%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA130-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:33:46 PM UTC 2026
% Result : Unsatisfiable 1.24s 1.44s
% Output : Proof 2.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA130-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.15/0.32 % Computer : n017.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 22:39:29 EDT 2026
% 0.15/0.33 % CPUTime :
% 1.24/1.44 % SZS status Unsatisfiable
% 1.24/1.44 % SZS output start Proof
% 1.24/1.44 tff(b_type, type, (
% 1.24/1.44 b: ( $i * $i ) > $o)).
% 1.24/1.44 tff(s_type, type, (
% 1.24/1.44 s: $i > $i)).
% 1.24/1.44 tff(z_type, type, (
% 1.24/1.44 z: $i)).
% 1.24/1.44 tff(r_type, type, (
% 1.24/1.44 r: ( $i * $i ) > $o)).
% 1.24/1.44 tff(elem_1_type, type, (
% 1.24/1.44 elem_1: $i)).
% 1.24/1.44 tff(inj_0_type, type, (
% 1.24/1.44 inj_0: $i > $i)).
% 1.24/1.44 tff(1,plain,
% 1.24/1.44 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.24/1.44 inference(commutativity,[status(thm)],[])).
% 1.24/1.44 tff(2,assumption,(~r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.24/1.44 tff(3,assumption,(~(s(s(s(s(z)))) = elem!1)), introduced(assumption)).
% 1.24/1.44 tff(4,assumption,(~b(s(s(z)), elem!1)), introduced(assumption)).
% 1.24/1.44 tff(5,assumption,(elem!1 = s(s(s(s(z))))), introduced(assumption)).
% 1.24/1.44 tff(6,plain,
% 1.24/1.44 (s(s(s(s(z)))) = elem!1),
% 1.24/1.44 inference(symmetry,[status(thm)],[5])).
% 1.24/1.44 tff(7,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[3, 6])).
% 1.24/1.44 tff(8,plain,((~(elem!1 = s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(9,plain,
% 1.24/1.44 (~(elem!1 = s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8, 3])).
% 1.24/1.44 tff(10,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 1.24/1.44 tff(11,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.44 tff(12,assumption,(s(s(z)) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.44 tff(13,plain,
% 1.24/1.44 (s(s(s(s(s(z))))) = s(s(z))),
% 1.24/1.44 inference(symmetry,[status(thm)],[12])).
% 1.24/1.44 tff(14,plain,
% 1.24/1.44 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(15,plain,
% 1.24/1.44 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(16,plain,
% 1.24/1.44 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(17,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sinj')).
% 1.24/1.44 tff(18,plain,
% 1.24/1.44 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.24/1.44 tff(19,plain,(
% 1.24/1.44 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.24/1.44 inference(skolemize,[status(sab)],[18])).
% 1.24/1.44 tff(20,plain,
% 1.24/1.44 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[19, 15])).
% 1.24/1.44 tff(21,plain,
% 1.24/1.44 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[20, 14])).
% 1.24/1.44 tff(22,plain,
% 1.24/1.44 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(23,plain,
% 1.24/1.44 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[22, 21])).
% 1.24/1.44 tff(24,assumption,(s(s(s(s(s(z))))) = s(s(z))), introduced(assumption)).
% 1.24/1.44 tff(25,plain,
% 1.24/1.44 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(z)))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[24])).
% 1.24/1.44 tff(26,plain,
% 1.24/1.44 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 1.24/1.44 inference(symmetry,[status(thm)],[25])).
% 1.24/1.44 tff(27,plain,
% 1.24/1.44 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(28,plain,
% 1.24/1.44 (inj_0(s(s(z))) = s(z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[27, 21])).
% 1.24/1.44 tff(29,plain,
% 1.24/1.44 (s(z) = inj_0(s(s(z)))),
% 1.24/1.44 inference(symmetry,[status(thm)],[28])).
% 1.24/1.44 tff(30,plain,
% 1.24/1.44 (s(z) = s(s(s(s(z))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[29, 26, 23])).
% 1.24/1.44 tff(31,plain,
% 1.24/1.44 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(32,plain,
% 1.24/1.44 (inj_0(s(z)) = z),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[31, 21])).
% 1.24/1.44 tff(33,assumption,(s(z) = s(s(s(s(z))))), introduced(assumption)).
% 1.24/1.44 tff(34,plain,
% 1.24/1.44 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[33])).
% 1.24/1.44 tff(35,plain,
% 1.24/1.44 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.24/1.44 inference(symmetry,[status(thm)],[34])).
% 1.24/1.44 tff(36,plain,
% 1.24/1.44 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(37,plain,
% 1.24/1.44 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[36, 21])).
% 1.24/1.44 tff(38,plain,
% 1.24/1.44 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.24/1.44 inference(symmetry,[status(thm)],[37])).
% 1.24/1.44 tff(39,plain,
% 1.24/1.44 (s(s(s(z))) = z),
% 1.24/1.44 inference(transitivity,[status(thm)],[38, 35, 32])).
% 1.24/1.44 tff(40,plain,
% 1.24/1.44 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 1.24/1.44 inference(bind,[status(th)],[])).
% 1.24/1.44 tff(41,plain,
% 1.24/1.44 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.24/1.44 inference(quant_intro,[status(thm)],[40])).
% 1.24/1.44 tff(42,plain,
% 1.24/1.44 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(43,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snz')).
% 1.24/1.44 tff(44,plain,
% 1.24/1.44 (![X: $i] : (~(s(X) = z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.24/1.44 tff(45,plain,(
% 1.24/1.44 ![X: $i] : (~(s(X) = z))),
% 1.24/1.44 inference(skolemize,[status(sab)],[44])).
% 1.24/1.44 tff(46,plain,
% 1.24/1.44 (![X: $i] : (~(s(X) = z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[45, 41])).
% 1.24/1.44 tff(47,plain,
% 1.24/1.44 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(48,plain,
% 1.24/1.44 (~(s(s(s(z))) = z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[47, 46])).
% 1.24/1.44 tff(49,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[48, 39])).
% 1.24/1.44 tff(50,plain,(~(s(z) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(51,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[50, 30])).
% 1.24/1.44 tff(52,plain,(~(s(s(s(s(s(z))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(53,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[52, 13])).
% 1.24/1.44 tff(54,plain,(~(s(s(z)) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(55,plain,
% 1.24/1.44 ((s(s(s(s(s(z))))) = elem!1) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.24/1.44 inference(commutativity,[status(thm)],[])).
% 1.24/1.44 tff(56,plain,
% 1.24/1.44 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.24/1.44 inference(symmetry,[status(thm)],[55])).
% 1.24/1.44 tff(57,plain,
% 1.24/1.44 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.24/1.44 inference(commutativity,[status(thm)],[])).
% 1.24/1.44 tff(58,assumption,(~b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.24/1.44 tff(59,assumption,(~(s(s(s(z))) = elem!1)), introduced(assumption)).
% 1.24/1.44 tff(60,plain,
% 1.24/1.44 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.24/1.44 inference(bind,[status(th)],[])).
% 1.24/1.44 tff(61,plain,
% 1.24/1.44 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.24/1.44 inference(quant_intro,[status(thm)],[60])).
% 1.24/1.44 tff(62,plain,
% 1.24/1.44 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(63,plain,
% 1.24/1.44 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.24/1.44 inference(bind,[status(th)],[])).
% 1.24/1.44 tff(64,plain,
% 1.24/1.44 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.24/1.44 inference(quant_intro,[status(thm)],[63])).
% 1.24/1.44 tff(65,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rb')).
% 1.24/1.44 tff(66,plain,
% 1.24/1.44 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[65, 64])).
% 1.24/1.44 tff(67,plain,
% 1.24/1.44 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[66, 62])).
% 1.24/1.44 tff(68,plain,(
% 1.24/1.44 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.24/1.44 inference(skolemize,[status(sab)],[67])).
% 1.24/1.44 tff(69,plain,
% 1.24/1.44 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[68, 61])).
% 1.24/1.44 tff(70,plain,
% 1.24/1.44 (((~![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))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(71,plain,
% 1.24/1.44 ((~![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))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(72,plain,
% 1.24/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.24/1.44 tff(73,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[72, 69, 58, 2, 59])).
% 1.24/1.44 tff(74,plain,(r(s(s(s(z))), elem!1) | b(s(s(s(z))), elem!1) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(75,plain,
% 1.24/1.44 (s(s(s(z))) = elem!1),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[74, 2, 58])).
% 1.24/1.44 tff(76,assumption,(s(s(s(z))) = elem!1), introduced(assumption)).
% 1.24/1.44 tff(77,plain,
% 1.24/1.44 (s(s(s(s(z)))) = s(elem!1)),
% 1.24/1.44 inference(monotonicity,[status(thm)],[76])).
% 1.24/1.44 tff(78,plain,
% 1.24/1.44 (s(elem!1) = s(s(s(s(z))))),
% 1.24/1.44 inference(symmetry,[status(thm)],[77])).
% 1.24/1.44 tff(79,assumption,(~(s(elem!1) = s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.44 tff(80,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[79, 78])).
% 1.24/1.44 tff(81,plain,((~(s(s(s(z))) = elem!1)) | (s(elem!1) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(82,plain,
% 1.24/1.44 (s(elem!1) = s(s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[81, 75])).
% 1.24/1.44 tff(83,plain,
% 1.24/1.44 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[82])).
% 1.24/1.44 tff(84,plain,
% 1.24/1.44 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(85,plain,
% 1.24/1.44 (inj_0(s(elem!1)) = elem!1),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[84, 21])).
% 1.24/1.44 tff(86,plain,
% 1.24/1.44 (elem!1 = inj_0(s(elem!1))),
% 1.24/1.44 inference(symmetry,[status(thm)],[85])).
% 1.24/1.44 tff(87,plain,
% 1.24/1.44 (elem!1 = s(s(s(z)))),
% 1.24/1.44 inference(transitivity,[status(thm)],[86, 83, 37])).
% 1.24/1.44 tff(88,plain,
% 1.24/1.44 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[87])).
% 1.24/1.44 tff(89,plain,
% 1.24/1.44 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[88, 57])).
% 1.24/1.44 tff(90,plain,
% 1.24/1.44 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.24/1.44 inference(symmetry,[status(thm)],[89])).
% 1.24/1.44 tff(91,plain,
% 1.24/1.44 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.24/1.44 inference(transitivity,[status(thm)],[90, 56])).
% 1.24/1.44 tff(92,plain,
% 1.24/1.44 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[91])).
% 1.24/1.44 tff(93,assumption,(s(s(s(s(s(z))))) = s(s(s(z)))), introduced(assumption)).
% 1.24/1.44 tff(94,plain,
% 1.24/1.44 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(z))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[93])).
% 1.24/1.44 tff(95,plain,
% 1.24/1.44 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.24/1.44 inference(symmetry,[status(thm)],[94])).
% 1.24/1.44 tff(96,plain,
% 1.24/1.44 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(97,plain,
% 1.24/1.44 (inj_0(s(s(s(z)))) = s(s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[96, 21])).
% 1.24/1.44 tff(98,plain,
% 1.24/1.44 (s(s(z)) = inj_0(s(s(s(z))))),
% 1.24/1.44 inference(symmetry,[status(thm)],[97])).
% 1.24/1.44 tff(99,plain,
% 1.24/1.44 (s(s(z)) = s(s(s(s(z))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[98, 95, 23])).
% 1.24/1.44 tff(100,plain,
% 1.24/1.44 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[99])).
% 1.24/1.44 tff(101,plain,
% 1.24/1.44 (s(z) = s(s(s(z)))),
% 1.24/1.44 inference(transitivity,[status(thm)],[29, 100, 37])).
% 1.24/1.44 tff(102,assumption,(s(z) = s(s(s(z)))), introduced(assumption)).
% 1.24/1.44 tff(103,plain,
% 1.24/1.44 (inj_0(s(z)) = inj_0(s(s(s(z))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[102])).
% 1.24/1.44 tff(104,plain,
% 1.24/1.44 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.24/1.44 inference(symmetry,[status(thm)],[103])).
% 1.24/1.44 tff(105,plain,
% 1.24/1.44 (s(s(z)) = z),
% 1.24/1.44 inference(transitivity,[status(thm)],[98, 104, 32])).
% 1.24/1.44 tff(106,plain,
% 1.24/1.44 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(107,plain,
% 1.24/1.44 (~(s(s(z)) = z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[106, 46])).
% 1.24/1.44 tff(108,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[107, 105])).
% 1.24/1.44 tff(109,plain,(~(s(z) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(110,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[109, 101])).
% 1.24/1.44 tff(111,plain,(~(s(s(s(s(s(z))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(112,plain,
% 1.24/1.44 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[111, 92])).
% 1.24/1.44 tff(113,plain,
% 1.24/1.44 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[90])).
% 1.24/1.44 tff(114,plain,
% 1.24/1.44 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[111, 113])).
% 1.24/1.44 tff(115,plain,
% 1.24/1.44 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 1.24/1.44 inference(monotonicity,[status(thm)],[76])).
% 1.24/1.44 tff(116,plain,
% 1.24/1.44 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[76])).
% 1.24/1.44 tff(117,plain,
% 1.24/1.44 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 1.24/1.44 inference(symmetry,[status(thm)],[116])).
% 1.24/1.44 tff(118,plain,
% 1.24/1.44 ((~b(elem!1, s(z))) <=> (~b(s(s(s(z))), s(z)))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[117])).
% 1.24/1.44 tff(119,plain,
% 1.24/1.44 (~b(s(s(s(z))), s(z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[10, 118])).
% 1.24/1.44 tff(120,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.24/1.44 tff(121,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[120, 119])).
% 1.24/1.44 tff(122,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(s(s(z))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(123,plain,
% 1.24/1.44 (~b(s(s(s(z))), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[122, 76, 10])).
% 1.24/1.44 tff(124,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 1.24/1.44 tff(125,plain,
% 1.24/1.44 (s(z) = s(s(s(z)))),
% 1.24/1.44 inference(symmetry,[status(thm)],[124])).
% 1.24/1.44 tff(126,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[109, 125])).
% 1.24/1.44 tff(127,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(128,assumption,(~b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.24/1.44 tff(129,assumption,(~r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.24/1.44 tff(130,plain,
% 1.24/1.44 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(131,plain,
% 1.24/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(132,plain,
% 1.24/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[131, 130])).
% 1.24/1.44 tff(133,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[132, 69, 129, 128, 127])).
% 1.24/1.44 tff(134,plain,(r(s(s(s(z))), s(z)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(135,plain,
% 1.24/1.44 (r(s(s(s(z))), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[134, 123])).
% 1.24/1.44 tff(136,plain,
% 1.24/1.44 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.24/1.44 inference(monotonicity,[status(thm)],[76])).
% 1.24/1.44 tff(137,plain,
% 1.24/1.44 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[136])).
% 1.24/1.44 tff(138,assumption,(s(s(s(s(z)))) = s(s(s(z)))), introduced(assumption)).
% 1.24/1.44 tff(139,plain,
% 1.24/1.44 (s(s(s(s(s(z))))) = s(s(s(s(z))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[138])).
% 1.24/1.44 tff(140,plain,
% 1.24/1.44 (s(s(s(s(s(z))))) = s(s(s(z)))),
% 1.24/1.44 inference(transitivity,[status(thm)],[139, 138])).
% 1.24/1.44 tff(141,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[111, 140])).
% 1.24/1.44 tff(142,plain,(~(s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(143,plain,
% 1.24/1.44 (~(s(s(s(s(z)))) = elem!1)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[142, 137])).
% 1.24/1.44 tff(144,plain,
% 1.24/1.44 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.24/1.44 inference(commutativity,[status(thm)],[])).
% 1.24/1.44 tff(145,plain,
% 1.24/1.44 ((s(s(s(z))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[76])).
% 1.24/1.44 tff(146,plain,
% 1.24/1.44 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.24/1.44 inference(transitivity,[status(thm)],[145, 144])).
% 1.24/1.44 tff(147,plain,
% 1.24/1.44 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[146])).
% 1.24/1.44 tff(148,assumption,(s(s(s(s(z)))) = s(s(z))), introduced(assumption)).
% 1.24/1.44 tff(149,plain,
% 1.24/1.44 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[148])).
% 1.24/1.44 tff(150,plain,
% 1.24/1.44 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.24/1.44 inference(symmetry,[status(thm)],[149])).
% 1.24/1.44 tff(151,plain,
% 1.24/1.44 (s(z) = s(s(s(z)))),
% 1.24/1.44 inference(transitivity,[status(thm)],[29, 150, 37])).
% 1.24/1.44 tff(152,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[109, 151])).
% 1.24/1.44 tff(153,plain,(~(s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(154,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 1.24/1.44 tff(155,plain,
% 1.24/1.44 (s(s(s(s(z)))) = s(s(s(z)))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[154])).
% 1.24/1.44 tff(156,plain,
% 1.24/1.44 (s(s(s(s(z)))) = s(s(z))),
% 1.24/1.44 inference(transitivity,[status(thm)],[155, 154])).
% 1.24/1.44 tff(157,assumption,(~(s(s(s(s(z)))) = s(s(z)))), introduced(assumption)).
% 1.24/1.44 tff(158,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[157, 156])).
% 1.24/1.44 tff(159,plain,((~(s(s(s(z))) = s(s(z)))) | (s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(160,plain,
% 1.24/1.44 (~(s(s(s(z))) = s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[159, 153])).
% 1.24/1.44 tff(161,plain,
% 1.24/1.44 (~(s(s(z)) = elem!1)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[160, 147])).
% 1.24/1.44 tff(162,plain,
% 1.24/1.44 (s(elem!1) = s(s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[81, 76])).
% 1.24/1.44 tff(163,assumption,(s(z) = s(elem!1)), introduced(assumption)).
% 1.24/1.44 tff(164,plain,
% 1.24/1.44 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[163])).
% 1.24/1.44 tff(165,plain,
% 1.24/1.44 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.24/1.44 inference(symmetry,[status(thm)],[164])).
% 1.24/1.44 tff(166,assumption,(s(elem!1) = s(s(s(s(z))))), introduced(assumption)).
% 1.24/1.44 tff(167,plain,
% 1.24/1.44 (s(s(s(s(z)))) = s(elem!1)),
% 1.24/1.44 inference(symmetry,[status(thm)],[166])).
% 1.24/1.44 tff(168,plain,
% 1.24/1.44 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[167])).
% 1.24/1.44 tff(169,plain,
% 1.24/1.44 (s(s(s(z))) = z),
% 1.24/1.44 inference(transitivity,[status(thm)],[38, 168, 165, 32])).
% 1.24/1.44 tff(170,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[48, 169])).
% 1.24/1.44 tff(171,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(172,plain,
% 1.24/1.44 (~(s(z) = s(elem!1))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[171, 162])).
