~![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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(17140,plain,
% 2.97/3.15 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(17141,plain,
% 2.97/3.15 (((~![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(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17140])).
% 2.97/3.15 tff(17142,plain,
% 2.97/3.15 (((~![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(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.97/3.15 inference(transitivity,[status(thm)],[17141, 17139])).
% 2.97/3.15 tff(17143,plain,
% 2.97/3.15 ((~![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(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.97/3.15 inference(quant_inst,[status(thm)],[])).
% 2.97/3.15 tff(17144,plain,
% 2.97/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[17143, 17142])).
% 2.97/3.15 tff(17145,plain,
% 2.97/3.15 ($false),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[17144, 97, 126, 124, 17138, 17126])).
% 2.97/3.15 tff(17146,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.15 tff(17147,plain,
% 2.97/3.15 ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1)))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[17146, 14660])).
% 2.97/3.15 tff(17148,plain,
% 2.97/3.15 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[17147, 17114, 81, 125, 17085, 3008])).
% 2.97/3.15 tff(17149,plain,
% 2.97/3.15 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[6239, 17148, 16341])).
% 2.97/3.15 tff(17150,plain,
% 2.97/3.15 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[17149, 17079])).
% 2.97/3.15 tff(17151,plain,
% 2.97/3.15 (((~![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(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(17152,plain,
% 2.97/3.15 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(17153,plain,
% 2.97/3.15 (((~![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(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17152])).
% 2.97/3.15 tff(17154,plain,
% 2.97/3.15 (((~![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(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.97/3.15 inference(transitivity,[status(thm)],[17153, 17151])).
% 2.97/3.15 tff(17155,plain,
% 2.97/3.15 ((~![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(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.97/3.15 inference(quant_inst,[status(thm)],[])).
% 2.97/3.15 tff(17156,plain,
% 2.97/3.15 ((~![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(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[17155, 17154])).
% 2.97/3.15 tff(17157,plain,
% 2.97/3.15 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[17156, 97, 17055, 17056, 17150])).
% 2.97/3.15 tff(17158,plain,
% 2.97/3.15 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(17159,plain,
% 2.97/3.15 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 2.97/3.15 inference(quant_inst,[status(thm)],[])).
% 2.97/3.15 tff(17160,plain,
% 2.97/3.15 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[17159, 17158])).
% 2.97/3.15 tff(17161,plain,
% 2.97/3.15 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[17160, 53])).
% 2.97/3.15 tff(17162,plain,
% 2.97/3.15 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[17161, 17157, 17078])).
% 2.97/3.15 tff(17163,plain,
% 2.97/3.15 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17045])).
% 2.97/3.15 tff(17164,plain,
% 2.97/3.15 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.97/3.15 inference(symmetry,[status(thm)],[17163])).
% 2.97/3.15 tff(17165,plain,
% 2.97/3.15 (~b(s(s(s(z))), s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[17064, 81, 125, 2597])).
% 2.97/3.15 tff(17166,plain,
% 2.97/3.15 (r(s(s(s(z))), s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[421, 17165])).
% 2.97/3.15 tff(17167,plain,
% 2.97/3.15 (~r(z, s(s(s(z))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[6652, 585, 16317])).
% 2.97/3.15 tff(17168,plain,
% 2.97/3.15 (b(z, s(s(s(z))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[1318, 17167])).
% 2.97/3.15 tff(17169,plain,
% 2.97/3.15 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[5741, 97, 126, 3008, 14263])).
% 2.97/3.15 tff(17170,plain,
% 2.97/3.15 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[212, 204, 87, 3008])).
% 2.97/3.15 tff(17171,plain,
% 2.97/3.15 (r(s(s(s(elem!1))), s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[58, 17170])).
% 2.97/3.15 tff(17172,plain,
% 2.97/3.15 (~r(s(z), s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[15698, 125, 645, 87, 126, 585])).
% 2.97/3.15 tff(17173,plain,
% 2.97/3.15 (b(s(z), s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[548, 17172])).
% 2.97/3.15 tff(17174,plain,
% 2.97/3.15 (~r(s(z), s(s(s(z))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[2638, 2630, 125, 2597])).
% 2.97/3.15 tff(17175,plain,
% 2.97/3.15 (b(s(z), s(s(s(z))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[253, 17174])).
% 2.97/3.15 tff(17176,plain,
% 2.97/3.15 ($false),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[4270, 11687, 17175, 535, 1216])).
% 2.97/3.15 tff(17177,plain,((~r(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.15 tff(17178,plain,
% 2.97/3.15 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[17177, 14263, 17173, 1960, 17171, 125, 2597])).
% 2.97/3.15 tff(17179,plain,
% 2.97/3.15 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[2687, 17178, 17169])).
% 2.97/3.15 tff(17180,plain,
% 2.97/3.15 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17179])).
% 2.97/3.15 tff(17181,plain,
% 2.97/3.15 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17180])).
% 2.97/3.15 tff(17182,plain,
% 2.97/3.15 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 2.97/3.15 inference(symmetry,[status(thm)],[17181])).
% 2.97/3.15 tff(17183,plain,
% 2.97/3.15 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17179])).
% 2.97/3.15 tff(17184,plain,
% 2.97/3.15 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.97/3.15 inference(symmetry,[status(thm)],[17183])).
% 2.97/3.15 tff(17185,plain,
% 2.97/3.15 (s(s(z)) = s(s(elem!1))),
% 2.97/3.15 inference(transitivity,[status(thm)],[73, 17184, 19])).
% 2.97/3.15 tff(17186,plain,
% 2.97/3.15 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17185, 17182])).
% 2.97/3.15 tff(17187,plain,
% 2.97/3.15 ((~r(s(s(z)), s(s(s(s(s(z))))))) <=> (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17186])).
% 2.97/3.15 tff(17188,plain,
% 2.97/3.15 (s(s(elem!1)) = s(s(z))),
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% 2.97/3.15 tff(17189,plain,
% 2.97/3.15 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17188])).
% 2.97/3.15 tff(17190,plain,
% 2.97/3.15 (s(elem!1) = s(z)),
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% 2.97/3.15 tff(17191,plain,
% 2.97/3.15 (inj_0(s(elem!1)) = inj_0(s(z))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17190])).
% 2.97/3.15 tff(17192,plain,
% 2.97/3.15 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.97/3.15 inference(symmetry,[status(thm)],[17191])).
% 2.97/3.15 tff(17193,plain,
% 2.97/3.15 (z = elem!1),
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% 2.97/3.15 tff(17194,plain,
% 2.97/3.15 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17182, 17193])).
% 2.97/3.15 tff(17195,plain,
% 2.97/3.15 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(s(s(s(z))))), z)),
% 2.97/3.15 inference(symmetry,[status(thm)],[17194])).
% 2.97/3.15 tff(17196,plain,
% 2.97/3.15 (elem!1 = z),
% 2.97/3.15 inference(transitivity,[status(thm)],[1450, 17191, 17])).
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% 2.97/3.15 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (z = s(s(s(s(s(z))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17196, 17181])).
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% 2.97/3.15 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(z))))) = z)),
% 2.97/3.15 inference(transitivity,[status(thm)],[17197, 16444])).
% 2.97/3.15 tff(17199,plain,
% 2.97/3.15 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 2.97/3.15 inference(symmetry,[status(thm)],[17198])).
% 2.97/3.15 tff(17200,plain,
% 2.97/3.15 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.97/3.15 inference(transitivity,[status(thm)],[17199, 6293])).
% 2.97/3.15 tff(17201,plain,
% 2.97/3.15 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17200])).
% 2.97/3.15 tff(17202,plain,
% 2.97/3.15 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[16452, 17201])).