% 1.24/1.44 tff(173,plain,
% 1.24/1.44 ((s(z) = s(elem!1)) <=> (s(elem!1) = s(z))),
% 1.24/1.44 inference(commutativity,[status(thm)],[])).
% 1.24/1.44 tff(174,plain,
% 1.24/1.44 ((s(elem!1) = s(z)) <=> (s(z) = s(elem!1))),
% 1.24/1.44 inference(symmetry,[status(thm)],[173])).
% 1.24/1.44 tff(175,assumption,(s(elem!1) = s(z)), introduced(assumption)).
% 1.24/1.44 tff(176,plain,
% 1.24/1.44 (s(z) = s(elem!1)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[175, 174])).
% 1.24/1.44 tff(177,assumption,(~(s(z) = s(elem!1))), introduced(assumption)).
% 1.24/1.44 tff(178,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[177, 176])).
% 1.24/1.44 tff(179,plain,((~(s(elem!1) = s(z))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(180,plain,
% 1.24/1.44 (~(s(elem!1) = s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[179, 172])).
% 1.24/1.44 tff(181,plain,
% 1.24/1.44 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[77])).
% 1.24/1.44 tff(182,plain,
% 1.24/1.44 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(183,plain,
% 1.24/1.44 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[182, 21])).
% 1.24/1.44 tff(184,plain,
% 1.24/1.44 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[181])).
% 1.24/1.44 tff(185,plain,
% 1.24/1.44 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.24/1.44 inference(symmetry,[status(thm)],[184])).
% 1.24/1.44 tff(186,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 1.24/1.44 tff(187,plain,
% 1.24/1.44 (elem!1 = s(s(s(elem!1)))),
% 1.24/1.44 inference(symmetry,[status(thm)],[186])).
% 1.24/1.44 tff(188,plain,
% 1.24/1.44 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[76, 187, 185])).
% 1.24/1.44 tff(189,plain,
% 1.24/1.44 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[188])).
% 1.24/1.44 tff(190,plain,
% 1.24/1.44 (s(s(z)) = s(s(elem!1))),
% 1.24/1.44 inference(transitivity,[status(thm)],[98, 189, 183, 181])).
% 1.24/1.44 tff(191,plain,
% 1.24/1.44 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[190])).
% 1.24/1.44 tff(192,plain,
% 1.24/1.44 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.24/1.44 inference(symmetry,[status(thm)],[191])).
% 1.24/1.44 tff(193,plain,
% 1.24/1.44 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(194,plain,
% 1.24/1.44 (inj_0(s(s(elem!1))) = s(elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[193, 21])).
% 1.24/1.44 tff(195,plain,
% 1.24/1.44 (s(elem!1) = inj_0(s(s(elem!1)))),
% 1.24/1.44 inference(symmetry,[status(thm)],[194])).
% 1.24/1.44 tff(196,plain,
% 1.24/1.44 (s(elem!1) = s(z)),
% 1.24/1.44 inference(transitivity,[status(thm)],[195, 192, 28])).
% 1.24/1.44 tff(197,assumption,(~(s(elem!1) = s(z))), introduced(assumption)).
% 1.24/1.44 tff(198,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[197, 196])).
% 1.24/1.44 tff(199,plain,((~(s(s(s(elem!1))) = elem!1)) | (s(elem!1) = s(z)) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(200,plain,
% 1.24/1.44 (~(s(s(s(elem!1))) = elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[199, 180, 76])).
% 1.24/1.44 tff(201,plain,
% 1.24/1.44 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[162])).
% 1.24/1.44 tff(202,plain,
% 1.24/1.44 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[201])).
% 1.24/1.44 tff(203,plain,
% 1.24/1.44 ((elem!1 = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(elem!1)))),
% 1.24/1.44 inference(symmetry,[status(thm)],[202])).
% 1.24/1.44 tff(204,plain,
% 1.24/1.44 ((~(elem!1 = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[203])).
% 1.24/1.44 tff(205,plain,
% 1.24/1.44 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.24/1.44 inference(monotonicity,[status(thm)],[76])).
% 1.24/1.44 tff(206,plain,
% 1.24/1.44 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[205, 55])).
% 1.24/1.44 tff(207,plain,
% 1.24/1.44 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[206])).
% 1.24/1.44 tff(208,plain,
% 1.24/1.44 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[111, 207])).
% 1.24/1.44 tff(209,plain,
% 1.24/1.44 (~(elem!1 = s(s(elem!1)))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[208, 204])).
% 1.24/1.44 tff(210,plain,
% 1.24/1.44 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[78])).
% 1.24/1.44 tff(211,plain,
% 1.24/1.44 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.24/1.44 inference(symmetry,[status(thm)],[210])).
% 1.24/1.44 tff(212,assumption,(s(s(s(s(s(s(z)))))) = s(elem!1)), introduced(assumption)).
% 1.24/1.44 tff(213,plain,
% 1.24/1.44 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(elem!1))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[212])).
% 1.24/1.44 tff(214,plain,
% 1.24/1.44 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.24/1.44 inference(symmetry,[status(thm)],[213])).
% 1.24/1.44 tff(215,plain,
% 1.24/1.44 (elem!1 = s(s(elem!1))),
% 1.24/1.44 inference(transitivity,[status(thm)],[86, 214, 183, 211])).
% 1.24/1.44 tff(216,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 1.24/1.44 tff(217,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[216, 215])).
% 1.24/1.44 tff(218,plain,((~(s(s(s(s(s(s(z)))))) = s(elem!1))) | (elem!1 = s(s(elem!1))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(219,plain,
% 1.24/1.44 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[218, 209, 76])).
% 1.24/1.44 tff(220,plain,
% 1.24/1.44 (r(s(z), s(s(s(z)))) <=> r(s(z), elem!1)),
% 1.24/1.44 inference(monotonicity,[status(thm)],[76])).
% 1.24/1.44 tff(221,assumption,(~b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.24/1.44 tff(222,assumption,(~r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.24/1.44 tff(223,plain,
% 1.24/1.44 (((~![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)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(224,plain,
% 1.24/1.44 ((~![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)))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(225,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[224, 223])).
% 1.24/1.45 tff(226,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[225, 69, 222, 109, 221])).
% 1.24/1.45 tff(227,plain,(r(s(z), s(s(s(z)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(228,plain,
% 1.24/1.45 (r(s(z), s(s(s(z))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[227, 221])).
% 1.24/1.45 tff(229,plain,
% 1.24/1.45 (r(s(z), elem!1)),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[228, 220])).
% 1.24/1.45 tff(230,plain,
% 1.24/1.45 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.24/1.45 inference(monotonicity,[status(thm)],[162])).
% 1.24/1.45 tff(231,plain,
% 1.24/1.45 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.24/1.45 inference(symmetry,[status(thm)],[230])).
% 1.24/1.45 tff(232,plain,
% 1.24/1.45 (r(s(s(s(z))), s(z)) <=> r(elem!1, s(z))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[76])).
% 1.24/1.45 tff(233,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.24/1.45 tff(234,plain,
% 1.24/1.45 (r(elem!1, s(z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[233, 232])).
% 1.24/1.45 tff(235,plain,
% 1.24/1.45 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[201, 162])).
% 1.24/1.45 tff(236,plain,
% 1.24/1.45 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.24/1.45 inference(symmetry,[status(thm)],[235])).
% 1.24/1.45 tff(237,plain,
% 1.24/1.45 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[236])).
% 1.24/1.45 tff(238,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 1.24/1.45 tff(239,assumption,(~r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.24/1.45 tff(240,plain,
% 1.24/1.45 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[201])).
% 1.24/1.45 tff(241,plain,
% 1.24/1.45 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.24/1.45 inference(symmetry,[status(thm)],[240])).
% 1.24/1.45 tff(242,plain,
% 1.24/1.45 (b(s(s(s(s(s(s(z)))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[241])).
% 1.24/1.45 tff(243,plain,
% 1.24/1.45 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 1.24/1.45 inference(symmetry,[status(thm)],[242])).
% 1.24/1.45 tff(244,plain,
% 1.24/1.45 ((s(z) = s(s(s(z)))) <=> (s(z) = elem!1)),
% 1.24/1.45 inference(monotonicity,[status(thm)],[76])).
% 1.24/1.45 tff(245,plain,
% 1.24/1.45 ((~(s(z) = s(s(s(z))))) <=> (~(s(z) = elem!1))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[244])).
% 1.24/1.45 tff(246,plain,
% 1.24/1.45 (~(s(z) = elem!1)),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[109, 245])).
% 1.24/1.45 tff(247,plain,
% 1.24/1.45 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[76])).
% 1.24/1.45 tff(248,plain,
% 1.24/1.45 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[247])).
% 1.24/1.45 tff(249,assumption,(~b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.24/1.45 tff(250,plain,
% 1.24/1.45 (((~![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))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(251,plain,
% 1.24/1.45 ((~![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))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(252,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[251, 250])).
% 1.24/1.45 tff(253,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[252, 69, 239, 3, 249])).
% 1.24/1.45 tff(254,plain,(r(s(s(s(s(z)))), elem!1) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(255,plain,
% 1.24/1.45 (b(s(s(s(s(z)))), elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[254, 239, 3])).
% 1.24/1.45 tff(256,assumption,(r(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.45 tff(257,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.24/1.45 tff(258,assumption,(r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.24/1.45 tff(259,plain,
% 1.24/1.45 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) <=> ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))))),
% 1.24/1.45 inference(bind,[status(th)],[])).
% 1.24/1.45 tff(260,plain,
% 1.24/1.45 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.24/1.45 inference(quant_intro,[status(thm)],[259])).
% 1.24/1.45 tff(261,plain,
% 1.24/1.45 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(262,plain,
% 1.24/1.45 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~r(X0, X1)) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X1)))), ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) <=> (((~r(X1, X2)) | (~r(X0, X1))) | (~r(X0, X3))))), rewrite((((~r(X1, X2)) | (~r(X0, X1))) | (~r(X0, X3))) <=> ((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))), ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) <=> ((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))))), (((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3))) <=> (((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) | (~r(X1, X3))))), rewrite((((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) | (~r(X1, X3))) <=> ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3))) <=> ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))))),
% 1.24/1.45 inference(bind,[status(th)],[])).
% 1.24/1.45 tff(263,plain,
% 1.24/1.45 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.24/1.45 inference(quant_intro,[status(thm)],[262])).
% 1.24/1.45 tff(264,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axr')).
% 1.24/1.45 tff(265,plain,
% 1.24/1.45 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[264, 263])).
% 1.24/1.45 tff(266,plain,
% 1.24/1.45 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[265, 261])).
% 1.24/1.45 tff(267,plain,(
% 1.24/1.45 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.24/1.45 inference(skolemize,[status(sab)],[266])).
% 1.24/1.45 tff(268,plain,
% 1.24/1.45 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[267, 260])).
% 1.24/1.45 tff(269,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(270,plain,
% 1.24/1.45 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(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(z))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(271,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[270])).
% 1.24/1.45 tff(272,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[271, 269])).
% 1.24/1.45 tff(273,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(274,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[273, 272])).
% 1.24/1.45 tff(275,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[274, 268, 256, 258, 257])).
% 1.24/1.45 tff(276,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(277,plain,
% 1.24/1.45 (~r(s(s(s(s(s(z))))), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[276, 256, 257])).
% 1.24/1.45 tff(278,assumption,(~b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.24/1.45 tff(279,assumption,(s(s(s(s(s(z))))) = s(z)), introduced(assumption)).
% 1.24/1.45 tff(280,plain,
% 1.24/1.45 (s(z) = s(s(s(s(s(z)))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[279])).
% 1.24/1.45 tff(281,assumption,(s(z) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.45 tff(282,plain,
% 1.24/1.45 (inj_0(s(z)) = inj_0(s(s(s(s(s(z))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[281])).
% 1.24/1.45 tff(283,plain,
% 1.24/1.45 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 1.24/1.45 inference(symmetry,[status(thm)],[282])).
% 1.24/1.45 tff(284,plain,
% 1.24/1.45 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[23])).
% 1.24/1.45 tff(285,plain,
% 1.24/1.45 (s(s(s(s(z)))) = z),
% 1.24/1.45 inference(transitivity,[status(thm)],[284, 283, 32])).
% 1.24/1.45 tff(286,plain,
% 1.24/1.45 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(287,plain,
% 1.24/1.45 (~(s(s(s(s(z)))) = z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[286, 46])).
% 1.24/1.45 tff(288,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[287, 285])).
% 1.24/1.45 tff(289,plain,(~(s(z) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(290,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[289, 280])).
% 1.24/1.45 tff(291,plain,(~(s(s(s(s(s(z))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(292,assumption,(~r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.24/1.45 tff(293,plain,
% 1.24/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(294,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(295,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[294, 293])).
% 1.24/1.45 tff(296,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[295, 69, 292, 291, 278])).
% 1.24/1.45 tff(297,plain,(r(s(s(s(s(s(z))))), s(z)) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(298,plain,
% 1.24/1.45 (b(s(s(s(s(s(z))))), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[297, 277])).
% 1.24/1.45 tff(299,assumption,(b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.24/1.45 tff(300,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.45 tff(301,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.45 tff(302,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~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)))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(303,plain,
% 1.24/1.45 (((~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(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(304,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~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))))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[303])).
% 1.24/1.45 tff(305,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~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)))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[304, 302])).
% 1.24/1.45 tff(306,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(307,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[306, 305])).
% 1.24/1.45 tff(308,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[307, 268, 256, 301, 300])).
% 1.24/1.45 tff(309,plain,((~r(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(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(310,plain,
% 1.24/1.45 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[309, 300, 256])).
% 1.24/1.45 tff(311,assumption,(s(s(s(s(s(z))))) = s(s(s(s(z))))), introduced(assumption)).
% 1.24/1.45 tff(312,plain,
% 1.24/1.45 (s(s(s(s(z)))) = s(s(s(s(s(z)))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[311])).
% 1.24/1.45 tff(313,plain,
% 1.24/1.45 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(z))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[312])).
% 1.24/1.45 tff(314,plain,
% 1.24/1.45 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(z)))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[313])).
% 1.24/1.45 tff(315,plain,
% 1.24/1.45 (s(s(s(s(z)))) = s(s(s(z)))),
% 1.24/1.45 inference(transitivity,[status(thm)],[284, 314, 37])).
% 1.24/1.45 tff(316,assumption,(~(s(s(s(s(z)))) = s(s(s(z))))), introduced(assumption)).
% 1.24/1.45 tff(317,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[316, 315])).
% 1.24/1.45 tff(318,plain,((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(319,plain,
% 1.24/1.45 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[318, 142])).
% 1.24/1.45 tff(320,assumption,(~b(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.45 tff(321,assumption,(~(s(s(s(s(s(z))))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.45 tff(322,assumption,(~r(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.45 tff(323,plain,
% 1.24/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(324,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(325,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[324, 323])).
% 1.24/1.45 tff(326,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[325, 69, 322, 321, 320])).
% 1.24/1.45 tff(327,plain,(b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))) | (s(s(s(s(s(z))))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(328,plain,
% 1.24/1.45 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[327, 319])).
% 1.24/1.45 tff(329,plain,
% 1.24/1.45 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[328, 310])).
% 1.24/1.45 tff(330,plain,
% 1.24/1.45 (b(s(elem!1), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[162])).
% 1.24/1.45 tff(331,plain,
% 1.24/1.45 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[78])).
% 1.24/1.45 tff(332,plain,
% 1.24/1.45 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(elem!1))),
% 1.24/1.45 inference(symmetry,[status(thm)],[331])).
% 1.24/1.45 tff(333,plain,
% 1.24/1.45 (r(elem!1, s(s(s(s(z)))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[300, 247])).
% 1.24/1.45 tff(334,plain,
% 1.24/1.45 (r(elem!1, s(elem!1))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[333, 332])).
% 1.24/1.45 tff(335,assumption,(~r(elem!1, s(elem!1))), introduced(assumption)).
% 1.24/1.45 tff(336,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[335, 334])).
% 1.24/1.45 tff(337,plain,((~(s(s(s(z))) = elem!1)) | r(elem!1, s(elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(338,plain,
% 1.24/1.45 (r(elem!1, s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[337, 300, 76])).
% 1.24/1.45 tff(339,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 1.24/1.45 tff(340,assumption,(r(s(elem!1), s(z))), introduced(assumption)).
% 1.24/1.45 tff(341,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(342,plain,
% 1.24/1.45 (((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1)))) <=> ((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(343,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[342])).
% 1.24/1.45 tff(344,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[343, 341])).
% 1.24/1.45 tff(345,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(346,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[345, 344])).
% 1.24/1.45 tff(347,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[346, 268, 340, 238, 339])).
% 1.24/1.45 tff(348,plain,((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(349,plain,
% 1.24/1.45 (~r(s(elem!1), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[348, 338, 238])).
% 1.24/1.45 tff(350,plain,
% 1.24/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(351,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(352,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[351, 350])).
% 1.24/1.45 tff(353,plain,
% 1.24/1.45 ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[352, 69])).
% 1.24/1.45 tff(354,plain,
% 1.24/1.45 (b(s(elem!1), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[353, 349, 180])).
% 1.24/1.45 tff(355,plain,
% 1.24/1.45 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[354, 330])).
% 1.24/1.45 tff(356,plain,
% 1.24/1.45 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.24/1.45 inference(monotonicity,[status(thm)],[76])).
% 1.24/1.45 tff(357,plain,
% 1.24/1.45 (r(s(s(s(s(s(z))))), elem!1)),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[256, 356])).
% 1.24/1.45 tff(358,plain,
% 1.24/1.45 (r(s(z), elem!1)),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[257, 220])).
% 1.24/1.45 tff(359,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(360,plain,
% 1.24/1.45 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(361,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[360])).
% 1.24/1.45 tff(362,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[361, 359])).
% 1.24/1.45 tff(363,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(364,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[363, 362])).
% 1.24/1.45 tff(365,plain,
% 1.24/1.45 (~r(s(z), s(s(s(s(s(z))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[364, 268, 358, 357])).
% 1.24/1.45 tff(366,assumption,(~b(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.45 tff(367,assumption,(~r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.45 tff(368,plain,
% 1.24/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(369,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(370,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[369, 368])).
% 1.24/1.45 tff(371,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[370, 69, 367, 289, 366])).
% 1.24/1.45 tff(372,plain,(b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(373,plain,
% 1.24/1.45 (b(s(z), s(s(s(s(s(z))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[372, 365])).
% 1.24/1.45 tff(374,assumption,(b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.24/1.45 tff(375,plain,
% 1.24/1.45 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(z)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[162])).
% 1.24/1.45 tff(376,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.45 tff(377,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(378,plain,
% 1.24/1.46 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(379,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[378])).
% 1.24/1.46 tff(380,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[379, 377])).
% 1.24/1.46 tff(381,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(382,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[381, 380])).
% 1.24/1.46 tff(383,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[382, 268, 300, 376, 257])).
% 1.24/1.46 tff(384,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(385,plain,
% 1.24/1.46 (~r(s(z), s(s(s(s(z)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[384, 300, 257])).
% 1.24/1.46 tff(386,plain,
% 1.24/1.46 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(elem!1))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[77])).
% 1.24/1.46 tff(387,plain,
% 1.24/1.46 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(s(z)))))),
% 1.24/1.46 inference(symmetry,[status(thm)],[386])).
% 1.24/1.46 tff(388,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 1.24/1.46 tff(389,plain,
% 1.24/1.46 (r(s(z), s(s(s(s(z)))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[388, 387])).
% 1.24/1.46 tff(390,assumption,(~r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.46 tff(391,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[390, 389])).
% 1.24/1.46 tff(392,plain,((~r(s(z), s(elem!1))) | r(s(z), s(s(s(s(z))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(393,plain,
% 1.24/1.46 (~r(s(z), s(elem!1))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[392, 385, 76])).
% 1.24/1.46 tff(394,plain,
% 1.24/1.46 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(395,plain,
% 1.24/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(396,plain,
% 1.24/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[395, 394])).
% 1.24/1.46 tff(397,plain,
% 1.24/1.46 ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[396, 69])).
% 1.24/1.46 tff(398,plain,
% 1.24/1.46 (b(s(z), s(elem!1))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[397, 393, 172])).
% 1.24/1.46 tff(399,plain,
% 1.24/1.46 (b(s(z), s(s(s(s(z)))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[398, 375])).
% 1.24/1.46 tff(400,plain,
% 1.24/1.46 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[201])).
% 1.24/1.46 tff(401,plain,
% 1.24/1.46 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[162])).
% 1.24/1.46 tff(402,plain,
% 1.24/1.46 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[401, 400])).
% 1.24/1.46 tff(403,plain,
% 1.24/1.46 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.24/1.46 inference(commutativity,[status(thm)],[])).
% 1.24/1.46 tff(404,plain,
% 1.24/1.46 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[162])).
% 1.24/1.46 tff(405,plain,
% 1.24/1.46 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[404, 403])).
% 1.24/1.46 tff(406,plain,
% 1.24/1.46 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.24/1.46 inference(symmetry,[status(thm)],[405])).
% 1.24/1.46 tff(407,plain,
% 1.24/1.46 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[201])).
% 1.24/1.46 tff(408,plain,
% 1.24/1.46 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.24/1.46 inference(symmetry,[status(thm)],[407])).
% 1.24/1.46 tff(409,plain,
% 1.24/1.46 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.24/1.46 inference(transitivity,[status(thm)],[408, 406])).
% 1.24/1.46 tff(410,plain,
% 1.24/1.46 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[409])).
% 1.24/1.46 tff(411,plain,
% 1.24/1.46 (~(s(elem!1) = s(s(elem!1)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[319, 410])).
% 1.24/1.46 tff(412,assumption,(r(elem!1, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.46 tff(413,plain,
% 1.24/1.46 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[162])).
% 1.24/1.46 tff(414,plain,
% 1.24/1.46 (elem!1 = s(s(s(z)))),
% 1.24/1.46 inference(transitivity,[status(thm)],[86, 413, 37])).
% 1.24/1.46 tff(415,plain,
% 1.24/1.46 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[414])).
% 1.24/1.46 tff(416,plain,
% 1.24/1.46 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.24/1.46 inference(symmetry,[status(thm)],[415])).
% 1.24/1.46 tff(417,plain,
% 1.24/1.46 (r(elem!1, s(s(s(s(z)))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[300, 416])).
% 1.24/1.46 tff(418,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.46 tff(419,assumption,(r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.46 tff(420,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(421,plain,
% 1.24/1.46 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(422,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[421])).
% 1.24/1.46 tff(423,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[422, 420])).
% 1.24/1.46 tff(424,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(425,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[424, 423])).
% 1.24/1.46 tff(426,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[425, 268, 412, 419, 418])).
% 1.24/1.46 tff(427,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(428,plain,
% 1.24/1.46 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[427, 417, 412])).
% 1.24/1.46 tff(429,plain,
% 1.24/1.46 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[77, 181])).
% 1.24/1.46 tff(430,plain,
% 1.24/1.46 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.24/1.46 inference(symmetry,[status(thm)],[429])).
% 1.24/1.46 tff(431,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.24/1.46 tff(432,plain,
% 1.24/1.46 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[431, 430])).
% 1.24/1.46 tff(433,assumption,(~r(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.46 tff(434,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[433, 432])).
% 1.24/1.46 tff(435,plain,((~r(s(elem!1), s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(436,plain,
% 1.24/1.46 (~r(s(elem!1), s(s(elem!1)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[435, 428, 76])).
% 1.24/1.46 tff(437,plain,
% 1.24/1.46 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(438,plain,
% 1.24/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(439,plain,
% 1.24/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[438, 437])).
% 1.24/1.46 tff(440,plain,
% 1.24/1.46 ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[439, 69])).
% 1.24/1.46 tff(441,plain,
% 1.24/1.46 (b(s(elem!1), s(s(elem!1)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[440, 436, 411])).
% 1.24/1.46 tff(442,plain,
% 1.24/1.46 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[441, 402])).
% 1.24/1.46 tff(443,assumption,(b(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.46 tff(444,plain,
% 1.24/1.46 (^[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))))),
% 1.24/1.46 inference(bind,[status(th)],[])).
% 1.24/1.46 tff(445,plain,
% 1.24/1.46 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.24/1.46 inference(quant_intro,[status(thm)],[444])).
% 1.24/1.46 tff(446,plain,
% 1.24/1.46 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(447,plain,
% 1.24/1.46 (^[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)))))),
% 1.24/1.46 inference(bind,[status(th)],[])).
% 1.24/1.46 tff(448,plain,
% 1.24/1.46 (![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)))),
% 1.24/1.46 inference(quant_intro,[status(thm)],[447])).
% 1.24/1.46 tff(449,axiom,(![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X2, X4))) | (~b(X3, X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axb')).
% 1.24/1.46 tff(450,plain,
% 1.24/1.46 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[449, 448])).
% 1.24/1.46 tff(451,plain,
% 1.24/1.46 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[450, 446])).
% 1.24/1.46 tff(452,plain,(
% 1.24/1.46 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.24/1.46 inference(skolemize,[status(sab)],[451])).
% 1.24/1.46 tff(453,plain,
% 1.24/1.46 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[452, 445])).
% 1.24/1.46 tff(454,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(455,plain,
% 1.24/1.46 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(456,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[455])).
% 1.24/1.46 tff(457,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[456, 454])).
% 1.24/1.46 tff(458,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(459,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[458, 457])).
% 1.24/1.46 tff(460,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[459, 453, 443, 442, 399, 374])).
% 1.24/1.46 tff(461,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~(s(s(s(z))) = elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(462,plain,
% 1.24/1.46 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[461, 300, 373, 76, 298, 257])).
% 1.24/1.46 tff(463,plain,
% 1.24/1.46 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(464,plain,
% 1.24/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(465,plain,
% 1.24/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z))))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[464, 463])).
% 1.24/1.46 tff(466,plain,
% 1.24/1.46 ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z))))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[465, 69])).
% 1.24/1.46 tff(467,plain,
% 1.24/1.46 (b(elem!1, s(s(s(s(s(z))))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[466, 462, 208])).
% 1.24/1.46 tff(468,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(469,plain,
% 1.24/1.46 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(470,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~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(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[469])).
% 1.24/1.46 tff(471,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~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(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[470, 468])).
% 1.24/1.46 tff(472,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(473,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[472, 471])).
% 1.24/1.46 tff(474,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[473, 453, 467, 373, 355, 329, 299, 298])).
% 1.24/1.46 tff(475,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(z))) | (~(s(s(s(z))) = elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(476,plain,
% 1.24/1.46 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[475, 256, 238, 76, 228, 255])).
% 1.24/1.46 tff(477,plain,
% 1.24/1.46 (~r(elem!1, s(s(s(s(z)))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[476, 248])).
% 1.24/1.46 tff(478,plain,
% 1.24/1.46 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(479,plain,
% 1.24/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(480,plain,
% 1.24/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[479, 478])).
% 1.24/1.46 tff(481,plain,
% 1.24/1.46 (b(elem!1, s(s(s(s(z)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[480, 69, 477, 9])).
% 1.24/1.46 tff(482,plain,
% 1.24/1.46 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.24/1.46 inference(symmetry,[status(thm)],[413])).
% 1.24/1.46 tff(483,plain,
% 1.24/1.46 (s(s(s(z))) = elem!1),
% 1.24/1.46 inference(transitivity,[status(thm)],[38, 482, 85])).
% 1.24/1.46 tff(484,plain,
% 1.24/1.46 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), elem!1)),
% 1.24/1.46 inference(monotonicity,[status(thm)],[483])).
% 1.24/1.46 tff(485,plain,
% 1.24/1.46 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(z))))),
% 1.24/1.46 inference(symmetry,[status(thm)],[484])).
% 1.24/1.46 tff(486,plain,
% 1.24/1.46 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 1.24/1.46 inference(commutativity,[status(thm)],[])).
% 1.24/1.46 tff(487,plain,
% 1.24/1.46 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(z))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[414])).
% 1.24/1.46 tff(488,plain,
% 1.24/1.46 ((s(s(z)) = elem!1) <=> (s(s(s(z))) = s(s(z)))),
% 1.24/1.46 inference(transitivity,[status(thm)],[487, 486])).
% 1.24/1.46 tff(489,plain,
% 1.24/1.46 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.24/1.46 inference(symmetry,[status(thm)],[488])).
% 1.24/1.46 tff(490,plain,
% 1.24/1.46 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[489])).
% 1.24/1.47 tff(491,plain,
% 1.24/1.47 (~(s(s(z)) = elem!1)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[160, 490])).
% 1.24/1.47 tff(492,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 1.24/1.47 tff(493,plain,
% 1.24/1.47 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[166])).
% 1.24/1.47 tff(494,plain,
% 1.24/1.47 (elem!1 = s(s(s(z)))),
% 1.24/1.47 inference(transitivity,[status(thm)],[86, 493, 37])).
% 1.24/1.47 tff(495,plain,
% 1.24/1.47 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[494])).
% 1.24/1.47 tff(496,plain,
% 1.24/1.47 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 1.24/1.47 inference(symmetry,[status(thm)],[495])).
% 1.24/1.47 tff(497,plain,
% 1.24/1.47 ((~b(s(z), s(s(s(z))))) <=> (~b(s(z), elem!1))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[496])).
% 1.24/1.47 tff(498,plain,
% 1.24/1.47 (~b(s(z), elem!1)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[221, 497])).
% 1.24/1.47 tff(499,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 1.24/1.47 tff(500,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[499, 498])).
% 1.24/1.47 tff(501,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(z), elem!1)) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(502,plain,
% 1.24/1.47 (~b(s(z), elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[501, 162, 221])).
% 1.24/1.47 tff(503,plain,
% 1.24/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(504,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(505,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[504, 503])).
% 1.24/1.47 tff(506,plain,
% 1.24/1.47 ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[505, 69])).
% 1.24/1.47 tff(507,plain,
% 1.24/1.47 (r(s(z), elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[506, 502, 492])).
% 1.24/1.47 tff(508,plain,
% 1.24/1.47 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[494])).
% 1.24/1.47 tff(509,plain,
% 1.24/1.47 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.24/1.47 inference(symmetry,[status(thm)],[508])).
% 1.24/1.47 tff(510,plain,
% 1.24/1.47 (r(s(s(s(s(z)))), elem!1)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[11, 509])).
% 1.24/1.47 tff(511,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[239, 510])).
% 1.24/1.47 tff(512,plain,((~(s(elem!1) = s(s(s(s(z)))))) | r(s(s(s(s(z)))), elem!1) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(513,plain,
% 1.24/1.47 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[512, 162, 239])).
% 1.24/1.47 tff(514,plain,
% 1.24/1.47 (((~![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)))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(515,plain,
% 1.24/1.47 ((~![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)))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(516,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[515, 514])).
% 1.24/1.47 tff(517,plain,
% 1.24/1.47 ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[516, 69])).
% 1.24/1.47 tff(518,plain,
% 1.24/1.47 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[517, 142])).
% 1.24/1.47 tff(519,plain,
% 1.24/1.47 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[518, 513])).
% 1.24/1.47 tff(520,plain,
% 1.24/1.47 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[162])).
% 1.24/1.47 tff(521,plain,
% 1.24/1.47 (b(s(s(s(s(z)))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.24/1.47 inference(symmetry,[status(thm)],[520])).
% 1.24/1.47 tff(522,plain,
% 1.24/1.47 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[76])).
% 1.24/1.47 tff(523,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.47 tff(524,plain,
% 1.24/1.47 (b(s(s(s(s(z)))), elem!1)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[523, 522])).
% 1.24/1.47 tff(525,plain,
% 1.24/1.47 (b(s(elem!1), elem!1)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[524, 521])).
% 1.24/1.47 tff(526,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 1.24/1.47 tff(527,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[526, 525])).
% 1.24/1.47 tff(528,plain,((~(s(s(s(z))) = elem!1)) | b(s(elem!1), elem!1) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(529,plain,
% 1.24/1.47 (b(s(elem!1), elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[528, 519, 76])).
% 1.24/1.47 tff(530,assumption,(b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.47 tff(531,plain,
% 1.24/1.47 (s(s(s(s(z)))) = s(elem!1)),
% 1.24/1.47 inference(symmetry,[status(thm)],[162])).
% 1.24/1.47 tff(532,plain,
% 1.24/1.47 (r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[531, 241])).
% 1.24/1.47 tff(533,plain,
% 1.24/1.47 ((s(elem!1) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.24/1.47 inference(commutativity,[status(thm)],[])).
% 1.24/1.47 tff(534,plain,
% 1.24/1.47 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(elem!1) = s(s(s(s(s(s(z)))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[531])).
% 1.24/1.47 tff(535,plain,
% 1.24/1.47 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.24/1.47 inference(transitivity,[status(thm)],[534, 533])).
% 1.24/1.47 tff(536,plain,
% 1.24/1.47 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[535])).
% 1.24/1.47 tff(537,plain,
% 1.24/1.47 ((~(s(s(s(s(s(s(z)))))) = s(elem!1))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(s(z))))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[536])).
% 1.24/1.47 tff(538,plain,
% 1.24/1.47 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[241, 162])).
% 1.24/1.47 tff(539,plain,
% 1.24/1.47 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.24/1.47 inference(symmetry,[status(thm)],[538])).
% 1.24/1.47 tff(540,plain,
% 1.24/1.47 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(s(z)))))) = s(elem!1)))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[539])).
% 1.24/1.47 tff(541,assumption,(s(s(s(z))) = s(s(elem!1))), introduced(assumption)).
% 1.24/1.47 tff(542,plain,
% 1.24/1.47 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[541])).
% 1.24/1.47 tff(543,plain,
% 1.24/1.47 (s(s(z)) = s(elem!1)),
% 1.24/1.47 inference(transitivity,[status(thm)],[98, 542, 194])).
% 1.24/1.47 tff(544,plain,
% 1.24/1.47 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[543])).
% 1.24/1.47 tff(545,plain,
% 1.24/1.47 (s(z) = elem!1),
% 1.24/1.47 inference(transitivity,[status(thm)],[29, 544, 85])).
% 1.24/1.47 tff(546,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[492, 545])).
% 1.24/1.47 tff(547,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(548,plain,
% 1.24/1.47 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[547, 492])).
% 1.24/1.47 tff(549,plain,
% 1.24/1.47 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(550,plain,
% 1.24/1.47 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[549, 21])).
% 1.24/1.47 tff(551,assumption,(s(s(s(elem!1))) = s(s(s(s(z))))), introduced(assumption)).
% 1.24/1.47 tff(552,plain,
% 1.24/1.47 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[551])).
% 1.24/1.47 tff(553,plain,
% 1.24/1.47 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[552])).
% 1.24/1.47 tff(554,plain,
% 1.24/1.47 (s(s(s(z))) = s(s(elem!1))),
% 1.24/1.47 inference(transitivity,[status(thm)],[38, 553, 550])).
% 1.24/1.47 tff(555,assumption,(~(s(s(s(z))) = s(s(elem!1)))), introduced(assumption)).
% 1.24/1.47 tff(556,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[555, 554])).
% 1.24/1.47 tff(557,plain,((~(s(s(s(elem!1))) = s(s(s(s(z)))))) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(558,plain,
% 1.24/1.47 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[557, 548])).
% 1.24/1.47 tff(559,plain,
% 1.24/1.47 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[558, 540])).
% 1.24/1.47 tff(560,plain,
% 1.24/1.47 (~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[559, 537])).
% 1.24/1.47 tff(561,plain,
% 1.24/1.47 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[483])).
% 1.24/1.47 tff(562,plain,
% 1.24/1.47 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[561])).
% 1.24/1.47 tff(563,assumption,(~r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.24/1.47 tff(564,plain,
% 1.24/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(565,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(566,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[565, 564])).
% 1.24/1.47 tff(567,plain,
% 1.24/1.47 ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[566, 69])).
% 1.24/1.47 tff(568,plain,
% 1.24/1.47 (b(s(s(s(elem!1))), elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[567, 200, 563])).
% 1.24/1.47 tff(569,plain,
% 1.24/1.47 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[181])).
% 1.24/1.47 tff(570,plain,
% 1.24/1.47 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[569])).
% 1.24/1.47 tff(571,plain,
% 1.24/1.47 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[570])).
% 1.24/1.47 tff(572,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.24/1.47 tff(573,plain,
% 1.24/1.47 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[572, 571])).
% 1.24/1.47 tff(574,assumption,(~b(s(s(s(s(s(s(z)))))), elem!1)), introduced(assumption)).
% 1.24/1.47 tff(575,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[574, 573])).
% 1.24/1.47 tff(576,plain,((~b(s(s(s(elem!1))), elem!1)) | b(s(s(s(s(s(s(z)))))), elem!1) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(577,plain,
% 1.24/1.47 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[576, 568, 76])).
% 1.24/1.47 tff(578,plain,
% 1.24/1.47 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[577, 562])).
% 1.24/1.47 tff(579,plain,
% 1.24/1.47 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[414])).
% 1.24/1.47 tff(580,plain,
% 1.24/1.47 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[530, 579])).
% 1.24/1.47 tff(581,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(582,plain,
% 1.24/1.47 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(583,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[582])).
% 1.24/1.47 tff(584,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[583, 581])).
% 1.24/1.47 tff(585,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(586,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[585, 584])).
% 1.24/1.47 tff(587,plain,
% 1.24/1.47 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[586, 453, 519, 580])).
% 1.24/1.47 tff(588,plain,
% 1.24/1.47 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[587, 578])).