% 2.97/3.15 tff(17203,plain,
% 2.97/3.15 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17182, 17193])).
% 2.97/3.15 tff(17204,plain,
% 2.97/3.15 ((~b(s(s(s(s(s(z))))), z)) <=> (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17203])).
% 2.97/3.15 tff(17205,plain,
% 2.97/3.15 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17182])).
% 2.97/3.15 tff(17206,plain,
% 2.97/3.15 (b(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.97/3.15 inference(symmetry,[status(thm)],[17205])).
% 2.97/3.15 tff(17207,plain,
% 2.97/3.15 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[2682, 17179])).
% 2.97/3.15 tff(17208,plain,
% 2.97/3.15 (~(s(s(s(s(s(elem!1))))) = s(s(s(z))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[7491, 17207])).
% 2.97/3.15 tff(17209,plain,
% 2.97/3.15 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17182])).
% 2.97/3.15 tff(17210,plain,
% 2.97/3.15 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17209])).
% 2.97/3.15 tff(17211,plain,
% 2.97/3.15 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17182, 17185])).
% 2.97/3.15 tff(17212,plain,
% 2.97/3.15 (r(s(s(s(s(s(elem!1))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.15 inference(symmetry,[status(thm)],[17211])).
% 2.97/3.15 tff(17213,plain,
% 2.97/3.15 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(z))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17180, 17190])).
% 2.97/3.15 tff(17214,plain,
% 2.97/3.15 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(z) = s(s(s(s(z)))))),
% 2.97/3.15 inference(transitivity,[status(thm)],[17213, 2831])).
% 2.97/3.15 tff(17215,plain,
% 2.97/3.15 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.97/3.15 inference(symmetry,[status(thm)],[17214])).
% 2.97/3.15 tff(17216,plain,
% 2.97/3.15 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17215])).
% 2.97/3.15 tff(17217,plain,
% 2.97/3.15 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[2833, 17216])).
% 2.97/3.15 tff(17218,plain,
% 2.97/3.15 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[6172, 17217])).
% 2.97/3.15 tff(17219,plain,
% 2.97/3.15 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17190])).
% 2.97/3.15 tff(17220,plain,
% 2.97/3.15 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 2.97/3.15 inference(symmetry,[status(thm)],[17219])).
% 2.97/3.15 tff(17221,plain,
% 2.97/3.15 (r(s(z), elem!1) <=> r(s(z), z)),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17196])).
% 2.97/3.15 tff(17222,plain,
% 2.97/3.15 (r(s(z), z) <=> r(s(z), elem!1)),
% 2.97/3.15 inference(symmetry,[status(thm)],[17221])).
% 2.97/3.15 tff(17223,plain,
% 2.97/3.15 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 2.97/3.15 inference(transitivity,[status(thm)],[17222, 17220])).
% 2.97/3.15 tff(17224,plain,
% 2.97/3.15 (r(s(elem!1), elem!1)),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[81, 17223])).
% 2.97/3.15 tff(17225,plain,
% 2.97/3.15 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17179])).
% 2.97/3.15 tff(17226,plain,
% 2.97/3.15 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.97/3.15 inference(symmetry,[status(thm)],[17225])).
% 2.97/3.15 tff(17227,plain,
% 2.97/3.15 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17196])).
% 2.97/3.15 tff(17228,plain,
% 2.97/3.15 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 2.97/3.15 inference(symmetry,[status(thm)],[17227])).
% 2.97/3.15 tff(17229,plain,
% 2.97/3.15 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.97/3.15 inference(transitivity,[status(thm)],[17228, 17226])).
% 2.97/3.15 tff(17230,plain,
% 2.97/3.15 (b(s(s(s(elem!1))), elem!1)),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[14263, 17229])).
% 2.97/3.15 tff(17231,plain,
% 2.97/3.15 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(z)))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17188])).
% 2.97/3.15 tff(17232,plain,
% 2.97/3.15 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.97/3.15 inference(symmetry,[status(thm)],[17231])).
% 2.97/3.15 tff(17233,plain,
% 2.97/3.15 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.97/3.15 inference(symmetry,[status(thm)],[17189])).
% 2.97/3.15 tff(17234,plain,
% 2.97/3.15 (s(z) = s(elem!1)),
% 2.97/3.15 inference(transitivity,[status(thm)],[24, 17233, 29])).
% 2.97/3.15 tff(17235,plain,
% 2.97/3.15 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17234])).
% 2.97/3.15 tff(17236,plain,
% 2.97/3.15 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.97/3.15 inference(transitivity,[status(thm)],[17235, 17232])).
% 2.97/3.15 tff(17237,plain,
% 2.97/3.15 (b(s(elem!1), s(s(elem!1)))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[17173, 17236])).
% 2.97/3.15 tff(17238,plain,
% 2.97/3.15 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17179, 17190])).
% 2.97/3.15 tff(17239,plain,
% 2.97/3.15 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.97/3.15 inference(symmetry,[status(thm)],[17238])).
% 2.97/3.15 tff(17240,plain,
% 2.97/3.15 (r(s(s(s(elem!1))), s(elem!1))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[2597, 17239])).
% 2.97/3.15 tff(17241,plain,
% 2.97/3.15 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17179])).
% 2.97/3.15 tff(17242,plain,
% 2.97/3.15 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.97/3.15 inference(symmetry,[status(thm)],[17241])).
% 2.97/3.15 tff(17243,plain,
% 2.97/3.15 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17196])).
% 2.97/3.15 tff(17244,plain,
% 2.97/3.15 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.97/3.15 inference(symmetry,[status(thm)],[17243])).
% 2.97/3.15 tff(17245,plain,
% 2.97/3.15 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.97/3.15 inference(transitivity,[status(thm)],[17244, 17242])).
% 2.97/3.15 tff(17246,plain,
% 2.97/3.15 (~r(z, s(s(s(z))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[6652, 17207, 585])).
% 2.97/3.15 tff(17247,plain,
% 2.97/3.15 (b(z, s(s(s(z))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[1318, 17246])).
% 2.97/3.15 tff(17248,plain,
% 2.97/3.15 (b(elem!1, s(s(s(elem!1))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[17247, 17245])).
% 2.97/3.15 tff(17249,plain,
% 2.97/3.15 (b(s(s(elem!1)), s(elem!1))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[9687, 17207, 87])).
% 2.97/3.15 tff(17250,plain,
% 2.97/3.15 (r(s(z), s(s(s(elem!1))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[17112, 17179, 87, 126, 204, 81, 3008, 125])).
% 2.97/3.15 tff(17251,plain,
% 2.97/3.15 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[9681, 17250, 17249, 17248, 17207, 17240, 17237, 17230, 17224])).
% 2.97/3.15 tff(17252,plain,
% 2.97/3.15 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[6269, 17251, 17218])).
% 2.97/3.15 tff(17253,plain,
% 2.97/3.15 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[17252, 17212])).
% 2.97/3.15 tff(17254,plain,
% 2.97/3.15 (~b(s(s(z)), s(s(s(z))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[13753, 17247, 204, 14263])).
% 2.97/3.15 tff(17255,plain,
% 2.97/3.15 (r(s(s(z)), s(s(s(z))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[437, 17254])).
% 2.97/3.15 tff(17256,plain,
% 2.97/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(17257,plain,
% 2.97/3.15 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(17258,plain,
% 2.97/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17257])).
% 2.97/3.15 tff(17259,plain,
% 2.97/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.97/3.15 inference(transitivity,[status(thm)],[17258, 17256])).
% 2.97/3.15 tff(17260,plain,
% 2.97/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.97/3.15 inference(quant_inst,[status(thm)],[])).