% 1.24/1.47 tff(589,plain,
% 1.24/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(590,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(591,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[590, 589])).
% 1.24/1.47 tff(592,plain,
% 1.24/1.47 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[591, 69, 588])).
% 1.24/1.47 tff(593,plain,
% 1.24/1.47 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[592, 560])).
% 1.24/1.47 tff(594,plain,
% 1.24/1.47 (r(s(elem!1), s(s(s(elem!1))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[593, 532])).
% 1.24/1.47 tff(595,plain,
% 1.24/1.47 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[162])).
% 1.24/1.47 tff(596,plain,
% 1.24/1.47 ((s(s(s(s(z)))) = elem!1) <=> (s(elem!1) = elem!1)),
% 1.24/1.47 inference(symmetry,[status(thm)],[595])).
% 1.24/1.47 tff(597,plain,
% 1.24/1.47 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(elem!1) = elem!1))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[596])).
% 1.24/1.47 tff(598,plain,
% 1.24/1.47 (~(s(elem!1) = elem!1)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3, 597])).
% 1.24/1.47 tff(599,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 1.24/1.47 tff(600,plain,
% 1.24/1.47 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[599])).
% 1.24/1.47 tff(601,plain,
% 1.24/1.47 (s(elem!1) = s(s(elem!1))),
% 1.24/1.47 inference(transitivity,[status(thm)],[195, 600, 550])).
% 1.24/1.47 tff(602,plain,
% 1.24/1.47 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[601])).
% 1.24/1.47 tff(603,plain,
% 1.24/1.47 (inj_0(s(s(elem!1))) = inj_0(s(elem!1))),
% 1.24/1.47 inference(symmetry,[status(thm)],[602])).
% 1.24/1.47 tff(604,plain,
% 1.24/1.47 (s(elem!1) = elem!1),
% 1.24/1.47 inference(transitivity,[status(thm)],[195, 603, 85])).
% 1.24/1.47 tff(605,assumption,(~(s(elem!1) = elem!1)), introduced(assumption)).
% 1.24/1.47 tff(606,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[605, 604])).
% 1.24/1.47 tff(607,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(608,plain,
% 1.24/1.47 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[607, 598])).
% 1.24/1.47 tff(609,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.47 tff(610,plain,
% 1.24/1.47 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[166])).
% 1.24/1.47 tff(611,plain,
% 1.24/1.47 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[610])).
% 1.24/1.47 tff(612,plain,
% 1.24/1.47 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.24/1.47 inference(symmetry,[status(thm)],[611])).
% 1.24/1.47 tff(613,plain,
% 1.24/1.47 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[612])).
% 1.24/1.47 tff(614,plain,
% 1.24/1.47 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[613])).
% 1.24/1.47 tff(615,plain,
% 1.24/1.47 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[610])).
% 1.24/1.47 tff(616,plain,
% 1.24/1.47 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[615, 614])).
% 1.24/1.47 tff(617,assumption,(~(s(s(elem!1)) = s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.47 tff(618,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.47 tff(619,plain,
% 1.24/1.47 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[166, 610])).
% 1.24/1.47 tff(620,plain,
% 1.24/1.47 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.24/1.47 inference(symmetry,[status(thm)],[619])).
% 1.24/1.47 tff(621,plain,
% 1.24/1.47 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[166])).
% 1.24/1.47 tff(622,plain,
% 1.24/1.47 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.24/1.47 inference(transitivity,[status(thm)],[621, 620])).
% 1.24/1.47 tff(623,plain,
% 1.24/1.47 ((s(elem!1) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.24/1.47 inference(commutativity,[status(thm)],[])).
% 1.24/1.47 tff(624,plain,
% 1.24/1.47 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[623])).
% 1.24/1.47 tff(625,plain,
% 1.24/1.47 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[167])).
% 1.24/1.47 tff(626,plain,
% 1.24/1.47 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[625, 624])).
% 1.24/1.47 tff(627,plain,
% 1.24/1.47 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(s(s(s(z)))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[626])).
% 1.24/1.47 tff(628,plain,
% 1.24/1.47 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[319, 627])).
% 1.24/1.47 tff(629,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 1.24/1.47 tff(630,plain,
% 1.24/1.47 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[494])).
% 1.24/1.47 tff(631,plain,
% 1.24/1.47 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[630, 57])).
% 1.24/1.47 tff(632,plain,
% 1.24/1.47 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[631])).
% 1.24/1.47 tff(633,plain,
% 1.24/1.47 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.24/1.47 inference(transitivity,[status(thm)],[632, 56])).
% 1.24/1.47 tff(634,plain,
% 1.24/1.47 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[633])).
% 1.24/1.47 tff(635,plain,
% 1.24/1.47 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[111, 634])).
% 1.24/1.47 tff(636,assumption,(~r(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.24/1.47 tff(637,assumption,(~(s(s(s(s(s(z))))) = elem!1)), introduced(assumption)).
% 1.24/1.47 tff(638,assumption,(~b(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.24/1.47 tff(639,plain,
% 1.24/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(640,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(641,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[640, 639])).
% 1.24/1.47 tff(642,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[641, 69, 636, 638, 637])).
% 1.24/1.47 tff(643,plain,(r(s(s(s(s(s(z))))), elem!1) | b(s(s(s(s(s(z))))), elem!1) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(644,plain,
% 1.24/1.47 (b(s(s(s(s(s(z))))), elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[643, 636, 635])).
% 1.24/1.47 tff(645,assumption,(b(s(elem!1), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.47 tff(646,assumption,(b(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.24/1.47 tff(647,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(648,plain,
% 1.24/1.47 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(649,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[648])).
% 1.24/1.47 tff(650,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.24/1.47 inference(transitivity,[status(thm)],[649, 647])).
% 1.24/1.47 tff(651,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(652,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[651, 650])).
% 1.24/1.47 tff(653,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[652, 453, 629, 646, 645, 530])).
% 1.24/1.47 tff(654,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(655,plain,
% 1.24/1.47 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[654, 644, 530, 629])).
% 1.24/1.47 tff(656,plain,
% 1.24/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(s(z)))))) | r(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(s(z)))))) | r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(657,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(s(z)))))) | r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(658,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(s(z)))))) | r(s(elem!1), s(s(s(s(s(z))))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[657, 656])).
% 1.24/1.47 tff(659,plain,
% 1.24/1.47 ((s(elem!1) = s(s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(s(z)))))) | r(s(elem!1), s(s(s(s(s(z))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[658, 69])).
% 1.24/1.47 tff(660,plain,
% 1.24/1.47 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[659, 655, 628])).
% 1.24/1.47 tff(661,plain,
% 1.24/1.47 (r(s(elem!1), s(s(elem!1)))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[660, 622])).
% 1.24/1.47 tff(662,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.47 tff(663,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(664,plain,
% 1.24/1.47 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(665,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[664])).
% 1.24/1.48 tff(666,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[665, 663])).
% 1.24/1.48 tff(667,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(668,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[667, 666])).
% 1.24/1.48 tff(669,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[668, 268, 662, 431, 618])).
% 1.24/1.48 tff(670,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(671,plain,
% 1.24/1.48 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[670, 661, 618])).
% 1.24/1.48 tff(672,plain,
% 1.24/1.48 (((~![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)))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(673,plain,
% 1.24/1.48 ((~![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)))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(674,plain,
% 1.24/1.48 ((~![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))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[673, 672])).
% 1.24/1.48 tff(675,plain,
% 1.24/1.48 ((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))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[674, 69])).
% 1.24/1.48 tff(676,plain,
% 1.24/1.48 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[675, 671, 617])).
% 1.24/1.48 tff(677,plain,
% 1.24/1.48 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[676, 616])).
% 1.24/1.48 tff(678,plain,
% 1.24/1.48 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[494])).
% 1.24/1.48 tff(679,plain,
% 1.24/1.48 ((~r(s(s(s(s(s(z))))), elem!1)) <=> (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[678])).
% 1.24/1.48 tff(680,plain,
% 1.24/1.48 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[636, 679])).
% 1.24/1.48 tff(681,assumption,(~b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.48 tff(682,assumption,(~r(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.48 tff(683,plain,
% 1.24/1.48 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(684,plain,
% 1.24/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(685,plain,
% 1.24/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[684, 683])).
% 1.24/1.48 tff(686,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[685, 69, 682, 111, 681])).
% 1.24/1.48 tff(687,plain,(b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(688,plain,
% 1.24/1.48 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[687, 680])).
% 1.24/1.48 tff(689,plain,
% 1.24/1.48 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[494])).
% 1.24/1.48 tff(690,plain,
% 1.24/1.48 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[530, 689])).
% 1.24/1.48 tff(691,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(692,plain,
% 1.24/1.48 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(693,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[692])).
% 1.24/1.48 tff(694,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[693, 691])).
% 1.24/1.48 tff(695,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(696,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[695, 694])).
% 1.24/1.48 tff(697,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[696, 453, 690, 688, 677, 609])).
% 1.24/1.48 tff(698,plain,(r(s(s(s(s(s(z))))), elem!1) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(699,plain,
% 1.24/1.48 (r(s(s(s(s(s(z))))), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[698, 578, 162, 608, 594, 530, 529])).
% 1.24/1.48 tff(700,assumption,(r(s(s(z)), elem!1)), introduced(assumption)).
% 1.24/1.48 tff(701,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 1.24/1.48 tff(702,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(703,plain,
% 1.24/1.48 (((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(704,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[703])).
% 1.24/1.48 tff(705,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.24/1.48 inference(transitivity,[status(thm)],[704, 702])).
% 1.24/1.48 tff(706,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(707,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[706, 705])).
% 1.24/1.48 tff(708,plain,
% 1.24/1.48 (~r(s(s(z)), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[707, 268, 701, 700])).
% 1.24/1.48 tff(709,assumption,(s(s(z)) = s(z)), introduced(assumption)).
% 1.24/1.48 tff(710,plain,
% 1.24/1.48 (s(z) = s(s(z))),
% 1.24/1.48 inference(symmetry,[status(thm)],[709])).
% 1.24/1.48 tff(711,plain,
% 1.24/1.48 (inj_0(s(z)) = inj_0(s(s(z)))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[710])).
% 1.24/1.48 tff(712,plain,
% 1.24/1.48 (inj_0(s(s(z))) = inj_0(s(z))),
% 1.24/1.48 inference(symmetry,[status(thm)],[711])).
% 1.24/1.48 tff(713,plain,
% 1.24/1.48 (s(z) = z),
% 1.24/1.48 inference(transitivity,[status(thm)],[29, 712, 32])).
% 1.24/1.48 tff(714,plain,
% 1.24/1.48 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(715,plain,
% 1.24/1.48 (~(s(z) = z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[714, 46])).
% 1.24/1.48 tff(716,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[715, 713])).
% 1.24/1.48 tff(717,plain,(~(s(s(z)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(718,plain,
% 1.24/1.48 (((~![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)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(719,plain,
% 1.24/1.48 ((~![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)))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(720,plain,
% 1.24/1.48 ((~![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))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[719, 718])).
% 1.24/1.48 tff(721,plain,
% 1.24/1.48 (b(s(s(z)), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[720, 69, 717, 708])).
% 1.24/1.48 tff(722,assumption,(r(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.24/1.48 tff(723,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(724,plain,
% 1.24/1.48 (((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(725,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[724])).
% 1.24/1.48 tff(726,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[725, 723])).
% 1.24/1.48 tff(727,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(728,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[727, 726])).
% 1.24/1.48 tff(729,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[728, 268, 701, 722, 258])).
% 1.24/1.48 tff(730,plain,((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(731,plain,
% 1.24/1.48 (~r(s(s(s(s(s(z))))), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[730, 701, 722])).
% 1.24/1.48 tff(732,plain,
% 1.24/1.48 (b(s(s(s(s(s(z))))), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[297, 731])).
% 1.24/1.48 tff(733,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 1.24/1.48 tff(734,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(735,plain,
% 1.24/1.48 (((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(736,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[735])).
% 1.24/1.48 tff(737,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.24/1.48 inference(transitivity,[status(thm)],[736, 734])).
% 1.24/1.48 tff(738,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(739,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[738, 737])).
% 1.24/1.48 tff(740,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[739, 268, 701, 700, 733])).
% 1.24/1.48 tff(741,plain,((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(742,plain,
% 1.24/1.48 (~r(s(z), s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[741, 700, 701])).
% 1.24/1.48 tff(743,assumption,(~r(s(z), s(s(z)))), introduced(assumption)).
% 1.24/1.48 tff(744,assumption,(~b(s(z), s(s(z)))), introduced(assumption)).
% 1.24/1.48 tff(745,plain,
% 1.24/1.48 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 1.24/1.48 inference(commutativity,[status(thm)],[])).
% 1.24/1.48 tff(746,plain,
% 1.24/1.48 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 1.24/1.48 inference(symmetry,[status(thm)],[745])).
% 1.24/1.48 tff(747,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 1.24/1.48 tff(748,plain,
% 1.24/1.48 (s(s(z)) = s(z)),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[747, 746])).
% 1.24/1.48 tff(749,assumption,(~(s(s(z)) = s(z))), introduced(assumption)).
% 1.24/1.48 tff(750,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[749, 748])).
% 1.24/1.48 tff(751,plain,((~(s(z) = s(s(z)))) | (s(s(z)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(752,plain,
% 1.24/1.48 (~(s(z) = s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[751, 717])).
% 1.24/1.48 tff(753,plain,
% 1.24/1.48 (((~![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))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(754,plain,
% 1.24/1.48 ((~![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))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(755,plain,
% 1.24/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[754, 753])).
% 1.24/1.48 tff(756,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[755, 69, 752, 744, 743])).
% 1.24/1.48 tff(757,plain,(r(s(z), s(s(z))) | b(s(z), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(758,plain,
% 1.24/1.48 (b(s(z), s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[757, 742])).
% 1.24/1.48 tff(759,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), 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(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(760,plain,
% 1.24/1.48 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), 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(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(761,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), 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(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[760])).
% 1.24/1.49 tff(762,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), 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(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[761, 759])).
% 1.24/1.49 tff(763,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), 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(s(z)))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(764,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[763, 762])).
% 1.24/1.49 tff(765,plain,
% 1.24/1.49 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[764, 453, 758, 732, 721])).
% 1.24/1.49 tff(766,plain,
% 1.24/1.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(767,plain,
% 1.24/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(768,plain,
% 1.24/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[767, 766])).
% 1.24/1.49 tff(769,plain,
% 1.24/1.49 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[768, 69, 52, 765])).
% 1.24/1.49 tff(770,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(771,plain,
% 1.24/1.49 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(772,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[771])).
% 1.24/1.49 tff(773,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[772, 770])).
% 1.24/1.49 tff(774,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(775,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[774, 773])).
% 1.24/1.49 tff(776,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[775, 268, 700, 722, 769])).
% 1.24/1.49 tff(777,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(778,plain,
% 1.24/1.49 (~r(s(s(z)), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[777, 699, 507])).
% 1.24/1.49 tff(779,plain,
% 1.24/1.49 (((~![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))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(780,plain,
% 1.24/1.49 ((~![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))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(781,plain,
% 1.24/1.49 ((~![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)),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[780, 779])).
% 1.24/1.49 tff(782,plain,
% 1.24/1.49 ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[781, 69])).
% 1.24/1.49 tff(783,plain,
% 1.24/1.49 (b(s(s(z)), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[782, 778, 491])).
% 1.24/1.49 tff(784,plain,
% 1.24/1.49 (b(s(s(z)), s(s(s(z))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[783, 485])).
% 1.24/1.49 tff(785,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(786,plain,
% 1.24/1.49 (((~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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(787,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[786])).
% 1.24/1.49 tff(788,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[787, 785])).
% 1.24/1.49 tff(789,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(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)))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(790,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[789, 788])).
% 1.24/1.49 tff(791,plain,
% 1.24/1.49 ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[790, 453, 519, 580])).
% 1.24/1.49 tff(792,plain,
% 1.24/1.49 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[791, 784])).
% 1.24/1.49 tff(793,plain,
% 1.24/1.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(794,plain,
% 1.24/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(795,plain,
% 1.24/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[794, 793])).
% 1.24/1.49 tff(796,plain,
% 1.24/1.49 (r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[795, 69, 153, 792])).
% 1.24/1.49 tff(797,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(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(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(798,plain,
% 1.24/1.49 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~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(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(799,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[798])).
% 1.24/1.49 tff(800,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[799, 797])).
% 1.24/1.49 tff(801,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(802,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[801, 800])).
% 1.24/1.49 tff(803,plain,
% 1.24/1.49 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[802, 453, 580, 578])).
% 1.24/1.49 tff(804,plain,
% 1.24/1.49 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[803, 784])).
% 1.24/1.49 tff(805,assumption,(s(s(z)) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.49 tff(806,plain,
% 1.24/1.49 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[805])).
% 1.24/1.49 tff(807,plain,
% 1.24/1.49 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(z)))),
% 1.24/1.49 inference(symmetry,[status(thm)],[806])).
% 1.24/1.49 tff(808,plain,
% 1.24/1.49 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[183])).
% 1.24/1.49 tff(809,plain,
% 1.24/1.49 (s(s(elem!1)) = s(z)),
% 1.24/1.49 inference(transitivity,[status(thm)],[569, 808, 807, 28])).
% 1.24/1.49 tff(810,assumption,(s(s(elem!1)) = s(z)), introduced(assumption)).
% 1.24/1.49 tff(811,plain,
% 1.24/1.49 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[810])).
% 1.24/1.49 tff(812,plain,
% 1.24/1.49 (s(elem!1) = z),
% 1.24/1.49 inference(transitivity,[status(thm)],[195, 811, 32])).
% 1.24/1.49 tff(813,plain,
% 1.24/1.49 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(814,plain,
% 1.24/1.49 (~(s(elem!1) = z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[813, 46])).
% 1.24/1.49 tff(815,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[814, 812])).
% 1.24/1.49 tff(816,plain,(~(s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(817,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[816, 809])).
% 1.24/1.49 tff(818,plain,((~(s(s(z)) = s(s(s(s(s(s(z)))))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(819,plain,
% 1.24/1.49 (~(s(s(z)) = s(s(s(s(s(s(z)))))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[818, 76])).
% 1.24/1.49 tff(820,plain,
% 1.24/1.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(821,plain,
% 1.24/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(822,plain,
% 1.24/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[821, 820])).
% 1.24/1.49 tff(823,plain,
% 1.24/1.49 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[822, 69, 819, 804])).
% 1.24/1.49 tff(824,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(825,plain,
% 1.24/1.49 (((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(826,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[825])).
% 1.24/1.49 tff(827,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[826, 824])).
% 1.24/1.49 tff(828,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(829,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[828, 827])).
% 1.24/1.49 tff(830,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[829, 268, 593, 823, 796])).
% 1.24/1.49 tff(831,plain,((~(s(s(s(z))) = elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1) | r(s(s(s(elem!1))), elem!1) | (s(z) = elem!1) | b(s(z), s(s(s(z)))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(832,plain,
% 1.24/1.49 (r(s(s(s(elem!1))), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[831, 481, 3, 76, 246, 221, 239])).
% 1.24/1.49 tff(833,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.24/1.49 tff(834,assumption,(r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.24/1.49 tff(835,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(836,plain,
% 1.24/1.49 (((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(837,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[836])).
% 1.24/1.49 tff(838,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.24/1.49 inference(transitivity,[status(thm)],[837, 835])).
% 1.24/1.49 tff(839,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(840,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[839, 838])).
% 1.24/1.49 tff(841,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[840, 268, 238, 834, 833])).
% 1.24/1.49 tff(842,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(843,plain,
% 1.24/1.49 (~r(s(s(s(elem!1))), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[842, 832, 238])).
% 1.24/1.49 tff(844,assumption,(s(s(s(elem!1))) = s(z)), introduced(assumption)).
% 1.24/1.49 tff(845,plain,
% 1.24/1.49 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[844])).
% 1.24/1.49 tff(846,plain,
% 1.24/1.49 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[550])).
% 1.24/1.49 tff(847,plain,
% 1.24/1.49 (s(s(elem!1)) = z),
% 1.24/1.49 inference(transitivity,[status(thm)],[846, 845, 32])).
% 1.24/1.49 tff(848,plain,
% 1.24/1.49 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(849,plain,
% 1.24/1.49 (~(s(s(elem!1)) = z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[848, 46])).
% 1.24/1.49 tff(850,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[849, 847])).
% 1.24/1.49 tff(851,plain,(~(s(s(s(elem!1))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(852,plain,
% 1.24/1.49 (((~![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)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(853,plain,
% 1.24/1.49 ((~![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)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(854,plain,
% 1.24/1.49 ((~![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))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[853, 852])).
% 1.24/1.49 tff(855,plain,
% 1.24/1.49 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[854, 69])).
% 1.24/1.49 tff(856,plain,
% 1.24/1.49 (b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[855, 851])).
% 1.24/1.49 tff(857,plain,
% 1.24/1.49 (b(s(s(s(elem!1))), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[856, 843])).
% 1.24/1.49 tff(858,plain,
% 1.24/1.49 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[857, 243])).
% 1.24/1.49 tff(859,plain,
% 1.24/1.49 (~r(s(s(s(s(s(z))))), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[276, 256, 228])).
% 1.24/1.49 tff(860,plain,
% 1.24/1.49 (b(s(s(s(s(s(z))))), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[297, 859])).
% 1.24/1.49 tff(861,plain,
% 1.24/1.49 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.24/1.50 inference(monotonicity,[status(thm)],[241])).
% 1.24/1.50 tff(862,plain,
% 1.24/1.50 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.24/1.50 inference(symmetry,[status(thm)],[861])).
% 1.24/1.50 tff(863,plain,
% 1.24/1.50 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.24/1.50 inference(monotonicity,[status(thm)],[201])).
% 1.24/1.50 tff(864,plain,
% 1.24/1.50 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.24/1.50 inference(transitivity,[status(thm)],[863, 862])).
% 1.24/1.50 tff(865,plain,
% 1.24/1.50 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.24/1.50 inference(monotonicity,[status(thm)],[201])).
% 1.24/1.50 tff(866,plain,
% 1.24/1.50 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.24/1.50 inference(symmetry,[status(thm)],[865])).
% 1.24/1.50 tff(867,plain,
% 1.24/1.50 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(elem!1)), elem!1)),
% 1.24/1.50 inference(transitivity,[status(thm)],[356, 866])).
% 1.24/1.50 tff(868,plain,
% 1.24/1.50 (r(s(s(elem!1)), elem!1)),
% 1.24/1.50 inference(modus_ponens,[status(thm)],[256, 867])).
% 1.24/1.50 tff(869,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.24/1.50 tff(870,plain,
% 1.24/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.24/1.50 inference(rewrite,[status(thm)],[])).
% 1.24/1.50 tff(871,plain,
% 1.24/1.50 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.24/1.50 inference(rewrite,[status(thm)],[])).
% 1.24/1.50 tff(872,plain,
% 1.24/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 1.24/1.50 inference(monotonicity,[status(thm)],[871])).
% 1.24/1.50 tff(873,plain,
% 1.24/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.24/1.50 inference(transitivity,[status(thm)],[872, 870])).
% 1.24/1.50 tff(874,plain,
% 1.24/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.24/1.50 inference(quant_inst,[status(thm)],[])).
% 1.24/1.50 tff(875,plain,
% 1.24/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 1.24/1.50 inference(modus_ponens,[status(thm)],[874, 873])).
% 1.24/1.50 tff(876,plain,
% 1.24/1.50 ($false),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[875, 268, 662, 869, 833])).
% 1.24/1.50 tff(877,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.50 tff(878,plain,
% 1.24/1.50 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[877, 832, 868])).
% 1.24/1.50 tff(879,plain,
% 1.24/1.50 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[675, 878, 608])).
% 1.24/1.50 tff(880,plain,
% 1.24/1.50 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.24/1.50 inference(modus_ponens,[status(thm)],[879, 864])).
% 1.24/1.50 tff(881,plain,
% 1.24/1.50 (~r(s(z), s(s(s(s(s(z))))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[364, 268, 229, 357])).
% 1.34/1.50 tff(882,plain,
% 1.34/1.50 (b(s(z), s(s(s(s(s(z))))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[372, 881])).
% 1.34/1.50 tff(883,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(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(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(884,plain,
% 1.34/1.50 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(885,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[884])).
% 1.34/1.50 tff(886,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[885, 883])).
% 1.34/1.50 tff(887,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(888,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[887, 886])).
% 1.34/1.50 tff(889,plain,
% 1.34/1.50 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[888, 453, 882, 880, 860])).
% 1.34/1.50 tff(890,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[889, 858])).
% 1.34/1.50 tff(891,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(z))) | (s(s(s(s(z)))) = elem!1) | (~(s(s(s(z))) = elem!1)) | b(s(z), s(s(s(z)))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(892,plain,
% 1.34/1.50 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[891, 239, 3, 76, 221, 238])).
% 1.34/1.50 tff(893,plain,
% 1.34/1.50 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[687, 892])).
% 1.34/1.50 tff(894,plain,
% 1.34/1.50 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[512, 239, 162])).
% 1.34/1.50 tff(895,plain,
% 1.34/1.50 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[518, 894])).
% 1.34/1.50 tff(896,plain,
% 1.34/1.50 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.50 inference(symmetry,[status(thm)],[247])).
% 1.34/1.50 tff(897,plain,
% 1.34/1.50 ((~r(elem!1, s(s(s(s(z)))))) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[896])).
% 1.34/1.50 tff(898,plain,
% 1.34/1.50 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[201])).
% 1.34/1.50 tff(899,plain,
% 1.34/1.50 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.50 inference(monotonicity,[status(thm)],[201])).
% 1.34/1.50 tff(900,plain,
% 1.34/1.50 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.34/1.50 inference(symmetry,[status(thm)],[899])).
% 1.34/1.50 tff(901,plain,
% 1.34/1.50 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.50 inference(monotonicity,[status(thm)],[76])).
% 1.34/1.50 tff(902,plain,
% 1.34/1.50 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(elem!1)), elem!1)),
% 1.34/1.50 inference(transitivity,[status(thm)],[901, 900])).
% 1.34/1.50 tff(903,plain,
% 1.34/1.50 (b(s(s(elem!1)), elem!1)),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[893, 902])).
% 1.34/1.50 tff(904,plain,
% 1.34/1.50 (b(s(elem!1), elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[528, 895, 76])).
% 1.34/1.50 tff(905,plain,
% 1.34/1.50 (b(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[893, 901])).
% 1.34/1.50 tff(906,plain,
% 1.34/1.50 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[201])).
% 1.34/1.50 tff(907,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.34/1.50 tff(908,plain,
% 1.34/1.50 (b(elem!1, s(s(s(s(s(z))))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[907, 906])).
% 1.34/1.50 tff(909,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.34/1.50 tff(910,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.50 tff(911,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(912,plain,
% 1.34/1.50 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(913,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[912])).
% 1.34/1.50 tff(914,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 1.34/1.50 inference(transitivity,[status(thm)],[913, 911])).
% 1.34/1.50 tff(915,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(916,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[915, 914])).
% 1.34/1.50 tff(917,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[916, 453, 629, 907, 909, 910])).
% 1.34/1.50 tff(918,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(919,plain,
% 1.34/1.50 (~b(s(elem!1), s(s(elem!1)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[918, 907, 629, 909])).
% 1.34/1.50 tff(920,plain,
% 1.34/1.50 (r(s(elem!1), s(s(elem!1)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[440, 919, 411])).
% 1.34/1.50 tff(921,plain,
% 1.34/1.50 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[435, 920, 76])).
% 1.34/1.50 tff(922,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 1.34/1.50 tff(923,assumption,(b(elem!1, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.34/1.50 tff(924,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(925,plain,
% 1.34/1.50 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(926,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[925])).
% 1.34/1.50 tff(927,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[926, 924])).
% 1.34/1.50 tff(928,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(929,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[928, 927])).
% 1.34/1.50 tff(930,plain,
% 1.34/1.50 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[929, 453, 923, 922, 646])).
% 1.34/1.50 tff(931,plain,
% 1.34/1.50 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[768, 69, 52, 930])).
% 1.34/1.50 tff(932,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(933,plain,
% 1.34/1.50 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(934,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), 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(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[933])).
% 1.34/1.50 tff(935,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), 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(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[934, 932])).
% 1.34/1.50 tff(936,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(937,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[936, 935])).
% 1.34/1.50 tff(938,plain,
% 1.34/1.50 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[937, 453, 923, 922, 299])).
% 1.34/1.50 tff(939,plain,
% 1.34/1.50 (r(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[795, 69, 153, 938])).
% 1.34/1.50 tff(940,plain,
% 1.34/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(941,plain,
% 1.34/1.50 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(942,plain,
% 1.34/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[941])).
% 1.34/1.50 tff(943,plain,
% 1.34/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[942, 940])).
% 1.34/1.50 tff(944,plain,
% 1.34/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(945,plain,
% 1.34/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[944, 943])).
% 1.34/1.50 tff(946,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[945, 268, 418, 939, 931])).
% 1.34/1.50 tff(947,plain,((~b(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(948,plain,
% 1.34/1.50 (~b(s(s(z)), elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[947, 921, 908, 299, 646])).
% 1.34/1.50 tff(949,plain,
% 1.34/1.50 (r(s(s(z)), elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[782, 948, 161])).
% 1.34/1.50 tff(950,plain,
% 1.34/1.50 (~r(s(z), s(s(z)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[741, 949, 701])).
% 1.34/1.50 tff(951,plain,
% 1.34/1.50 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(elem!1) = s(s(s(s(s(s(z)))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[167])).
% 1.34/1.50 tff(952,plain,
% 1.34/1.50 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.34/1.50 inference(transitivity,[status(thm)],[951, 533])).
% 1.34/1.50 tff(953,plain,
% 1.34/1.50 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 1.34/1.50 inference(symmetry,[status(thm)],[952])).
% 1.34/1.50 tff(954,plain,
% 1.34/1.50 ((~(s(s(s(s(s(s(z)))))) = s(elem!1))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(s(z))))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[953])).
% 1.34/1.50 tff(955,assumption,(~(s(s(s(s(s(s(z)))))) = s(elem!1))), introduced(assumption)).
% 1.34/1.50 tff(956,plain,
% 1.34/1.50 (~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[955, 954])).
% 1.34/1.50 tff(957,plain,
% 1.34/1.50 (r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[167, 612])).
% 1.34/1.50 tff(958,plain,
% 1.34/1.50 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.34/1.50 inference(symmetry,[status(thm)],[957])).
% 1.34/1.50 tff(959,plain,
% 1.34/1.50 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[958])).
% 1.34/1.51 tff(960,plain,
% 1.34/1.51 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.51 inference(symmetry,[status(thm)],[615])).
% 1.34/1.51 tff(961,plain,
% 1.34/1.51 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[613, 960])).
% 1.34/1.51 tff(962,plain,
% 1.34/1.51 ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[961])).
% 1.34/1.51 tff(963,assumption,(b(s(s(s(s(s(s(z)))))), elem!1)), introduced(assumption)).
% 1.34/1.51 tff(964,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(965,plain,
% 1.34/1.51 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(966,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[965])).
% 1.34/1.51 tff(967,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[966, 964])).
% 1.34/1.51 tff(968,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(969,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[968, 967])).
% 1.34/1.51 tff(970,plain,
% 1.34/1.51 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[969, 453, 923, 646, 963])).
% 1.34/1.51 tff(971,plain,
% 1.34/1.51 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[970, 962])).
% 1.34/1.51 tff(972,plain,
% 1.34/1.51 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[675, 971, 617])).
% 1.34/1.51 tff(973,plain,
% 1.34/1.51 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[670, 972, 431])).
% 1.34/1.51 tff(974,plain,
% 1.34/1.51 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[973, 959])).
% 1.34/1.51 tff(975,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, 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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(976,plain,
% 1.34/1.51 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(977,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[976])).
% 1.34/1.51 tff(978,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[977, 975])).
% 1.34/1.51 tff(979,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(980,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[979, 978])).
% 1.34/1.51 tff(981,plain,
% 1.34/1.51 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[980, 453, 923, 963, 299])).
% 1.34/1.51 tff(982,plain,
% 1.34/1.51 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[591, 69, 981])).
% 1.34/1.51 tff(983,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[982, 974, 956])).
% 1.34/1.51 tff(984,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~(s(elem!1) = s(s(s(s(z)))))) | (s(s(s(s(s(s(z)))))) = s(elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(985,plain,
% 1.34/1.51 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[984, 920, 219, 162, 617, 908, 299, 646])).
% 1.34/1.51 tff(986,plain,
% 1.34/1.51 (~b(s(s(s(elem!1))), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[576, 985, 76])).
% 1.34/1.51 tff(987,plain,
% 1.34/1.51 (r(s(s(s(elem!1))), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[567, 986, 200])).
% 1.34/1.51 tff(988,plain,
% 1.34/1.51 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.34/1.51 inference(monotonicity,[status(thm)],[611])).
% 1.34/1.51 tff(989,plain,
% 1.34/1.51 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[833, 988])).
% 1.34/1.51 tff(990,assumption,(~r(s(s(s(s(s(s(z)))))), elem!1)), introduced(assumption)).
% 1.34/1.51 tff(991,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[990, 989])).
% 1.34/1.51 tff(992,plain,((~r(s(s(s(elem!1))), elem!1)) | r(s(s(s(s(s(s(z)))))), elem!1) | (~(s(elem!1) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(993,plain,
% 1.34/1.51 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[992, 987, 162])).
% 1.34/1.51 tff(994,plain,
% 1.34/1.51 (~r(s(s(s(elem!1))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[842, 987, 238])).
% 1.34/1.51 tff(995,plain,
% 1.34/1.51 (b(s(s(s(elem!1))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[856, 994])).
% 1.34/1.51 tff(996,plain,
% 1.34/1.51 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[995, 243])).
% 1.34/1.51 tff(997,assumption,(r(s(s(s(s(s(s(z)))))), elem!1)), introduced(assumption)).
% 1.34/1.51 tff(998,plain,
% 1.34/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(999,plain,
% 1.34/1.51 (((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1000,plain,
% 1.34/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[999])).
% 1.34/1.51 tff(1001,plain,
% 1.34/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[1000, 998])).
% 1.34/1.51 tff(1002,plain,
% 1.34/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1003,plain,
% 1.34/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 1.34/1.51 tff(1004,plain,
% 1.34/1.51 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1003, 268, 700, 997])).
% 1.34/1.51 tff(1005,assumption,(~(s(s(z)) = s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.34/1.51 tff(1006,plain,
% 1.34/1.51 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[822, 69, 1005, 1004])).
% 1.34/1.51 tff(1007,assumption,(b(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 1.34/1.51 tff(1008,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 1.34/1.51 tff(1009,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1010,plain,
% 1.34/1.51 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1011,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1010])).
% 1.34/1.51 tff(1012,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[1011, 1009])).
% 1.34/1.51 tff(1013,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1014,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 1.34/1.51 tff(1015,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1014, 453, 1008, 1007, 721, 1006])).
% 1.34/1.51 tff(1016,plain,((~r(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (s(s(z)) = s(s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1017,plain,
% 1.34/1.51 (~b(s(z), s(s(z)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1016, 949, 996, 819, 993, 701])).
% 1.34/1.51 tff(1018,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[757, 1017, 950])).
% 1.34/1.51 tff(1019,plain,((~b(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(z))) | (~(s(s(s(z))) = elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1020,plain,
% 1.34/1.51 (~b(elem!1, s(s(elem!1)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1019, 255, 229, 905, 238, 76, 608, 904, 903])).
% 1.34/1.51 tff(1021,plain,
% 1.34/1.51 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1022,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1023,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 1.34/1.51 tff(1024,plain,
% 1.34/1.51 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1023, 69])).
% 1.34/1.51 tff(1025,plain,
% 1.34/1.51 (r(elem!1, s(s(elem!1)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1024, 1020, 209])).
% 1.34/1.51 tff(1026,plain,
% 1.34/1.51 (r(elem!1, s(s(s(s(s(z))))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1025, 898])).
% 1.34/1.51 tff(1027,plain,
% 1.34/1.51 ((elem!1 = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 1.34/1.51 inference(commutativity,[status(thm)],[])).
% 1.34/1.51 tff(1028,plain,
% 1.34/1.51 ((s(elem!1) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.34/1.51 inference(symmetry,[status(thm)],[1027])).
% 1.34/1.51 tff(1029,plain,
% 1.34/1.51 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.34/1.51 inference(transitivity,[status(thm)],[596, 1028])).
% 1.34/1.51 tff(1030,plain,
% 1.34/1.51 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(elem!1)))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1029])).
% 1.34/1.51 tff(1031,plain,
% 1.34/1.51 (~(elem!1 = s(elem!1))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[3, 1030])).
% 1.34/1.51 tff(1032,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.34/1.51 tff(1033,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.34/1.51 tff(1034,plain,
% 1.34/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1035,plain,
% 1.34/1.51 (((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1036,plain,
% 1.34/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1035])).
% 1.34/1.51 tff(1037,plain,
% 1.34/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[1036, 1034])).
% 1.34/1.51 tff(1038,plain,
% 1.34/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1039,plain,
% 1.34/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 1.34/1.51 tff(1040,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1039, 268, 238, 1033, 1032])).
% 1.34/1.51 tff(1041,plain,((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1042,plain,
% 1.34/1.51 (~r(s(s(elem!1)), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1041, 1025, 238])).