% 2.97/3.15 tff(17261,plain,
% 2.97/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[17260, 17259])).
% 2.97/3.15 tff(17262,plain,
% 2.97/3.15 ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[17261, 155, 17255, 1960])).
% 2.97/3.15 tff(17263,plain,
% 2.97/3.15 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[17262, 17253])).
% 2.97/3.15 tff(17264,plain,
% 2.97/3.15 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[17263, 17210])).
% 2.97/3.15 tff(17265,plain,
% 2.97/3.15 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[6289, 17264, 17208])).
% 2.97/3.15 tff(17266,plain,
% 2.97/3.15 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[17265, 17206])).
% 2.97/3.15 tff(17267,plain,
% 2.97/3.15 (((~![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(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(17268,plain,
% 2.97/3.15 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.97/3.15 inference(rewrite,[status(thm)],[])).
% 2.97/3.15 tff(17269,plain,
% 2.97/3.15 (((~![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(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(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(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.97/3.15 inference(monotonicity,[status(thm)],[17268])).
% 2.97/3.15 tff(17270,plain,
% 2.97/3.15 (((~![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(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(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(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.97/3.15 inference(transitivity,[status(thm)],[17269, 17267])).
% 2.97/3.15 tff(17271,plain,
% 2.97/3.15 ((~![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(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.97/3.15 inference(quant_inst,[status(thm)],[])).
% 2.97/3.15 tff(17272,plain,
% 2.97/3.15 ((~![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(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.97/3.15 inference(modus_ponens,[status(thm)],[17271, 17270])).
% 2.97/3.15 tff(17273,plain,
% 2.97/3.15 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.97/3.15 inference(unit_resolution,[status(thm)],[17272, 97, 17247, 14263])).
% 2.97/3.15 tff(17274,plain,
% 2.97/3.15 (~b(s(s(s(s(s(z))))), z)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[17273, 17266])).
% 2.97/3.16 tff(17275,plain,
% 2.97/3.16 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[17274, 17204])).
% 2.97/3.16 tff(17276,plain,
% 2.97/3.16 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[6313, 17275, 17202])).
% 2.97/3.16 tff(17277,plain,
% 2.97/3.16 (r(s(s(s(s(s(z))))), z)),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[17276, 17195])).
% 2.97/3.16 tff(17278,plain,
% 2.97/3.16 (r(z, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[17193, 17182])).
% 2.97/3.16 tff(17279,plain,
% 2.97/3.16 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(z, s(s(s(s(s(z))))))),
% 2.97/3.16 inference(symmetry,[status(thm)],[17278])).
% 2.97/3.16 tff(17280,plain,
% 2.97/3.16 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[17199])).
% 2.97/3.16 tff(17281,plain,
% 2.97/3.16 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[16452, 17280])).
% 2.97/3.16 tff(17282,plain,
% 2.97/3.16 (b(z, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[17193, 17182])).
% 2.97/3.16 tff(17283,plain,
% 2.97/3.16 ((~b(z, s(s(s(s(s(z))))))) <=> (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[17282])).
% 2.97/3.16 tff(17284,plain,
% 2.97/3.16 (((~![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(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), 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(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(17285,plain,
% 2.97/3.16 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(17286,plain,
% 2.97/3.16 (((~![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(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[17285])).
% 2.97/3.16 tff(17287,plain,
% 2.97/3.16 (((~![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(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.97/3.16 inference(transitivity,[status(thm)],[17286, 17284])).
% 2.97/3.16 tff(17288,plain,
% 2.97/3.16 ((~![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(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.97/3.16 inference(quant_inst,[status(thm)],[])).
% 2.97/3.16 tff(17289,plain,
% 2.97/3.16 ((~![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(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[17288, 17287])).
% 2.97/3.16 tff(17290,plain,
% 2.97/3.16 ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[17289, 97, 17247, 14263])).
% 2.97/3.16 tff(17291,plain,
% 2.97/3.16 (~b(z, s(s(s(s(s(z))))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[17290, 17266])).
% 2.97/3.16 tff(17292,plain,
% 2.97/3.16 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[17291, 17283])).
% 2.97/3.16 tff(17293,plain,
% 2.97/3.16 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[9672, 17292, 17281])).
% 2.97/3.16 tff(17294,plain,
% 2.97/3.16 (r(z, s(s(s(s(s(z))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[17293, 17279])).
% 2.97/3.16 tff(17295,plain,
% 2.97/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(17296,plain,
% 2.97/3.16 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(17297,plain,
% 2.97/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[17296])).
% 2.97/3.16 tff(17298,plain,
% 2.97/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.97/3.16 inference(transitivity,[status(thm)],[17297, 17295])).
% 2.97/3.16 tff(17299,plain,
% 2.97/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), z)))),
% 2.97/3.16 inference(quant_inst,[status(thm)],[])).
% 2.97/3.16 tff(17300,plain,
% 2.97/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[17299, 17298])).
% 2.97/3.16 tff(17301,plain,
% 2.97/3.16 ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[17300, 155, 645])).
% 2.97/3.16 tff(17302,plain,
% 2.97/3.16 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[17301, 17294, 17277])).
% 2.97/3.16 tff(17303,plain,
% 2.97/3.16 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[17302, 17187])).
% 2.97/3.16 tff(17304,plain,
% 2.97/3.16 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[17185, 17182])).
% 2.97/3.16 tff(17305,plain,
% 2.97/3.16 ((~b(s(s(z)), s(s(s(s(s(z))))))) <=> (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[17304])).
% 2.97/3.16 tff(17306,plain,
% 2.97/3.16 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[17182])).
% 2.97/3.16 tff(17307,plain,
% 2.97/3.16 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.97/3.16 inference(symmetry,[status(thm)],[17306])).
% 2.97/3.16 tff(17308,plain,
% 2.97/3.16 (~(s(s(s(s(s(elem!1))))) = s(z))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[6222, 17207])).
% 2.97/3.16 tff(17309,plain,
% 2.97/3.16 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(elem!1))))), s(z))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[17182])).
% 2.97/3.16 tff(17310,plain,
% 2.97/3.16 ((~r(s(s(s(s(s(z))))), s(z))) <=> (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[17309])).
% 2.97/3.16 tff(17311,plain,
% 2.97/3.16 (((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(17312,plain,
% 2.97/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[17311])).
% 2.97/3.16 tff(17313,plain,
% 2.97/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.97/3.16 inference(transitivity,[status(thm)],[17312, 16456])).
% 2.97/3.16 tff(17314,plain,
% 2.97/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.97/3.16 inference(quant_inst,[status(thm)],[])).
% 2.97/3.16 tff(17315,plain,
% 2.97/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[17314, 17313])).
% 2.97/3.16 tff(17316,plain,
% 2.97/3.16 ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[17315, 155, 11419, 81])).
% 2.97/3.16 tff(17317,plain,
% 2.97/3.16 (~r(s(s(s(s(s(z))))), s(z))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[17316, 17277])).
% 2.97/3.16 tff(17318,plain,
% 2.97/3.16 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[17317, 17310])).
% 2.97/3.16 tff(17319,plain,
% 2.97/3.16 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[6239, 17318, 17308])).
% 2.97/3.16 tff(17320,plain,
% 2.97/3.16 (b(s(s(s(s(s(z))))), s(z))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[17319, 17307])).
% 2.97/3.16 tff(17321,plain,
% 2.97/3.16 (((~![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(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(17322,plain,
% 2.97/3.16 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(17323,plain,
% 2.97/3.16 (((~![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(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(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(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[17322])).
% 2.97/3.16 tff(17324,plain,
% 2.97/3.16 (((~![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(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(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(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.97/3.16 inference(transitivity,[status(thm)],[17323, 17321])).