% 1.34/1.51 tff(1043,plain,
% 1.34/1.51 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1044,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1045,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1044, 1043])).
% 1.34/1.51 tff(1046,plain,
% 1.34/1.51 ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1045, 69])).
% 1.34/1.51 tff(1047,plain,
% 1.34/1.51 (b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1046, 816])).
% 1.34/1.51 tff(1048,plain,
% 1.34/1.51 (b(s(s(elem!1)), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1047, 1042])).
% 1.34/1.51 tff(1049,plain,
% 1.34/1.51 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[610])).
% 1.34/1.51 tff(1050,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.34/1.51 tff(1051,plain,
% 1.34/1.51 (b(s(s(s(s(s(z))))), s(z))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1050, 1049])).
% 1.34/1.51 tff(1052,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[278, 1051])).
% 1.34/1.51 tff(1053,plain,((~b(s(s(elem!1)), s(z))) | b(s(s(s(s(s(z))))), s(z)) | (~(s(elem!1) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1054,plain,
% 1.34/1.51 (b(s(s(s(s(s(z))))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1053, 1048, 162])).
% 1.34/1.51 tff(1055,assumption,(~(elem!1 = s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.51 tff(1056,assumption,(~(elem!1 = s(elem!1))), introduced(assumption)).
% 1.34/1.51 tff(1057,assumption,(~b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.34/1.51 tff(1058,plain,
% 1.34/1.51 (b(s(elem!1), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[166])).
% 1.34/1.51 tff(1059,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 1.34/1.51 tff(1060,plain,
% 1.34/1.51 (b(s(s(s(s(z)))), s(z))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1059, 1058])).
% 1.34/1.51 tff(1061,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1057, 1060])).
% 1.34/1.51 tff(1062,plain,((~b(s(elem!1), s(z))) | b(s(s(s(s(z)))), s(z)) | (~(s(elem!1) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1063,plain,
% 1.34/1.51 (~b(s(elem!1), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1062, 1057, 162])).
% 1.34/1.51 tff(1064,plain,
% 1.34/1.51 (r(s(elem!1), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[353, 1063, 180])).
% 1.34/1.51 tff(1065,plain,
% 1.34/1.51 (~r(elem!1, s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[348, 1064, 238])).
% 1.34/1.51 tff(1066,plain,
% 1.34/1.51 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1067,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1068,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1067, 1066])).
% 1.34/1.51 tff(1069,plain,
% 1.34/1.51 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1068, 69])).
% 1.34/1.52 tff(1070,plain,
% 1.34/1.52 (b(elem!1, s(elem!1))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1069, 1065, 1056])).
% 1.34/1.52 tff(1071,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 1.34/1.52 tff(1072,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), 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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1073,plain,
% 1.34/1.52 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1074,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1073])).
% 1.34/1.52 tff(1075,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1074, 1072])).
% 1.34/1.52 tff(1076,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1077,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 1.34/1.52 tff(1078,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1077, 453, 629, 1071, 909, 910])).
% 1.34/1.52 tff(1079,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1080,plain,
% 1.34/1.52 (~b(s(elem!1), s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1079, 1070, 629, 909])).
% 1.34/1.52 tff(1081,plain,
% 1.34/1.52 (r(s(elem!1), s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[440, 1080, 411])).
% 1.34/1.52 tff(1082,plain,
% 1.34/1.52 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[435, 1081, 76])).
% 1.34/1.52 tff(1083,plain,
% 1.34/1.52 (~r(elem!1, s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[427, 1082, 412])).
% 1.34/1.52 tff(1084,assumption,(~b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.52 tff(1085,assumption,(~r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.52 tff(1086,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[480, 69, 1085, 1084, 1055])).
% 1.34/1.52 tff(1087,plain,(b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1088,plain,
% 1.34/1.52 (b(elem!1, s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1087, 1083, 1055])).
% 1.34/1.52 tff(1089,assumption,(s(s(s(s(z)))) = s(z)), introduced(assumption)).
% 1.34/1.52 tff(1090,plain,
% 1.34/1.52 (s(z) = s(s(s(s(z))))),
% 1.34/1.52 inference(symmetry,[status(thm)],[1089])).
% 1.34/1.52 tff(1091,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[50, 1090])).
% 1.34/1.52 tff(1092,plain,(~(s(s(s(s(z)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1093,assumption,(~r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.34/1.52 tff(1094,plain,
% 1.34/1.52 (((~![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)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1095,plain,
% 1.34/1.52 ((~![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)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1096,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1095, 1094])).
% 1.34/1.52 tff(1097,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1096, 69, 1093, 1057, 1092])).
% 1.34/1.52 tff(1098,plain,(r(s(s(s(s(z)))), s(z)) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1099,plain,
% 1.34/1.52 (r(s(s(s(s(z)))), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1098, 1057])).
% 1.34/1.52 tff(1100,assumption,(elem!1 = s(z)), introduced(assumption)).
% 1.34/1.52 tff(1101,plain,
% 1.34/1.52 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1100])).
% 1.34/1.52 tff(1102,plain,
% 1.34/1.52 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 1.34/1.52 inference(symmetry,[status(thm)],[1101])).
% 1.34/1.52 tff(1103,plain,
% 1.34/1.52 (s(elem!1) = s(s(z))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1100])).
% 1.34/1.52 tff(1104,plain,
% 1.34/1.52 (s(s(elem!1)) = s(s(s(z)))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1103])).
% 1.34/1.52 tff(1105,plain,
% 1.34/1.52 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1104])).
% 1.34/1.52 tff(1106,plain,
% 1.34/1.52 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1105])).
% 1.34/1.52 tff(1107,plain,
% 1.34/1.52 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.34/1.52 inference(symmetry,[status(thm)],[1106])).
% 1.34/1.52 tff(1108,plain,
% 1.34/1.52 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1107])).
% 1.34/1.52 tff(1109,plain,
% 1.34/1.52 (~b(s(s(s(elem!1))), s(z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1057, 1108])).
% 1.34/1.52 tff(1110,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.34/1.52 tff(1111,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1110, 1109])).
% 1.34/1.52 tff(1112,plain,((~(elem!1 = s(z))) | (~b(s(s(s(elem!1))), s(z))) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1113,plain,
% 1.34/1.52 (~b(s(s(s(elem!1))), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1112, 1100, 1057])).
% 1.34/1.52 tff(1114,plain,
% 1.34/1.52 (r(s(s(s(elem!1))), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[856, 1113])).
% 1.34/1.52 tff(1115,plain,
% 1.34/1.52 (r(s(s(s(elem!1))), elem!1)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1114, 1102])).
% 1.34/1.52 tff(1116,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[563, 1115])).
% 1.34/1.52 tff(1117,plain,((~(elem!1 = s(z))) | r(s(s(s(elem!1))), elem!1) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1118,plain,
% 1.34/1.52 (~(elem!1 = s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1117, 563, 1057])).
% 1.34/1.52 tff(1119,plain,
% 1.34/1.52 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 1.34/1.52 inference(commutativity,[status(thm)],[])).
% 1.34/1.52 tff(1120,plain,
% 1.34/1.52 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 1.34/1.52 inference(symmetry,[status(thm)],[1119])).
% 1.34/1.52 tff(1121,assumption,(s(z) = elem!1), introduced(assumption)).
% 1.34/1.52 tff(1122,plain,
% 1.34/1.52 (elem!1 = s(z)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 1.34/1.52 tff(1123,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 1.34/1.52 tff(1124,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1123, 1122])).
% 1.34/1.52 tff(1125,plain,((~(s(z) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1126,plain,
% 1.34/1.52 (~(s(z) = elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1125, 1118])).
% 1.34/1.52 tff(1127,plain,
% 1.34/1.52 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1128,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1129,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1128, 1127])).
% 1.34/1.52 tff(1130,plain,
% 1.34/1.52 ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1129, 69])).
% 1.34/1.52 tff(1131,plain,
% 1.34/1.52 (r(elem!1, s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1130, 1118, 10])).
% 1.34/1.52 tff(1132,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.34/1.52 tff(1133,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1134,plain,
% 1.34/1.52 (((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1135,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1134])).
% 1.34/1.52 tff(1136,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1135, 1133])).
% 1.34/1.52 tff(1137,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1138,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 1.34/1.52 tff(1139,plain,
% 1.34/1.52 (~r(s(s(s(s(z)))), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1138, 268, 238, 1132])).
% 1.34/1.52 tff(1140,plain,
% 1.34/1.52 (s(s(s(s(z)))) = elem!1),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[252, 69, 1139, 249])).
% 1.34/1.52 tff(1141,plain,
% 1.34/1.52 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1140])).
% 1.34/1.52 tff(1142,plain,
% 1.34/1.52 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1141])).
% 1.34/1.52 tff(1143,plain,
% 1.34/1.52 ((s(z) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(z))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1142, 173])).
% 1.34/1.52 tff(1144,plain,
% 1.34/1.52 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(elem!1) = s(z)))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1143])).
% 1.34/1.52 tff(1145,plain,
% 1.34/1.52 (~(s(elem!1) = s(z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[289, 1144])).
% 1.34/1.52 tff(1146,plain,
% 1.34/1.52 ((s(elem!1) = s(s(s(s(z))))) <=> (s(elem!1) = elem!1)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1140])).
% 1.34/1.52 tff(1147,plain,
% 1.34/1.52 ((s(elem!1) = s(s(s(s(z))))) <=> (elem!1 = s(elem!1))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1146, 1028])).
% 1.34/1.52 tff(1148,plain,
% 1.34/1.52 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(elem!1 = s(elem!1)))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1147])).
% 1.34/1.52 tff(1149,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.34/1.52 tff(1150,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1151,plain,
% 1.34/1.52 (((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1152,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1151])).
% 1.34/1.52 tff(1153,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1152, 1150])).
% 1.34/1.52 tff(1154,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1155,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1154, 1153])).
% 1.34/1.52 tff(1156,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1155, 268, 238, 1149, 257])).
% 1.34/1.52 tff(1157,plain,((~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1158,plain,
% 1.34/1.52 (~r(elem!1, s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1157, 238, 228])).
% 1.34/1.52 tff(1159,assumption,(r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.34/1.52 tff(1160,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1161,plain,
% 1.34/1.52 (((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1162,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1161])).
% 1.34/1.52 tff(1163,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1162, 1160])).
% 1.34/1.52 tff(1164,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1165,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1164, 1163])).
% 1.34/1.52 tff(1166,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1165, 268, 701, 1132, 1159])).
% 1.34/1.52 tff(1167,plain,((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1168,plain,
% 1.34/1.52 (~r(s(s(s(s(z)))), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1167, 701, 1132])).
% 1.34/1.52 tff(1169,plain,
% 1.34/1.52 (s(s(s(s(z)))) = elem!1),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[254, 1168, 249])).
% 1.34/1.52 tff(1170,assumption,(s(s(s(s(z)))) = elem!1), introduced(assumption)).
% 1.34/1.52 tff(1171,plain,
% 1.34/1.52 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1170])).
% 1.34/1.52 tff(1172,plain,
% 1.34/1.52 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1171])).
% 1.34/1.52 tff(1173,plain,
% 1.34/1.52 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z)))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1174,plain,
% 1.34/1.52 (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1173, 21])).
% 1.34/1.52 tff(1175,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(s(z)))), introduced(assumption)).
% 1.34/1.52 tff(1176,plain,
% 1.34/1.52 (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))),
% 1.34/1.52 inference(symmetry,[status(thm)],[1175])).
% 1.34/1.52 tff(1177,plain,
% 1.34/1.52 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1176])).
% 1.34/1.52 tff(1178,plain,
% 1.34/1.52 (s(s(z)) = s(s(elem!1))),
% 1.34/1.52 inference(transitivity,[status(thm)],[98, 1177, 1174, 1172])).
% 1.34/1.52 tff(1179,plain,
% 1.34/1.52 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1171])).
% 1.34/1.52 tff(1180,plain,
% 1.34/1.52 ((s(z) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(z))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1179, 173])).
% 1.34/1.52 tff(1181,plain,
% 1.34/1.52 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(elem!1) = s(z)))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1180])).
% 1.34/1.52 tff(1182,plain,
% 1.34/1.52 (~(s(elem!1) = s(z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[289, 1181])).
% 1.34/1.52 tff(1183,assumption,(s(s(z)) = s(s(elem!1))), introduced(assumption)).
% 1.34/1.52 tff(1184,plain,
% 1.34/1.52 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1183])).
% 1.34/1.52 tff(1185,plain,
% 1.34/1.52 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.34/1.52 inference(symmetry,[status(thm)],[1184])).
% 1.34/1.52 tff(1186,plain,
% 1.34/1.52 (s(elem!1) = s(z)),
% 1.34/1.52 inference(transitivity,[status(thm)],[195, 1185, 28])).
% 1.34/1.52 tff(1187,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[197, 1186])).
% 1.34/1.52 tff(1188,plain,((~(s(s(z)) = s(s(elem!1)))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1189,plain,
% 1.34/1.52 (~(s(s(z)) = s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1188, 1182])).
% 1.34/1.52 tff(1190,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1189, 1178])).
% 1.34/1.52 tff(1191,plain,((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1192,plain,
% 1.34/1.52 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1191, 1169])).
% 1.34/1.52 tff(1193,plain,
% 1.34/1.52 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.34/1.52 inference(commutativity,[status(thm)],[])).
% 1.34/1.52 tff(1194,plain,
% 1.34/1.52 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 1.34/1.52 inference(symmetry,[status(thm)],[1193])).
% 1.34/1.52 tff(1195,plain,
% 1.34/1.52 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1169])).
% 1.34/1.52 tff(1196,plain,
% 1.34/1.52 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.34/1.52 inference(transitivity,[status(thm)],[1195, 1193])).
% 1.34/1.52 tff(1197,plain,
% 1.34/1.52 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1196, 1194])).
% 1.34/1.52 tff(1198,plain,
% 1.34/1.52 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1197])).
% 1.34/1.52 tff(1199,plain,
% 1.34/1.52 (~(elem!1 = s(s(s(z))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[142, 1198])).
% 1.34/1.52 tff(1200,assumption,(~r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.34/1.52 tff(1201,plain,
% 1.34/1.52 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1202,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1203,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1202, 1201])).
% 1.34/1.52 tff(1204,plain,
% 1.34/1.52 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1203, 69, 1200])).
% 1.34/1.52 tff(1205,plain,
% 1.34/1.52 (b(elem!1, s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1204, 1199])).
% 1.34/1.52 tff(1206,plain,
% 1.34/1.52 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1169])).
% 1.34/1.52 tff(1207,plain,
% 1.34/1.52 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1206])).
% 1.34/1.52 tff(1208,plain,
% 1.34/1.52 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.34/1.52 inference(symmetry,[status(thm)],[1207])).
% 1.34/1.52 tff(1209,plain,
% 1.34/1.52 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1208])).
% 1.34/1.52 tff(1210,plain,
% 1.34/1.52 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1209])).
% 1.34/1.52 tff(1211,plain,
% 1.34/1.52 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1170, 187])).
% 1.34/1.52 tff(1212,plain,
% 1.34/1.52 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1211])).
% 1.34/1.52 tff(1213,plain,
% 1.34/1.52 (s(s(s(z))) = s(s(elem!1))),
% 1.34/1.52 inference(transitivity,[status(thm)],[38, 1212, 550])).
% 1.34/1.52 tff(1214,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[555, 1213])).
% 1.34/1.52 tff(1215,plain,((~(s(s(s(s(z)))) = elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1216,plain,
% 1.34/1.52 (~(s(s(s(elem!1))) = elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1215, 1169, 555])).
% 1.34/1.52 tff(1217,plain,
% 1.34/1.52 (b(s(s(s(elem!1))), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[567, 1216, 563])).
% 1.34/1.52 tff(1218,plain,
% 1.34/1.52 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1217, 1210])).
% 1.34/1.52 tff(1219,plain,
% 1.34/1.52 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1196])).
% 1.34/1.52 tff(1220,plain,
% 1.34/1.52 (~(s(s(s(z))) = elem!1)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[142, 1219])).
% 1.34/1.52 tff(1221,plain,
% 1.34/1.52 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), elem!1)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1169])).
% 1.34/1.52 tff(1222,plain,
% 1.34/1.52 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), elem!1))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1221])).
% 1.34/1.52 tff(1223,plain,
% 1.34/1.52 (r(s(z), s(s(s(s(z))))) <=> r(s(z), elem!1)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1169])).
% 1.34/1.52 tff(1224,plain,
% 1.34/1.52 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(z)))))),
% 1.34/1.52 inference(symmetry,[status(thm)],[1223])).
% 1.34/1.52 tff(1225,plain,
% 1.34/1.52 (r(s(z), s(s(s(s(z)))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[701, 1224])).
% 1.34/1.52 tff(1226,plain,
% 1.34/1.52 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[384, 1225, 257])).
% 1.34/1.52 tff(1227,plain,
% 1.34/1.52 (~r(s(s(s(z))), elem!1)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1226, 1222])).
% 1.34/1.52 tff(1228,plain,
% 1.34/1.52 (b(s(s(s(z))), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[72, 69, 1227, 1220])).
% 1.34/1.52 tff(1229,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1230,plain,
% 1.34/1.52 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1231,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1230])).
% 1.34/1.52 tff(1232,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1231, 1229])).
% 1.34/1.52 tff(1233,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1234,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1233, 1232])).
% 1.34/1.52 tff(1235,plain,
% 1.34/1.52 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1234, 453, 1228, 1218, 1205])).
% 1.34/1.52 tff(1236,plain,
% 1.34/1.52 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1237,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1238,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 1.34/1.53 tff(1239,plain,
% 1.34/1.53 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1238, 69, 1235])).
% 1.34/1.53 tff(1240,plain,
% 1.34/1.53 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1239, 1192])).
% 1.34/1.53 tff(1241,plain,
% 1.34/1.53 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[486])).
% 1.34/1.53 tff(1242,plain,
% 1.34/1.53 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1241])).
% 1.34/1.53 tff(1243,plain,
% 1.34/1.53 (~(s(s(z)) = s(s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[160, 1242])).
% 1.34/1.53 tff(1244,plain,
% 1.34/1.53 ((s(s(s(s(z)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1169])).
% 1.34/1.53 tff(1245,plain,
% 1.34/1.53 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.34/1.53 inference(transitivity,[status(thm)],[1244, 144])).
% 1.34/1.53 tff(1246,plain,
% 1.34/1.53 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1245])).
% 1.34/1.53 tff(1247,plain,
% 1.34/1.53 (~(s(s(z)) = elem!1)),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[153, 1246])).
% 1.34/1.53 tff(1248,plain,
% 1.34/1.53 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1169])).
% 1.34/1.53 tff(1249,plain,
% 1.34/1.53 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[1248, 55])).
% 1.34/1.53 tff(1250,plain,
% 1.34/1.53 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.34/1.53 inference(transitivity,[status(thm)],[1249, 56])).
% 1.34/1.53 tff(1251,plain,
% 1.34/1.53 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1250])).
% 1.34/1.53 tff(1252,plain,
% 1.34/1.53 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[319, 1251])).
% 1.34/1.53 tff(1253,plain,
% 1.34/1.53 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[1206])).
% 1.34/1.53 tff(1254,plain,
% 1.34/1.53 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1253])).
% 1.34/1.53 tff(1255,plain,
% 1.34/1.53 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[1254])).
% 1.34/1.53 tff(1256,plain,
% 1.34/1.53 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1255])).
% 1.34/1.53 tff(1257,plain,
% 1.34/1.53 (~(s(elem!1) = s(s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[111, 1256])).
% 1.34/1.53 tff(1258,plain,
% 1.34/1.53 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[1171])).
% 1.34/1.53 tff(1259,plain,
% 1.34/1.53 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1258])).
% 1.34/1.53 tff(1260,plain,
% 1.34/1.53 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.34/1.53 inference(symmetry,[status(thm)],[1259])).
% 1.34/1.53 tff(1261,assumption,(s(s(s(s(s(s(s(z))))))) = s(elem!1)), introduced(assumption)).
% 1.34/1.53 tff(1262,plain,
% 1.34/1.53 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(elem!1))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1261])).
% 1.34/1.53 tff(1263,plain,
% 1.34/1.53 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[1262])).
% 1.34/1.53 tff(1264,plain,
% 1.34/1.53 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.34/1.53 inference(transitivity,[status(thm)],[1170, 86, 1263, 1174, 1260])).
% 1.34/1.53 tff(1265,plain,
% 1.34/1.53 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1264])).
% 1.34/1.53 tff(1266,plain,
% 1.34/1.53 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[1265])).
% 1.34/1.53 tff(1267,plain,
% 1.34/1.53 (s(elem!1) = s(s(s(z)))),
% 1.34/1.53 inference(transitivity,[status(thm)],[195, 1266, 37])).
% 1.34/1.53 tff(1268,plain,
% 1.34/1.53 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1258])).
% 1.34/1.53 tff(1269,plain,
% 1.34/1.53 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[1268])).
% 1.34/1.53 tff(1270,plain,
% 1.34/1.53 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1269])).
% 1.34/1.53 tff(1271,plain,
% 1.34/1.53 (~(s(elem!1) = s(s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[111, 1270])).
% 1.34/1.53 tff(1272,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1271, 1267])).
% 1.34/1.53 tff(1273,plain,((~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(1274,plain,
% 1.34/1.53 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1273, 1169])).
% 1.34/1.53 tff(1275,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.34/1.53 tff(1276,assumption,(b(s(s(s(s(s(s(s(z))))))), elem!1)), introduced(assumption)).
% 1.34/1.53 tff(1277,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1278,plain,
% 1.34/1.53 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1279,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1278])).
% 1.34/1.53 tff(1280,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[1279, 1277])).
% 1.34/1.53 tff(1281,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1282,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 1.34/1.53 tff(1283,plain,
% 1.34/1.53 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1282, 453, 629, 1276, 1275])).
% 1.34/1.53 tff(1284,assumption,(~(s(s(s(s(s(s(s(z))))))) = s(elem!1))), introduced(assumption)).
% 1.34/1.53 tff(1285,plain,
% 1.34/1.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1286,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1287,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1286, 1285])).
% 1.34/1.53 tff(1288,plain,
% 1.34/1.53 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1287, 69, 1284, 1283])).
% 1.34/1.53 tff(1289,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), introduced(assumption)).
% 1.34/1.53 tff(1290,assumption,(~(s(elem!1) = s(s(s(z))))), introduced(assumption)).
% 1.34/1.53 tff(1291,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.34/1.53 tff(1292,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1293,plain,
% 1.34/1.53 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1294,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1293])).
% 1.34/1.53 tff(1295,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[1294, 1292])).
% 1.34/1.53 tff(1296,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1297,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1296, 1295])).
% 1.34/1.53 tff(1298,plain,
% 1.34/1.53 (~b(s(elem!1), s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1297, 453, 629, 1291, 1275])).
% 1.34/1.53 tff(1299,assumption,(~r(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.34/1.53 tff(1300,assumption,(~b(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.34/1.53 tff(1301,plain,
% 1.34/1.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1302,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1303,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 1.34/1.53 tff(1304,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1303, 69, 1300, 1290, 1299])).
% 1.34/1.53 tff(1305,plain,(r(s(elem!1), s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | (s(elem!1) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(1306,plain,
% 1.34/1.53 (r(s(elem!1), s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1305, 1298, 1290])).
% 1.34/1.53 tff(1307,plain,
% 1.34/1.53 ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.34/1.53 inference(commutativity,[status(thm)],[])).
% 1.34/1.53 tff(1308,plain,
% 1.34/1.53 ((~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1307])).
% 1.34/1.53 tff(1309,plain,
% 1.34/1.53 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1284, 1308])).
% 1.34/1.53 tff(1310,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(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(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1311,plain,
% 1.34/1.53 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1312,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(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(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1311])).
% 1.34/1.53 tff(1313,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(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(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[1312, 1310])).
% 1.34/1.53 tff(1314,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1315,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 1.34/1.53 tff(1316,plain,
% 1.34/1.53 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1315, 453, 629, 1276, 1275])).
% 1.34/1.53 tff(1317,plain,
% 1.34/1.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1318,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1319,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 1.34/1.53 tff(1320,plain,
% 1.34/1.53 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1319, 69])).
% 1.34/1.53 tff(1321,plain,
% 1.34/1.53 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1320, 1316, 1309])).
% 1.34/1.53 tff(1322,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1323,plain,
% 1.34/1.53 (((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1324,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1323])).
% 1.34/1.53 tff(1325,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[1324, 1322])).
% 1.34/1.53 tff(1326,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1327,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1326, 1325])).
% 1.34/1.53 tff(1328,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1327, 268, 1321, 1306, 1289, 1288])).
% 1.34/1.53 tff(1329,plain,((~b(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (s(elem!1) = s(s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(1330,plain,
% 1.34/1.53 (~b(s(elem!1), elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1329, 1240, 1274, 1257, 1218, 1205, 1228])).
% 1.34/1.53 tff(1331,plain,
% 1.34/1.53 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1171])).
% 1.34/1.53 tff(1332,plain,
% 1.34/1.53 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.53 inference(symmetry,[status(thm)],[1331])).
% 1.34/1.53 tff(1333,plain,
% 1.34/1.53 ((~b(s(elem!1), elem!1)) <=> (~b(s(s(s(s(s(z))))), elem!1))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1332])).
% 1.34/1.53 tff(1334,plain,
% 1.34/1.53 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[526, 1333])).
% 1.34/1.53 tff(1335,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[646, 1334])).
% 1.34/1.53 tff(1336,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(1337,plain,
% 1.34/1.53 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1336, 1330, 1169])).
% 1.34/1.53 tff(1338,plain,
% 1.34/1.53 (r(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[643, 1337, 1252])).
% 1.34/1.53 tff(1339,plain,
% 1.34/1.53 (~r(s(s(z)), elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[777, 1338, 701])).
% 1.34/1.53 tff(1340,plain,
% 1.34/1.53 (b(s(s(z)), elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[782, 1339, 1247])).
% 1.34/1.53 tff(1341,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1342,plain,
% 1.34/1.53 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1343,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1342])).
% 1.34/1.54 tff(1344,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.34/1.54 inference(transitivity,[status(thm)],[1343, 1341])).
% 1.34/1.54 tff(1345,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(1346,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1345, 1344])).
% 1.34/1.54 tff(1347,plain,
% 1.34/1.54 (~b(s(s(z)), s(s(s(z))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1346, 453, 1228, 1340, 1205])).
% 1.34/1.54 tff(1348,plain,
% 1.34/1.54 (((~![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)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1349,plain,
% 1.34/1.54 ((~![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)))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(1350,plain,
% 1.34/1.54 ((~![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))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1349, 1348])).
% 1.34/1.54 tff(1351,plain,
% 1.34/1.54 ((s(s(z)) = s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1350, 69, 1347])).
% 1.34/1.54 tff(1352,plain,
% 1.34/1.54 (r(s(s(z)), s(s(s(z))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1351, 1243])).
% 1.34/1.54 tff(1353,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1354,plain,
% 1.34/1.54 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1355,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1354])).
% 1.34/1.54 tff(1356,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[1355, 1353])).
% 1.34/1.54 tff(1357,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(1358,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1357, 1356])).
% 1.34/1.54 tff(1359,plain,
% 1.34/1.54 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1358, 268, 1352, 1240])).
% 1.34/1.54 tff(1360,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1361,plain,
% 1.34/1.54 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1362,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1361])).
% 1.34/1.54 tff(1363,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[1362, 1360])).
% 1.34/1.54 tff(1364,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(1365,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1364, 1363])).
% 1.34/1.54 tff(1366,plain,
% 1.34/1.54 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1365, 453, 1340, 1218, 1205])).
% 1.34/1.54 tff(1367,plain,
% 1.34/1.54 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1368,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(1369,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1368, 1367])).
% 1.34/1.54 tff(1370,plain,
% 1.34/1.54 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1369, 69, 1366])).
% 1.34/1.54 tff(1371,plain,
% 1.34/1.54 (s(s(s(s(s(s(s(z))))))) = s(s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1370, 1359])).
% 1.34/1.54 tff(1372,plain,
% 1.34/1.54 (s(s(z)) = s(s(s(s(s(s(s(z)))))))),
% 1.34/1.54 inference(symmetry,[status(thm)],[1371])).
% 1.34/1.54 tff(1373,plain,
% 1.34/1.54 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1372])).
% 1.34/1.54 tff(1374,plain,
% 1.34/1.54 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(z)))),
% 1.34/1.54 inference(symmetry,[status(thm)],[1373])).
% 1.34/1.54 tff(1375,plain,
% 1.34/1.54 (s(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(symmetry,[status(thm)],[1174])).
% 1.34/1.54 tff(1376,plain,
% 1.34/1.54 (s(s(elem!1)) = s(z)),
% 1.34/1.54 inference(transitivity,[status(thm)],[1208, 1375, 1374, 28])).
% 1.34/1.54 tff(1377,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[816, 1376])).
% 1.34/1.54 tff(1378,plain,((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | r(elem!1, s(s(s(z)))) | r(s(s(s(elem!1))), elem!1) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(s(z)))), elem!1) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(1379,plain,
% 1.34/1.54 (~r(s(z), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1378, 249, 1158, 563, 548, 228, 1132])).
% 1.34/1.54 tff(1380,plain,
% 1.34/1.54 (b(s(z), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[506, 1379, 492])).
% 1.34/1.54 tff(1381,plain,
% 1.34/1.54 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[501, 1380, 221])).
% 1.34/1.54 tff(1382,plain,
% 1.34/1.54 (~(elem!1 = s(elem!1))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1381, 1148])).
% 1.34/1.54 tff(1383,plain,
% 1.34/1.54 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1141])).
% 1.34/1.54 tff(1384,plain,
% 1.34/1.54 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.34/1.54 inference(symmetry,[status(thm)],[1383])).
% 1.34/1.54 tff(1385,plain,
% 1.34/1.54 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1384])).
% 1.34/1.54 tff(1386,plain,
% 1.34/1.54 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1385])).
% 1.34/1.54 tff(1387,plain,
% 1.34/1.54 (~(s(s(s(elem!1))) = elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1215, 1140, 548])).
% 1.34/1.54 tff(1388,plain,
% 1.34/1.54 (b(s(s(s(elem!1))), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[567, 1387, 563])).
% 1.34/1.54 tff(1389,plain,
% 1.34/1.54 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1388, 1386])).
% 1.34/1.54 tff(1390,plain,
% 1.34/1.54 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1385])).
% 1.34/1.54 tff(1391,plain,
% 1.34/1.54 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 1.34/1.54 inference(commutativity,[status(thm)],[])).
% 1.34/1.54 tff(1392,plain,
% 1.34/1.54 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1140])).
% 1.34/1.54 tff(1393,plain,
% 1.34/1.54 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[1392, 1391])).
% 1.34/1.54 tff(1394,plain,
% 1.34/1.54 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1393])).
% 1.34/1.54 tff(1395,plain,
% 1.34/1.54 (~(elem!1 = s(s(s(elem!1))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[558, 1394])).
% 1.34/1.54 tff(1396,plain,
% 1.34/1.54 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 1.34/1.54 inference(symmetry,[status(thm)],[1385])).
% 1.34/1.54 tff(1397,plain,
% 1.34/1.54 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1396])).
% 1.34/1.54 tff(1398,plain,
% 1.34/1.54 ((~b(s(s(s(s(s(s(s(z))))))), s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1397])).
% 1.34/1.54 tff(1399,plain,
% 1.34/1.54 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1140])).
% 1.34/1.54 tff(1400,plain,
% 1.34/1.54 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1140])).
% 1.34/1.54 tff(1401,plain,
% 1.34/1.54 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.54 inference(symmetry,[status(thm)],[1400])).
% 1.34/1.54 tff(1402,plain,
% 1.34/1.54 ((~r(elem!1, s(s(s(z))))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1401])).
% 1.34/1.54 tff(1403,plain,
% 1.34/1.54 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1158, 1402])).
% 1.34/1.54 tff(1404,plain,
% 1.34/1.54 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[518, 1403])).
% 1.34/1.54 tff(1405,plain,
% 1.34/1.54 (b(elem!1, s(s(s(z))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1404, 1399])).
% 1.34/1.54 tff(1406,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(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(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1407,plain,
% 1.34/1.54 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1408,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(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(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1407])).
% 1.34/1.54 tff(1409,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(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(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[1408, 1406])).
% 1.34/1.54 tff(1410,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(1411,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1410, 1409])).
% 1.34/1.54 tff(1412,plain,
% 1.34/1.54 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1411, 453, 1380, 1389, 1405])).
% 1.34/1.54 tff(1413,plain,
% 1.34/1.54 (~b(s(s(s(elem!1))), s(z))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1412, 1398])).
% 1.34/1.54 tff(1414,plain,
% 1.34/1.54 (r(s(s(s(elem!1))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[856, 1413])).
% 1.34/1.54 tff(1415,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.54 tff(1416,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1417,plain,
% 1.34/1.54 (((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1418,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1417])).
% 1.34/1.54 tff(1419,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[1418, 1416])).
% 1.34/1.54 tff(1420,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(1421,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 1.34/1.54 tff(1422,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1421, 268, 238, 834, 1415])).
% 1.34/1.54 tff(1423,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(1424,plain,
% 1.34/1.54 (~r(elem!1, s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1423, 1414, 238])).
% 1.34/1.54 tff(1425,plain,
% 1.34/1.54 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1426,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(1427,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1426, 1425])).
% 1.34/1.54 tff(1428,plain,
% 1.34/1.54 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1427, 69])).
% 1.34/1.54 tff(1429,plain,
% 1.34/1.54 (b(elem!1, s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1428, 1424, 1395])).
% 1.34/1.54 tff(1430,plain,
% 1.34/1.54 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1429, 1390])).
% 1.34/1.54 tff(1431,plain,
% 1.34/1.54 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1273, 1140])).
% 1.34/1.54 tff(1432,plain,
% 1.34/1.54 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.34/1.54 inference(symmetry,[status(thm)],[1307])).
% 1.34/1.54 tff(1433,assumption,(s(elem!1) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.34/1.54 tff(1434,plain,
% 1.34/1.54 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1433, 1432])).
% 1.34/1.54 tff(1435,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1284, 1434])).
% 1.34/1.54 tff(1436,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(1437,plain,
% 1.34/1.54 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1436, 1431])).
% 1.34/1.54 tff(1438,plain,
% 1.34/1.54 (r(s(s(s(s(s(s(s(z))))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1396])).
% 1.34/1.54 tff(1439,plain,
% 1.34/1.54 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.34/1.54 inference(symmetry,[status(thm)],[1438])).
% 1.34/1.54 tff(1440,plain,
% 1.34/1.54 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1414, 1439])).
% 1.34/1.54 tff(1441,assumption,(r(s(s(s(s(s(s(s(z))))))), s(z))), introduced(assumption)).
% 1.34/1.54 tff(1442,assumption,(~(s(elem!1) = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.34/1.54 tff(1443,assumption,(b(elem!1, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.34/1.54 tff(1444,plain,
% 1.34/1.54 (~r(elem!1, s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[348, 340, 238])).
% 1.34/1.54 tff(1445,plain,
% 1.34/1.54 (b(elem!1, s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1069, 1444, 1056])).
% 1.34/1.54 tff(1446,assumption,(b(s(elem!1), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.34/1.54 tff(1447,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(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(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1448,plain,
% 1.34/1.54 (((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1449,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1448])).
% 1.34/1.55 tff(1450,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[1449, 1447])).
% 1.34/1.55 tff(1451,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(1452,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1451, 1450])).
% 1.34/1.55 tff(1453,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1452, 453, 1071, 1443, 1446, 1276])).
% 1.34/1.55 tff(1454,plain,((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(1455,plain,
% 1.34/1.55 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1454, 1445, 1443, 1276])).
% 1.34/1.55 tff(1456,plain,
% 1.34/1.55 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1320, 1455, 1442])).
% 1.34/1.55 tff(1457,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1458,plain,
% 1.34/1.55 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1459,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1458])).
% 1.34/1.55 tff(1460,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[1459, 1457])).
% 1.34/1.55 tff(1461,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(1462,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1461, 1460])).
% 1.34/1.55 tff(1463,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1462, 268, 340, 1456, 1441])).
% 1.34/1.55 tff(1464,plain,((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (elem!1 = s(elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(1465,plain,
% 1.34/1.55 (~r(s(elem!1), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1464, 1440, 1437, 1430, 1389, 1382, 238])).
% 1.34/1.55 tff(1466,plain,
% 1.34/1.55 (b(s(elem!1), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[353, 1465, 1145])).
% 1.34/1.55 tff(1467,plain,
% 1.34/1.55 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 1.34/1.55 inference(transitivity,[status(thm)],[1143, 174])).
% 1.34/1.55 tff(1468,plain,
% 1.34/1.55 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(z) = s(elem!1)))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1467])).
% 1.34/1.55 tff(1469,plain,
% 1.34/1.55 (~(s(z) = s(elem!1))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[289, 1468])).
% 1.34/1.55 tff(1470,plain,
% 1.34/1.55 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 1.34/1.55 inference(commutativity,[status(thm)],[])).
% 1.34/1.55 tff(1471,plain,
% 1.34/1.55 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (s(z) = s(s(s(elem!1))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1396])).