% 2.97/3.16 tff(17325,plain,
% 2.97/3.16 ((~![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(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.97/3.16 inference(quant_inst,[status(thm)],[])).
% 2.97/3.16 tff(17326,plain,
% 2.97/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[17325, 17324])).
% 2.97/3.16 tff(17327,plain,
% 2.97/3.16 ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[17326, 97, 87, 17173])).
% 2.97/3.16 tff(17328,plain,
% 2.97/3.16 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[17327, 17320])).
% 2.97/3.16 tff(17329,plain,
% 2.97/3.16 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[17328, 17305])).
% 2.97/3.16 tff(17330,plain,
% 2.97/3.16 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[17161, 17329, 17303])).
% 2.97/3.16 tff(17331,plain,
% 2.97/3.16 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[17330, 11819])).
% 2.97/3.16 tff(17332,plain,
% 2.97/3.16 ($false),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[17218, 17331])).
% 2.97/3.16 tff(17333,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.16 tff(17334,plain,
% 2.97/3.16 ((~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | r(z, s(s(s(elem!1))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[17333, 14660])).
% 2.97/3.16 tff(17335,plain,
% 2.97/3.16 (~r(s(s(z)), z)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[17334, 585, 2597, 81, 17166, 16893, 125, 204])).
% 2.97/3.16 tff(17336,plain,
% 2.97/3.16 (b(s(s(z)), z)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[625, 17335])).
% 2.97/3.16 tff(17337,plain,
% 2.97/3.16 (~b(s(s(s(s(elem!1)))), z)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[11562, 17336, 17168, 17166, 16323])).
% 2.97/3.16 tff(17338,plain,
% 2.97/3.16 (r(s(s(s(s(elem!1)))), z)),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[842, 17337])).
% 2.97/3.16 tff(17339,plain,
% 2.97/3.16 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[11568, 17338, 81])).
% 2.97/3.16 tff(17340,plain,
% 2.97/3.16 (b(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[511, 17339])).
% 2.97/3.16 tff(17341,plain,
% 2.97/3.16 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[17340, 17164])).
% 2.97/3.16 tff(17342,plain,
% 2.97/3.16 (((~![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(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(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(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(17343,plain,
% 2.97/3.16 (((~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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.97/3.16 inference(rewrite,[status(thm)],[])).
% 2.97/3.16 tff(17344,plain,
% 2.97/3.16 (((~![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(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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 2.97/3.16 inference(monotonicity,[status(thm)],[17343])).
% 2.97/3.16 tff(17345,plain,
% 2.97/3.16 (((~![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(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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.97/3.16 inference(transitivity,[status(thm)],[17344, 17342])).
% 2.97/3.16 tff(17346,plain,
% 2.97/3.16 ((~![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(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)))))))),
% 2.97/3.16 inference(quant_inst,[status(thm)],[])).
% 2.97/3.16 tff(17347,plain,
% 2.97/3.16 ((~![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(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.97/3.16 inference(modus_ponens,[status(thm)],[17346, 17345])).
% 2.97/3.16 tff(17348,plain,
% 2.97/3.16 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[17347, 97, 17055, 17150, 17341])).
% 2.97/3.16 tff(17349,plain,
% 2.97/3.16 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.97/3.16 inference(unit_resolution,[status(thm)],[6254, 17348, 17039])).
% 2.97/3.16 tff(17350,plain,
% 2.97/3.16 (((~![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(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(17351,plain,
% 2.97/3.17 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(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(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(17352,plain,
% 2.97/3.17 (((~![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(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[17351])).
% 2.97/3.17 tff(17353,plain,
% 2.97/3.17 (((~![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(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.97/3.17 inference(transitivity,[status(thm)],[17352, 17350])).
% 2.97/3.17 tff(17354,plain,
% 2.97/3.17 ((~![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(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(17355,plain,
% 2.97/3.17 ((~![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(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[17354, 17353])).
% 2.97/3.17 tff(17356,plain,
% 2.97/3.17 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[17355, 97, 17055, 17150, 17341])).
% 2.97/3.17 tff(17357,plain,
% 2.97/3.17 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(17358,plain,
% 2.97/3.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(17359,plain,
% 2.97/3.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[17358, 17357])).
% 2.97/3.17 tff(17360,plain,
% 2.97/3.17 ((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[17359, 53])).
% 2.97/3.17 tff(17361,plain,
% 2.97/3.17 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[17360, 17356, 17038])).
% 2.97/3.17 tff(17362,plain,
% 2.97/3.17 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(transitivity,[status(thm)],[16931, 1505])).
% 2.97/3.17 tff(17363,plain,
% 2.97/3.17 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[17362])).
% 2.97/3.17 tff(17364,plain,
% 2.97/3.17 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[331, 17363])).
% 2.97/3.17 tff(17365,plain,
% 2.97/3.17 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[14361, 97, 17055, 17056, 17341])).
% 2.97/3.17 tff(17366,plain,
% 2.97/3.17 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[1631, 17365, 17364])).
% 2.97/3.17 tff(17367,plain,
% 2.97/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(17368,plain,
% 2.97/3.17 (((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(17369,plain,
% 2.97/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[17368])).
% 2.97/3.17 tff(17370,plain,
% 2.97/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.97/3.17 inference(transitivity,[status(thm)],[17369, 17367])).
% 2.97/3.17 tff(17371,plain,
% 2.97/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(17372,plain,
% 2.97/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[17371, 17370])).
% 2.97/3.17 tff(17373,plain,
% 2.97/3.17 ($false),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[17372, 155, 17366, 17361, 17349, 17162])).
% 2.97/3.17 tff(17374,plain,(r(z, s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.17 tff(17375,plain,
% 2.97/3.17 (r(z, s(s(s(elem!1))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[17374, 204, 125, 81, 2597])).
% 2.97/3.17 tff(17376,plain,
% 2.97/3.17 (r(z, s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[6374, 17375, 16324])).
% 2.97/3.17 tff(17377,plain,
% 2.97/3.17 (~r(s(z), s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[14376, 17376, 2597])).
% 2.97/3.17 tff(17378,plain,
% 2.97/3.17 (b(s(z), s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[253, 17377])).
% 2.97/3.17 tff(17379,plain,
% 2.97/3.17 (~b(s(s(z)), s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[4270, 17378, 16910, 16323])).
% 2.97/3.17 tff(17380,plain,
% 2.97/3.17 (r(s(s(z)), s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[437, 17379])).
% 2.97/3.17 tff(17381,plain,
% 2.97/3.17 (r(s(s(z)), s(s(s(elem!1))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[10091, 17380, 16317])).
% 2.97/3.17 tff(17382,plain,
% 2.97/3.17 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[2677, 17165, 16317])).
% 2.97/3.17 tff(17383,plain,
% 2.97/3.17 (r(s(s(s(elem!1))), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[58, 17382])).
% 2.97/3.17 tff(17384,plain,
% 2.97/3.17 (~r(s(z), s(s(s(elem!1))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[11807, 17375, 125])).
% 2.97/3.17 tff(17385,plain,
% 2.97/3.17 (b(s(z), s(s(s(elem!1))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[181, 17384])).
% 2.97/3.17 tff(17386,plain,
% 2.97/3.17 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.97/3.17 inference(symmetry,[status(thm)],[16928])).
% 2.97/3.17 tff(17387,plain,
% 2.97/3.17 (s(s(elem!1)) = s(s(z))),
% 2.97/3.17 inference(transitivity,[status(thm)],[167, 17386, 72])).
% 2.97/3.17 tff(17388,plain,
% 2.97/3.17 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[17387])).
% 2.97/3.17 tff(17389,plain,
% 2.97/3.17 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.97/3.17 inference(symmetry,[status(thm)],[17388])).
% 2.97/3.17 tff(17390,plain,
% 2.97/3.17 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[17383, 17389])).
% 2.97/3.17 tff(17391,plain,
% 2.97/3.17 ((~r(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(z), z))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[17100, 14660])).
% 2.97/3.17 tff(17392,plain,
% 2.97/3.17 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[17391, 824, 16317, 16893, 81, 193])).
% 2.97/3.17 tff(17393,plain,
% 2.97/3.17 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[486, 17392, 16926])).
% 2.97/3.17 tff(17394,plain,
% 2.97/3.17 (b(s(s(s(s(z)))), s(z))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13104, 11585, 16324])).
% 2.97/3.17 tff(17395,plain,
% 2.97/3.17 ($false),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[16740, 17394, 17393, 81, 570, 86, 4497, 16323, 204])).
% 2.97/3.17 tff(17396,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.17 tff(17397,plain,
% 2.97/3.17 (~r(s(s(s(s(elem!1)))), z)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[17396, 17375, 81, 17378, 17390, 204, 17385])).
% 2.97/3.17 tff(17398,plain,
% 2.97/3.17 (b(s(s(s(s(elem!1)))), z)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[842, 17397])).
% 2.97/3.17 tff(17399,plain,
% 2.97/3.17 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[4806, 17398, 16893, 204])).
% 2.97/3.17 tff(17400,plain,
% 2.97/3.17 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[452, 17399])).
% 2.97/3.17 tff(17401,plain,
% 2.97/3.17 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[1822, 17400, 16317])).
% 2.97/3.17 tff(17402,plain,
% 2.97/3.17 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[5371, 17401, 16317, 17383, 17381])).
% 2.97/3.17 tff(17403,plain,
% 2.97/3.17 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[821, 17402, 17074])).
% 2.97/3.17 tff(17404,plain,
% 2.97/3.17 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[4474, 17398, 16985])).
% 2.97/3.17 tff(17405,plain,
% 2.97/3.17 ($false),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[4704, 97, 17050, 17404, 17403, 17071])).
% 2.97/3.17 tff(17406,plain,((~b(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.17 tff(17407,plain,
% 2.97/3.17 (~b(z, s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[17406, 16981, 16912, 494])).
% 2.97/3.17 tff(17408,plain,
% 2.97/3.17 (r(z, s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[222, 17407])).
% 2.97/3.17 tff(17409,plain,
% 2.97/3.17 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[145, 17389])).
% 2.97/3.17 tff(17410,plain,
% 2.97/3.17 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[16929])).
% 2.97/3.17 tff(17411,plain,
% 2.97/3.17 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(symmetry,[status(thm)],[17410])).
% 2.97/3.17 tff(17412,plain,
% 2.97/3.17 ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) <=> (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[17411])).
% 2.97/3.17 tff(17413,plain,
% 2.97/3.17 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[16987])).
% 2.97/3.17 tff(17414,plain,
% 2.97/3.17 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.97/3.17 inference(transitivity,[status(thm)],[17413, 17164])).
% 2.97/3.17 tff(17415,plain,
% 2.97/3.17 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[10217, 17414])).
% 2.97/3.17 tff(17416,plain,
% 2.97/3.17 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[14361, 97, 17055, 17056, 17415])).
% 2.97/3.17 tff(17417,plain,
% 2.97/3.17 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[17416, 17412])).
% 2.97/3.17 tff(17418,plain,
% 2.97/3.17 (((~![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(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(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(17419,plain,
% 2.97/3.17 (((~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(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)))))),
% 2.97/3.17 inference(rewrite,[status(thm)],[])).
% 2.97/3.17 tff(17420,plain,
% 2.97/3.17 (((~![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(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(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))))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[17419])).
% 2.97/3.17 tff(17421,plain,
% 2.97/3.17 (((~![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(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(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)))))),
% 2.97/3.17 inference(transitivity,[status(thm)],[17420, 17418])).
% 2.97/3.17 tff(17422,plain,
% 2.97/3.17 ((~![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(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)))))),
% 2.97/3.17 inference(quant_inst,[status(thm)],[])).
% 2.97/3.17 tff(17423,plain,
% 2.97/3.17 ((~![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(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(s(elem!1))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[17422, 17421])).
% 2.97/3.17 tff(17424,plain,
% 2.97/3.17 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[17423, 97, 17055, 17056, 17415])).
% 2.97/3.17 tff(17425,plain,
% 2.97/3.17 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[1484, 17424, 16933])).
% 2.97/3.17 tff(17426,plain,
% 2.97/3.17 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[7352, 17425, 16317])).
% 2.97/3.17 tff(17427,plain,
% 2.97/3.17 (b(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[10217, 17413])).
% 2.97/3.17 tff(17428,plain,
% 2.97/3.17 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[1631, 17416, 17364])).
% 2.97/3.17 tff(17429,plain,
% 2.97/3.17 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[4505, 17428, 4497, 17425])).
% 2.97/3.17 tff(17430,plain,
% 2.97/3.17 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[486, 17429, 16926])).
% 2.97/3.17 tff(17431,plain,
% 2.97/3.17 (~b(z, s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[701, 17430, 124, 17427])).
% 2.97/3.17 tff(17432,plain,
% 2.97/3.17 (r(z, s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[1093, 17431])).
% 2.97/3.17 tff(17433,plain,
% 2.97/3.17 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[3852, 17432, 16317, 226, 17426])).
% 2.97/3.17 tff(17434,plain,
% 2.97/3.17 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[336, 17433])).
% 2.97/3.17 tff(17435,plain,
% 2.97/3.17 ($false),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[17434, 17417])).
% 2.97/3.17 tff(17436,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.17 tff(17437,plain,
% 2.97/3.17 (~b(s(s(s(s(z)))), s(z))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[17436, 124, 226, 17409])).
% 2.97/3.17 tff(17438,plain,
% 2.97/3.17 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13104, 17437, 16324])).
% 2.97/3.17 tff(17439,plain,
% 2.97/3.17 (r(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[511, 17438])).
% 2.97/3.17 tff(17440,plain,
% 2.97/3.17 (~r(s(s(s(s(elem!1)))), z)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[11568, 17439, 81])).
% 2.97/3.17 tff(17441,plain,
% 2.97/3.17 (b(s(s(s(s(elem!1)))), z)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[842, 17440])).
% 2.97/3.17 tff(17442,plain,
% 2.97/3.17 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[15794, 17441, 124])).
% 2.97/3.17 tff(17443,plain,
% 2.97/3.17 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[486, 17442, 16926])).
% 2.97/3.17 tff(17444,plain,
% 2.97/3.17 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[503, 17443, 125, 17439])).
% 2.97/3.17 tff(17445,plain,
% 2.97/3.17 (b(s(z), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[280, 17444])).
% 2.97/3.17 tff(17446,plain,
% 2.97/3.17 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[16317])).
% 2.97/3.17 tff(17447,plain,
% 2.97/3.17 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 2.97/3.17 inference(transitivity,[status(thm)],[17446, 8367])).
% 2.97/3.17 tff(17448,plain,
% 2.97/3.17 ((~(s(s(s(z))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[17447])).
% 2.97/3.17 tff(17449,plain,
% 2.97/3.17 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[2824, 17448])).
% 2.97/3.17 tff(17450,plain,
% 2.97/3.17 (r(s(s(s(s(z)))), s(z))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13335, 17437])).
% 2.97/3.17 tff(17451,plain,
% 2.97/3.17 (~r(s(z), s(s(s(elem!1))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[15845, 17450, 81, 125, 17449])).
% 2.97/3.17 tff(17452,plain,
% 2.97/3.17 (~r(s(z), s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13916, 17451, 16324])).
% 2.97/3.17 tff(17453,plain,
% 2.97/3.17 (b(s(z), s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[253, 17452])).
% 2.97/3.17 tff(17454,plain,
% 2.97/3.17 (b(s(z), s(s(s(elem!1))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[181, 17451])).
% 2.97/3.17 tff(17455,plain,
% 2.97/3.17 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[5279, 488, 145, 1170])).
% 2.97/3.17 tff(17456,plain,
% 2.97/3.17 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[336, 17455])).
% 2.97/3.17 tff(17457,plain,
% 2.97/3.17 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[4824, 17456, 193, 87, 126, 876])).
% 2.97/3.17 tff(17458,plain,
% 2.97/3.17 (r(s(z), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[280, 17457])).
% 2.97/3.17 tff(17459,plain,
% 2.97/3.17 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[5023, 17456, 87, 86])).
% 2.97/3.17 tff(17460,plain,
% 2.97/3.17 (r(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[511, 17459])).
% 2.97/3.17 tff(17461,plain,
% 2.97/3.17 ($false),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[503, 17460, 17458, 125, 488])).
% 2.97/3.17 tff(17462,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.17 tff(17463,plain,
% 2.97/3.17 ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[17462, 14660])).
% 2.97/3.17 tff(17464,plain,
% 2.97/3.17 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[17463, 17443, 16893, 125, 17454, 17453, 145, 17441])).
% 2.97/3.17 tff(17465,plain,
% 2.97/3.17 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[452, 17464])).
% 2.97/3.17 tff(17466,plain,
% 2.97/3.17 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[3267, 17465, 16910, 17445])).
% 2.97/3.17 tff(17467,plain,
% 2.97/3.17 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[336, 17466])).
% 2.97/3.17 tff(17468,plain,
% 2.97/3.17 (~r(z, s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[16275, 17467, 226, 17439])).
% 2.97/3.17 tff(17469,plain,
% 2.97/3.17 (b(z, s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[1093, 17468])).
% 2.97/3.17 tff(17470,plain,
% 2.97/3.17 (~b(s(s(z)), s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[4270, 17453, 16910, 16323])).
% 2.97/3.17 tff(17471,plain,
% 2.97/3.17 (r(s(s(z)), s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[437, 17470])).
% 2.97/3.17 tff(17472,plain,
% 2.97/3.17 (r(s(s(z)), s(s(s(elem!1))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[10091, 17471, 16317])).
% 2.97/3.17 tff(17473,plain,
% 2.97/3.17 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[12643, 17467, 17472, 17443])).
% 2.97/3.17 tff(17474,plain,
% 2.97/3.17 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[821, 17473, 17074])).
% 2.97/3.17 tff(17475,plain,
% 2.97/3.17 ($false),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[16251, 17474, 17469, 124])).
% 2.97/3.17 tff(17476,plain,((~b(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.17 tff(17477,plain,
% 2.97/3.17 (~b(z, s(s(s(elem!1))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[17476, 17408, 494, 17067, 16981])).
% 2.97/3.17 tff(17478,plain,
% 2.97/3.17 (r(z, s(s(s(elem!1))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[590, 17477])).
% 2.97/3.17 tff(17479,plain,
% 2.97/3.17 (r(z, s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[6374, 17478, 16324])).
% 2.97/3.17 tff(17480,plain,
% 2.97/3.17 (~r(s(z), s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[14376, 17479, 16912])).
% 2.97/3.17 tff(17481,plain,
% 2.97/3.17 (b(s(z), s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[253, 17480])).
% 2.97/3.17 tff(17482,plain,
% 2.97/3.17 (~r(s(s(z)), s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[11460, 17479, 16912, 17408])).
% 2.97/3.17 tff(17483,plain,
% 2.97/3.17 (b(s(s(z)), s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[437, 17482])).
% 2.97/3.17 tff(17484,plain,
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% 2.97/3.17 inference(unit_resolution,[status(thm)],[4270, 17483, 17481, 16910, 16323])).
% 2.97/3.17 tff(17485,plain,(b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.17 tff(17486,plain,
% 2.97/3.17 (b(s(s(s(z))), s(z))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[1846, 17485, 16317])).
% 2.97/3.17 tff(17487,plain,
% 2.97/3.17 (~b(s(s(z)), s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[15907, 17486, 16893, 16910])).
% 2.97/3.17 tff(17488,plain,
% 2.97/3.17 (r(s(s(z)), s(s(s(z))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[437, 17487])).
% 2.97/3.17 tff(17489,plain,
% 2.97/3.17 (r(s(s(z)), s(s(s(elem!1))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[10091, 17488, 16317])).
% 2.97/3.17 tff(17490,plain,
% 2.97/3.17 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[14277, 97, 17485, 16893, 16910])).
% 2.97/3.17 tff(17491,plain,
% 2.97/3.17 (r(s(s(s(elem!1))), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[58, 17490])).
% 2.97/3.17 tff(17492,plain,
% 2.97/3.17 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 2.97/3.17 inference(monotonicity,[status(thm)],[16445])).
% 2.97/3.17 tff(17493,plain,
% 2.97/3.17 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 2.97/3.17 inference(monotonicity,[status(thm)],[16328])).
% 2.97/3.17 tff(17494,plain,
% 2.97/3.17 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 2.97/3.17 inference(transitivity,[status(thm)],[17493, 17492])).
% 2.97/3.17 tff(17495,plain,
% 2.97/3.17 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[16324])).
% 2.97/3.17 tff(17496,plain,
% 2.97/3.17 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.97/3.17 inference(symmetry,[status(thm)],[17495])).
% 2.97/3.17 tff(17497,plain,
% 2.97/3.17 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[16445])).
% 2.97/3.17 tff(17498,plain,
% 2.97/3.17 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.97/3.17 inference(symmetry,[status(thm)],[17497])).
% 2.97/3.17 tff(17499,plain,
% 2.97/3.17 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.97/3.17 inference(transitivity,[status(thm)],[17498, 17496])).
% 2.97/3.17 tff(17500,plain,
% 2.97/3.17 (b(elem!1, s(s(s(elem!1))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[17168, 17499])).
% 2.97/3.17 tff(17501,plain,
% 2.97/3.17 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 2.97/3.17 inference(monotonicity,[status(thm)],[16436])).
% 2.97/3.17 tff(17502,plain,
% 2.97/3.17 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.97/3.17 inference(symmetry,[status(thm)],[17501])).
% 2.97/3.17 tff(17503,plain,
% 2.97/3.17 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 2.97/3.17 inference(monotonicity,[status(thm)],[16445])).
% 2.97/3.17 tff(17504,plain,
% 2.97/3.17 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 2.97/3.17 inference(symmetry,[status(thm)],[17503])).
% 2.97/3.17 tff(17505,plain,
% 2.97/3.17 (r(s(s(z)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.97/3.17 inference(transitivity,[status(thm)],[17504, 17502])).
% 2.97/3.17 tff(17506,plain,
% 2.97/3.17 (~r(z, s(s(s(elem!1))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[15944, 550, 16893, 16910, 17489])).
% 2.97/3.17 tff(17507,plain,
% 2.97/3.17 (~b(z, s(s(s(elem!1))))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[14724, 550, 17485])).
% 2.97/3.17 tff(17508,plain,
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% 2.97/3.17 inference(unit_resolution,[status(thm)],[590, 17507, 17506])).
% 2.97/3.17 tff(17509,plain,(~b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.97/3.17 tff(17510,plain,
% 2.97/3.17 (r(s(z), z)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[568, 17509])).
% 2.97/3.17 tff(17511,plain,
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% 2.97/3.17 inference(unit_resolution,[status(thm)],[16871, 17167, 16910, 17486, 17510])).
% 2.97/3.17 tff(17512,plain,
% 2.97/3.17 (r(s(s(z)), z)),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[625, 17511])).
% 2.97/3.17 tff(17513,plain,
% 2.97/3.17 (r(s(s(elem!1)), elem!1)),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[17512, 17505])).
% 2.97/3.17 tff(17514,plain,
% 2.97/3.17 (~b(s(s(s(z))), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[16124, 97, 16893, 16910, 17486])).
% 2.97/3.17 tff(17515,plain,
% 2.97/3.17 (r(s(s(s(z))), s(s(z)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[421, 17514])).
% 2.97/3.17 tff(17516,plain,
% 2.97/3.17 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[17515, 16552])).
% 2.97/3.17 tff(17517,plain,
% 2.97/3.17 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[16436, 16324])).
% 2.97/3.17 tff(17518,plain,
% 2.97/3.17 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.97/3.17 inference(symmetry,[status(thm)],[17517])).
% 2.97/3.17 tff(17519,plain,
% 2.97/3.17 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[17488, 17518])).
% 2.97/3.17 tff(17520,plain,
% 2.97/3.17 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.97/3.17 inference(monotonicity,[status(thm)],[16324])).
% 2.97/3.17 tff(17521,plain,
% 2.97/3.17 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.97/3.17 inference(symmetry,[status(thm)],[17520])).
% 2.97/3.17 tff(17522,plain,
% 2.97/3.17 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 2.97/3.17 inference(monotonicity,[status(thm)],[16445])).
% 2.97/3.17 tff(17523,plain,
% 2.97/3.17 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 2.97/3.17 inference(symmetry,[status(thm)],[17522])).
% 2.97/3.17 tff(17524,plain,
% 2.97/3.17 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.97/3.17 inference(transitivity,[status(thm)],[17523, 17521])).
% 2.97/3.17 tff(17525,plain,
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% 2.97/3.17 inference(modus_ponens,[status(thm)],[16323, 17524])).
% 2.97/3.17 tff(17526,plain,
% 2.97/3.17 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[16436])).
% 2.97/3.17 tff(17527,plain,
% 2.97/3.17 (r(elem!1, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 2.97/3.17 inference(symmetry,[status(thm)],[17526])).
% 2.97/3.17 tff(17528,plain,
% 2.97/3.17 (r(elem!1, s(s(z))) <=> r(z, s(s(z)))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[16445])).
% 2.97/3.17 tff(17529,plain,
% 2.97/3.17 (r(z, s(s(z))) <=> r(elem!1, s(s(z)))),
% 2.97/3.17 inference(symmetry,[status(thm)],[17528])).
% 2.97/3.17 tff(17530,plain,
% 2.97/3.17 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 2.97/3.17 inference(transitivity,[status(thm)],[17529, 17527])).
% 2.97/3.17 tff(17531,plain,
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% 2.97/3.17 inference(modus_ponens,[status(thm)],[226, 17530])).
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% 2.97/3.17 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[6325, 17531, 16317, 16381, 17525, 17519, 6302, 6315, 17516])).
% 2.97/3.17 tff(17533,plain,
% 2.97/3.17 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(z)))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[16436])).
% 2.97/3.17 tff(17534,plain,
% 2.97/3.17 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.97/3.17 inference(symmetry,[status(thm)],[17533])).
% 2.97/3.17 tff(17535,plain,
% 2.97/3.17 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.97/3.17 inference(symmetry,[status(thm)],[16437])).
% 2.97/3.17 tff(17536,plain,
% 2.97/3.17 (s(z) = s(elem!1)),
% 2.97/3.17 inference(transitivity,[status(thm)],[24, 17535, 29])).
% 2.97/3.17 tff(17537,plain,
% 2.97/3.17 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[17536])).
% 2.97/3.17 tff(17538,plain,
% 2.97/3.17 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.97/3.17 inference(transitivity,[status(thm)],[17537, 17534])).
% 2.97/3.17 tff(17539,plain,
% 2.97/3.17 (b(s(elem!1), s(s(elem!1)))),
% 2.97/3.17 inference(modus_ponens,[status(thm)],[16910, 17538])).
% 2.97/3.17 tff(17540,plain,
% 2.97/3.17 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(monotonicity,[status(thm)],[16436])).
% 2.97/3.17 tff(17541,plain,
% 2.97/3.17 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.97/3.17 inference(symmetry,[status(thm)],[17540])).
% 2.97/3.17 tff(17542,plain,
% 2.97/3.17 (~b(s(s(s(s(z)))), s(z))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[17436, 226, 124, 17516])).
% 2.97/3.17 tff(17543,plain,
% 2.97/3.17 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[13104, 17542, 16324])).
% 2.97/3.17 tff(17544,plain,
% 2.97/3.17 (r(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.17 inference(unit_resolution,[status(thm)],[511, 17543])).
% 2.97/3.18 tff(17545,plain,
% 2.97/3.18 (~r(s(s(s(s(elem!1)))), z)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[11568, 17544, 17510])).
% 2.97/3.18 tff(17546,plain,
% 2.97/3.18 (b(s(s(s(s(elem!1)))), z)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[842, 17545])).
% 2.97/3.18 tff(17547,plain,
% 2.97/3.18 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[15794, 17546, 124])).
% 2.97/3.18 tff(17548,plain,
% 2.97/3.18 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[486, 17547, 16492])).
% 2.97/3.18 tff(17549,plain,
% 2.97/3.18 ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(z), s(s(z))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[12864, 11419])).
% 2.97/3.18 tff(17550,plain,
% 2.97/3.18 ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(z), s(s(z))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[17549, 14660])).
% 2.97/3.18 tff(17551,plain,
% 2.97/3.18 (~r(z, s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[17550, 17546, 16910, 17485, 17544, 16492])).
% 2.97/3.18 tff(17552,plain,
% 2.97/3.18 (b(z, s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[1093, 17551])).
% 2.97/3.18 tff(17553,plain,
% 2.97/3.18 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[16251, 17552, 124])).
% 2.97/3.18 tff(17554,plain,
% 2.97/3.18 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[821, 17553, 16572])).
% 2.97/3.18 tff(17555,plain,
% 2.97/3.18 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[12643, 17554, 17489, 17548])).
% 2.97/3.18 tff(17556,plain,
% 2.97/3.18 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[336, 17555])).
% 2.97/3.18 tff(17557,plain,
% 2.97/3.18 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[17556, 17541])).
% 2.97/3.18 tff(17558,plain,
% 2.97/3.18 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[6197, 16492, 16317])).
% 2.97/3.18 tff(17559,plain,
% 2.97/3.18 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[7544, 17558])).
% 2.97/3.18 tff(17560,plain,
% 2.97/3.18 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3812, 17556, 16910, 17546])).
% 2.97/3.18 tff(17561,plain,
% 2.97/3.18 (r(s(z), s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[280, 17560])).
% 2.97/3.18 tff(17562,plain,
% 2.97/3.18 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[1909, 17561, 16317])).
% 2.97/3.18 tff(17563,plain,
% 2.97/3.18 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[5371, 17554, 16317, 17491, 17489])).
% 2.97/3.18 tff(17564,plain,
% 2.97/3.18 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[1484, 17563, 16510])).
% 2.97/3.18 tff(17565,plain,
% 2.97/3.18 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(z))),
% 2.97/3.18 inference(monotonicity,[status(thm)],[16328, 16438])).
% 2.97/3.18 tff(17566,plain,
% 2.97/3.18 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.97/3.18 inference(symmetry,[status(thm)],[17565])).
% 2.97/3.18 tff(17567,plain,
% 2.97/3.18 (r(s(s(s(s(z)))), s(z))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[13335, 17542])).
% 2.97/3.18 tff(17568,plain,
% 2.97/3.18 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[17567, 17566])).
% 2.97/3.18 tff(17569,plain,
% 2.97/3.18 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[6264, 17568, 17564, 17562, 17559, 17557, 17539, 16317])).
% 2.97/3.18 tff(17570,plain,
% 2.97/3.18 ($false),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[6269, 17569, 17532, 16336])).
% 2.97/3.18 tff(17571,plain,((~r(z, s(s(z)))) | (~r(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.18 tff(17572,plain,
% 2.97/3.18 (~r(z, s(s(z)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[17571, 17513, 17500, 3008])).
% 2.97/3.18 tff(17573,plain,
% 2.97/3.18 (b(z, s(s(z)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[222, 17572])).
% 2.97/3.18 tff(17574,plain,
% 2.97/3.18 (~b(s(s(s(s(elem!1)))), z)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[14323, 17573, 16317, 16893, 17486, 17491, 17489, 17168])).
% 2.97/3.18 tff(17575,plain,
% 2.97/3.18 (r(s(s(s(s(elem!1)))), z)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[842, 17574])).
% 2.97/3.18 tff(17576,plain,
% 2.97/3.18 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3107, 17575, 16317])).
% 2.97/3.18 tff(17577,plain,
% 2.97/3.18 (r(s(s(s(s(z)))), z)),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[17576, 17494])).
% 2.97/3.18 tff(17578,plain,
% 2.97/3.18 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[11568, 17575, 17510])).
% 2.97/3.18 tff(17579,plain,
% 2.97/3.18 (b(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[511, 17578])).
% 2.97/3.18 tff(17580,plain,
% 2.97/3.18 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[2129, 17579, 16910, 17485])).
% 2.97/3.18 tff(17581,plain,
% 2.97/3.18 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[486, 17580, 16492])).
% 2.97/3.18 tff(17582,plain,
% 2.97/3.18 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[17581, 16536])).
% 2.97/3.18 tff(17583,plain,
% 2.97/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(17584,plain,
% 2.97/3.18 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.97/3.18 inference(rewrite,[status(thm)],[])).
% 2.97/3.18 tff(17585,plain,
% 2.97/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.97/3.18 inference(monotonicity,[status(thm)],[17584])).
% 2.97/3.18 tff(17586,plain,
% 2.97/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.97/3.18 inference(transitivity,[status(thm)],[17585, 17583])).
% 2.97/3.18 tff(17587,plain,
% 2.97/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.97/3.18 inference(quant_inst,[status(thm)],[])).
% 2.97/3.18 tff(17588,plain,
% 2.97/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.97/3.18 inference(modus_ponens,[status(thm)],[17587, 17586])).
% 2.97/3.18 tff(17589,plain,
% 2.97/3.18 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[17588, 155, 17512, 17488, 17582, 17577])).
% 2.97/3.18 tff(17590,plain,
% 2.97/3.18 (b(s(s(s(s(z)))), s(z))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[13104, 17579, 16324])).
% 2.97/3.18 tff(17591,plain,
% 2.97/3.18 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[15853, 97, 16893, 16910, 17590])).
% 2.97/3.18 tff(17592,plain,
% 2.97/3.18 ($false),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[15855, 17591, 17589])).
% 2.97/3.18 tff(17593,plain,(r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.18 tff(17594,plain,
% 2.97/3.18 (r(z, s(s(s(z))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[6374, 17593, 16324])).
% 2.97/3.18 tff(17595,plain,
% 2.97/3.18 (~r(z, s(s(z)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[5949, 17593, 17489, 17515, 17594])).
% 2.97/3.18 tff(17596,plain,
% 2.97/3.18 (b(z, s(s(z)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[222, 17595])).
% 2.97/3.18 tff(17597,plain,
% 2.97/3.18 (~r(s(s(s(s(elem!1)))), z)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[11568, 495, 17510])).
% 2.97/3.18 tff(17598,plain,
% 2.97/3.18 (b(s(s(s(s(elem!1)))), z)),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[842, 17597])).
% 2.97/3.18 tff(17599,plain,
% 2.97/3.18 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[4806, 17598, 16893, 17596])).
% 2.97/3.18 tff(17600,plain,
% 2.97/3.18 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[452, 17599])).
% 2.97/3.18 tff(17601,plain,
% 2.97/3.18 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[1822, 17600, 16317])).
% 2.97/3.18 tff(17602,plain,
% 2.97/3.18 (~r(z, s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[17550, 17598, 16910, 17485, 495, 16492])).
% 2.97/3.18 tff(17603,plain,
% 2.97/3.18 (b(z, s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[1093, 17602])).
% 2.97/3.18 tff(17604,plain,
% 2.97/3.18 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[16586, 17603, 17598])).
% 2.97/3.18 tff(17605,plain,
% 2.97/3.18 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[821, 17604, 16572])).
% 2.97/3.18 tff(17606,plain,
% 2.97/3.18 ($false),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[5371, 17605, 17601, 16317, 17491, 17489])).
% 2.97/3.18 tff(17607,plain,(~r(s(s(s(s(elem!1)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.97/3.18 tff(17608,plain,
% 2.97/3.18 (b(s(s(s(s(elem!1)))), s(z))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[511, 17607])).
% 2.97/3.18 tff(17609,plain,
% 2.97/3.18 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[2129, 17608, 16910, 17485])).
% 2.97/3.18 tff(17610,plain,
% 2.97/3.18 (~b(s(z), s(s(s(elem!1))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[16050, 17608, 16893, 17485, 16492, 17609])).
% 2.97/3.18 tff(17611,plain,
% 2.97/3.18 (r(s(z), s(s(s(elem!1))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[181, 17610])).
% 2.97/3.18 tff(17612,plain,
% 2.97/3.18 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[486, 17609, 16492])).
% 2.97/3.18 tff(17613,plain,
% 2.97/3.18 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[578, 17612, 17510, 17593, 17611])).
% 2.97/3.18 tff(17614,plain,
% 2.97/3.18 (b(s(z), s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[280, 17613])).
% 2.97/3.18 tff(17615,plain,
% 2.97/3.18 (elem!1 = z),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[1888, 16441])).
% 2.97/3.18 tff(17616,plain,
% 2.97/3.18 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[10998, 17614, 17486, 17608])).
% 2.97/3.18 tff(17617,plain,
% 2.97/3.18 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[10862, 17616, 17615])).
% 2.97/3.18 tff(17618,plain,
% 2.97/3.18 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[821, 17617, 16572])).
% 2.97/3.18 tff(17619,plain,
% 2.97/3.18 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[12643, 17618, 17489, 17612])).
% 2.97/3.18 tff(17620,plain,
% 2.97/3.18 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[336, 17619])).
% 2.97/3.18 tff(17621,plain,
% 2.97/3.18 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[5371, 17618, 16317, 17491, 17489])).
% 2.97/3.18 tff(17622,plain,
% 2.97/3.18 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[1822, 17621, 16317])).
% 2.97/3.18 tff(17623,plain,
% 2.97/3.18 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[452, 17622])).
% 2.97/3.18 tff(17624,plain,
% 2.97/3.18 ($false),
% 2.97/3.18 inference(unit_resolution,[status(thm)],[3267, 17623, 17620, 16910, 17614])).
% 2.97/3.18 % SZS output end Proof
% 2.97/3.19 % E exiting
%------------------------------------------------------------------------------