% 1.34/1.55 tff(1472,plain,
% 1.34/1.55 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(z))),
% 1.34/1.55 inference(transitivity,[status(thm)],[1471, 1470])).
% 1.34/1.55 tff(1473,plain,
% 1.34/1.55 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(symmetry,[status(thm)],[1472])).
% 1.34/1.55 tff(1474,plain,
% 1.34/1.55 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = s(s(s(s(s(s(s(z)))))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1473])).
% 1.34/1.55 tff(1475,plain,
% 1.34/1.55 (~(s(z) = s(s(s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[851, 1474])).
% 1.34/1.55 tff(1476,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1477,plain,
% 1.34/1.55 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1478,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(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(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1477])).
% 1.34/1.55 tff(1479,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(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(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.34/1.55 inference(transitivity,[status(thm)],[1478, 1476])).
% 1.34/1.55 tff(1480,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(1481,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 1.34/1.55 tff(1482,plain,
% 1.34/1.55 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1481, 453, 1380, 1389, 1405])).
% 1.34/1.55 tff(1483,plain,
% 1.34/1.55 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1484,plain,
% 1.34/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(1485,plain,
% 1.34/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1484, 1483])).
% 1.34/1.55 tff(1486,plain,
% 1.34/1.55 ((s(z) = s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1485, 69, 1482])).
% 1.34/1.55 tff(1487,plain,
% 1.34/1.55 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1486, 1475])).
% 1.34/1.55 tff(1488,assumption,(r(s(z), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.34/1.55 tff(1489,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1490,plain,
% 1.34/1.55 (((~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1491,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1490])).
% 1.34/1.55 tff(1492,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[1491, 1489])).
% 1.34/1.55 tff(1493,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(1494,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1493, 1492])).
% 1.34/1.55 tff(1495,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1494, 268, 388, 238, 339])).
% 1.34/1.55 tff(1496,plain,((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(1497,plain,
% 1.34/1.55 (~r(elem!1, s(elem!1))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1496, 388, 238])).
% 1.34/1.55 tff(1498,plain,
% 1.34/1.55 (b(elem!1, s(elem!1))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1069, 1497, 1056])).
% 1.34/1.55 tff(1499,plain,
% 1.34/1.55 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1454, 1498, 1443, 1276])).
% 1.34/1.55 tff(1500,plain,
% 1.34/1.55 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1320, 1499, 1442])).
% 1.34/1.55 tff(1501,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1502,plain,
% 1.34/1.55 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1503,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1502])).
% 1.34/1.55 tff(1504,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[1503, 1501])).
% 1.34/1.55 tff(1505,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(1506,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1505, 1504])).
% 1.34/1.55 tff(1507,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1506, 268, 388, 1500, 1488])).
% 1.34/1.55 tff(1508,plain,((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (elem!1 = s(elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(1509,plain,
% 1.34/1.55 (~r(s(z), s(elem!1))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1508, 1487, 1437, 1430, 1389, 1382, 238])).
% 1.34/1.55 tff(1510,plain,
% 1.34/1.55 (b(s(z), s(elem!1))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[397, 1509, 1469])).
% 1.34/1.55 tff(1511,plain,
% 1.34/1.55 (~(s(s(s(z))) = elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[81, 1381])).
% 1.34/1.55 tff(1512,plain,
% 1.34/1.55 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1191, 1140])).
% 1.34/1.55 tff(1513,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1514,plain,
% 1.34/1.55 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1515,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1514])).
% 1.34/1.55 tff(1516,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.34/1.55 inference(transitivity,[status(thm)],[1515, 1513])).
% 1.34/1.55 tff(1517,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(1518,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1517, 1516])).
% 1.34/1.55 tff(1519,plain,
% 1.34/1.55 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1518, 453, 1291, 1443, 1276])).
% 1.34/1.55 tff(1520,assumption,(~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))), introduced(assumption)).
% 1.34/1.55 tff(1521,plain,
% 1.34/1.55 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1238, 69, 1520, 1519])).
% 1.34/1.55 tff(1522,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(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(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1523,plain,
% 1.34/1.55 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1524,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1523])).
% 1.34/1.55 tff(1525,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[1524, 1522])).
% 1.34/1.56 tff(1526,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(1527,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1526, 1525])).
% 1.34/1.56 tff(1528,plain,
% 1.34/1.56 (~b(s(s(s(z))), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1527, 453, 499, 1291, 1443])).
% 1.34/1.56 tff(1529,plain,
% 1.34/1.56 (r(s(s(s(z))), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[132, 69, 1528, 127])).
% 1.34/1.56 tff(1530,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1531,plain,
% 1.34/1.56 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1532,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1531])).
% 1.34/1.56 tff(1533,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[1532, 1530])).
% 1.34/1.56 tff(1534,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(1535,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1534, 1533])).
% 1.34/1.56 tff(1536,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1535, 268, 1529, 1521, 1441])).
% 1.34/1.56 tff(1537,plain,((~b(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(1538,plain,
% 1.34/1.56 (~b(s(s(s(z))), elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1537, 1440, 1512, 1430, 1389, 1380])).
% 1.34/1.56 tff(1539,plain,
% 1.34/1.56 (r(s(s(s(z))), elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[74, 1538, 1511])).
% 1.34/1.56 tff(1540,plain,
% 1.34/1.56 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1170])).
% 1.34/1.56 tff(1541,plain,
% 1.34/1.56 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[1540, 55])).
% 1.34/1.56 tff(1542,plain,
% 1.34/1.56 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.34/1.56 inference(transitivity,[status(thm)],[1541, 56])).
% 1.34/1.56 tff(1543,plain,
% 1.34/1.56 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1542])).
% 1.34/1.56 tff(1544,plain,
% 1.34/1.56 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[319, 1543])).
% 1.34/1.56 tff(1545,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.34/1.56 tff(1546,plain,
% 1.34/1.56 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1171])).
% 1.34/1.56 tff(1547,plain,
% 1.34/1.56 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[1546])).
% 1.34/1.56 tff(1548,plain,
% 1.34/1.56 ((~b(s(elem!1), s(s(s(z))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1547])).
% 1.34/1.56 tff(1549,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 1.34/1.56 tff(1550,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1551,plain,
% 1.34/1.56 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1552,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1551])).
% 1.34/1.56 tff(1553,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[1552, 1550])).
% 1.34/1.56 tff(1554,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(1555,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1554, 1553])).
% 1.34/1.56 tff(1556,plain,
% 1.34/1.56 (~b(s(elem!1), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1555, 453, 1059, 1549, 120])).
% 1.34/1.56 tff(1557,plain,
% 1.34/1.56 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1556, 1548])).
% 1.34/1.56 tff(1558,plain,
% 1.34/1.56 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[687, 1557])).
% 1.34/1.56 tff(1559,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1560,plain,
% 1.34/1.56 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1561,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1560])).
% 1.34/1.56 tff(1562,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.34/1.56 inference(transitivity,[status(thm)],[1561, 1559])).
% 1.34/1.56 tff(1563,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(1564,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1563, 1562])).
% 1.34/1.56 tff(1565,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1564, 268, 722, 256, 1545])).
% 1.34/1.56 tff(1566,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(1567,plain,
% 1.34/1.56 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1566, 1558, 1545])).
% 1.34/1.56 tff(1568,plain,
% 1.34/1.56 (b(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[643, 1567, 1544])).
% 1.34/1.56 tff(1569,plain,
% 1.34/1.56 (b(s(elem!1), elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1336, 1568, 1170])).
% 1.34/1.56 tff(1570,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(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(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1571,plain,
% 1.34/1.56 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1572,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1571])).
% 1.34/1.56 tff(1573,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[1572, 1570])).
% 1.34/1.56 tff(1574,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(1575,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1574, 1573])).
% 1.34/1.56 tff(1576,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1575, 453, 1059, 499, 1569, 1443])).
% 1.34/1.56 tff(1577,plain,((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~(s(s(s(s(z)))) = elem!1)) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(1578,plain,
% 1.34/1.56 (~b(s(s(s(z))), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1577, 1539, 1430, 1140, 1380, 1510, 1466])).
% 1.34/1.56 tff(1579,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1580,plain,
% 1.34/1.56 (((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1581,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1580])).
% 1.34/1.56 tff(1582,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.34/1.56 inference(transitivity,[status(thm)],[1581, 1579])).
% 1.34/1.56 tff(1583,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(1584,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1583, 1582])).
% 1.34/1.56 tff(1585,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1584, 268, 238, 233, 1545])).
% 1.34/1.56 tff(1586,plain,((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(1587,plain,
% 1.34/1.56 (~r(s(s(s(z))), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1586, 1539, 238])).
% 1.34/1.56 tff(1588,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[132, 69, 1587, 1578, 127])).
% 1.34/1.56 tff(1589,plain,(b(s(s(s(s(z)))), elem!1) | (~r(elem!1, s(z))) | r(s(s(s(elem!1))), elem!1) | (~r(s(s(s(s(z)))), s(z))) | b(s(z), s(s(s(z)))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(1590,plain,
% 1.34/1.56 (b(s(s(s(s(z)))), elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1589, 238, 563, 1132, 221, 492])).
% 1.34/1.56 tff(1591,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1592,plain,
% 1.34/1.56 (((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1593,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1592])).
% 1.34/1.56 tff(1594,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[1593, 1591])).
% 1.34/1.56 tff(1595,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(1596,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1595, 1594])).
% 1.34/1.56 tff(1597,plain,
% 1.34/1.56 (~r(elem!1, s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1596, 268, 238, 1132])).
% 1.34/1.56 tff(1598,plain,
% 1.34/1.56 (b(elem!1, s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1087, 9, 1597])).
% 1.34/1.56 tff(1599,plain,
% 1.34/1.56 ((~(s(s(s(z))) = elem!1)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1194])).
% 1.34/1.56 tff(1600,plain,
% 1.34/1.56 (~(s(s(s(z))) = elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[831, 1598, 3, 563, 492, 221, 1139])).
% 1.34/1.56 tff(1601,plain,
% 1.34/1.56 (~(elem!1 = s(s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1600, 1599])).
% 1.34/1.56 tff(1602,plain,
% 1.34/1.56 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1203, 69, 1158])).
% 1.34/1.56 tff(1603,plain,
% 1.34/1.56 (b(elem!1, s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1602, 1601])).
% 1.34/1.56 tff(1604,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1605,plain,
% 1.34/1.56 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1606,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1605])).
% 1.34/1.56 tff(1607,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[1606, 1604])).
% 1.34/1.57 tff(1608,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(1609,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1608, 1607])).
% 1.34/1.57 tff(1610,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1609, 268, 701, 11, 1132, 257])).
% 1.34/1.57 tff(1611,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(1612,plain,
% 1.34/1.57 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1611, 701, 1132, 257])).
% 1.34/1.57 tff(1613,plain,
% 1.34/1.57 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[518, 1612])).
% 1.34/1.57 tff(1614,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1615,plain,
% 1.34/1.57 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1616,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z)))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1615])).
% 1.34/1.57 tff(1617,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[1616, 1614])).
% 1.34/1.57 tff(1618,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(1619,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1618, 1617])).
% 1.34/1.57 tff(1620,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1619, 453, 523, 530, 120, 1275])).
% 1.34/1.57 tff(1621,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(1622,plain,
% 1.34/1.57 (~b(s(s(s(z))), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1621, 1613, 530, 1275])).
% 1.34/1.57 tff(1623,plain,
% 1.34/1.57 (r(s(s(s(z))), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[132, 69, 1622, 127])).
% 1.34/1.57 tff(1624,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1625,plain,
% 1.34/1.57 (((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1626,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1625])).
% 1.34/1.57 tff(1627,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.34/1.57 inference(transitivity,[status(thm)],[1626, 1624])).
% 1.34/1.57 tff(1628,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(1629,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1628, 1627])).
% 1.34/1.57 tff(1630,plain,
% 1.34/1.57 ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1629, 268])).
% 1.34/1.57 tff(1631,plain,
% 1.34/1.57 (~r(s(s(s(z))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1630, 1623, 701, 257])).
% 1.34/1.57 tff(1632,plain,
% 1.34/1.57 (b(s(s(s(z))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[74, 1631, 59])).
% 1.34/1.57 tff(1633,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.57 tff(1634,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1635,plain,
% 1.34/1.57 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1636,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1635])).
% 1.34/1.57 tff(1637,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.34/1.57 inference(transitivity,[status(thm)],[1636, 1634])).
% 1.34/1.57 tff(1638,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(1639,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1638, 1637])).
% 1.34/1.57 tff(1640,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1639, 453, 1291, 1633, 530, 299])).
% 1.34/1.57 tff(1641,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(1642,plain,
% 1.34/1.57 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1641, 1632, 299, 530])).
% 1.34/1.57 tff(1643,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 1.34/1.57 tff(1644,plain,
% 1.34/1.57 (s(s(s(s(z)))) = s(s(s(z)))),
% 1.34/1.57 inference(symmetry,[status(thm)],[1643])).
% 1.34/1.57 tff(1645,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[316, 1644])).
% 1.34/1.57 tff(1646,plain,((~(s(s(s(z))) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(1647,plain,
% 1.34/1.57 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1646, 142])).
% 1.34/1.57 tff(1648,assumption,(~b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.57 tff(1649,assumption,(~(s(s(s(z))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.57 tff(1650,assumption,(~r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.57 tff(1651,plain,
% 1.34/1.57 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1652,plain,
% 1.34/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(1653,plain,
% 1.34/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1652, 1651])).
% 1.34/1.57 tff(1654,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1653, 69, 1650, 1649, 1648])).
% 1.34/1.57 tff(1655,plain,(b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))) | (s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(1656,plain,
% 1.34/1.57 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1655, 1647])).
% 1.34/1.57 tff(1657,plain,
% 1.34/1.57 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1656, 1642])).
% 1.34/1.57 tff(1658,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1659,plain,
% 1.34/1.57 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1660,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1659])).
% 1.34/1.57 tff(1661,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[1660, 1658])).
% 1.34/1.57 tff(1662,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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)))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(1663,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1662, 1661])).
% 1.34/1.57 tff(1664,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1663, 268, 1623, 1132, 1657])).
% 1.34/1.57 tff(1665,plain,((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (s(s(s(z))) = elem!1) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(1666,plain,
% 1.34/1.57 (~r(s(z), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1665, 1598, 1590, 1132, 1600, 228, 1603])).
% 1.34/1.57 tff(1667,plain,
% 1.34/1.57 (b(s(z), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[506, 1666, 492])).
% 1.34/1.57 tff(1668,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1669,plain,
% 1.34/1.57 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1670,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1669])).
% 1.34/1.57 tff(1671,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[1670, 1668])).
% 1.34/1.57 tff(1672,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(1673,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1672, 1671])).
% 1.34/1.57 tff(1674,plain,
% 1.34/1.57 (~b(s(z), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1673, 453, 1667, 1598, 1590])).
% 1.34/1.57 tff(1675,plain,
% 1.34/1.57 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1676,plain,
% 1.34/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(1677,plain,
% 1.34/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1676, 1675])).
% 1.34/1.57 tff(1678,plain,
% 1.34/1.57 (r(s(z), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1677, 69, 50, 1674])).
% 1.34/1.57 tff(1679,plain,
% 1.34/1.57 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[384, 1678, 228])).
% 1.34/1.57 tff(1680,plain,
% 1.34/1.57 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1656, 1679])).
% 1.34/1.57 tff(1681,plain,
% 1.34/1.57 (~b(s(s(s(z))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1641, 1680, 1590, 1598])).
% 1.34/1.57 tff(1682,plain,
% 1.34/1.57 (r(s(s(s(z))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[74, 1681, 1600])).
% 1.34/1.57 tff(1683,plain,
% 1.34/1.57 (~r(s(s(s(z))), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1586, 1682, 238])).
% 1.34/1.57 tff(1684,plain,
% 1.34/1.57 (b(s(s(s(z))), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[132, 69, 1683, 127])).
% 1.34/1.57 tff(1685,plain,
% 1.34/1.57 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1621, 1684, 1598, 1603])).
% 1.34/1.57 tff(1686,plain,
% 1.34/1.57 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[518, 1685])).
% 1.34/1.57 tff(1687,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1688,plain,
% 1.34/1.57 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1689,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1688])).
% 1.34/1.57 tff(1690,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[1689, 1687])).
% 1.34/1.57 tff(1691,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(1692,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1691, 1690])).
% 1.34/1.57 tff(1693,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1692, 268, 1686, 1678, 228])).
% 1.34/1.57 tff(1694,plain,((s(s(s(s(z)))) = elem!1) | (~r(elem!1, s(z))) | (s(z) = elem!1) | (~r(s(s(s(s(z)))), s(z))) | r(s(s(s(elem!1))), elem!1) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(1695,plain,
% 1.34/1.57 (s(s(s(s(z)))) = elem!1),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1694, 1131, 1126, 1099, 563, 221])).
% 1.34/1.57 tff(1696,plain,
% 1.34/1.57 (b(s(s(s(s(z)))), elem!1) <=> b(elem!1, elem!1)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1695])).
% 1.34/1.57 tff(1697,plain,
% 1.34/1.57 (b(elem!1, elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.34/1.57 inference(symmetry,[status(thm)],[1696])).
% 1.34/1.57 tff(1698,plain,
% 1.34/1.57 ((~b(elem!1, elem!1)) <=> (~b(s(s(s(s(z)))), elem!1))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1697])).
% 1.34/1.57 tff(1699,plain,
% 1.34/1.57 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 1.34/1.57 inference(bind,[status(th)],[])).
% 1.34/1.57 tff(1700,plain,
% 1.34/1.57 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.34/1.57 inference(quant_intro,[status(thm)],[1699])).
% 1.34/1.57 tff(1701,plain,
% 1.34/1.57 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(1702,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bi')).
% 1.34/1.57 tff(1703,plain,
% 1.34/1.57 (![X: $i] : (~b(X, X))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1702, 1701])).
% 1.34/1.57 tff(1704,plain,(
% 1.34/1.57 ![X: $i] : (~b(X, X))),
% 1.34/1.57 inference(skolemize,[status(sab)],[1703])).
% 1.34/1.57 tff(1705,plain,
% 1.34/1.57 (![X: $i] : (~b(X, X))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1704, 1700])).
% 1.34/1.57 tff(1706,plain,
% 1.34/1.57 ((~![X: $i] : (~b(X, X))) | (~b(elem!1, elem!1))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(1707,plain,
% 1.34/1.57 (~b(elem!1, elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1706, 1705])).
% 1.34/1.57 tff(1708,plain,
% 1.34/1.57 (~b(s(s(s(s(z)))), elem!1)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1707, 1698])).
% 1.34/1.57 tff(1709,plain,
% 1.34/1.57 (b(s(s(s(s(z)))), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1589, 1131, 563, 1099, 221, 1126])).
% 1.34/1.58 tff(1710,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1709, 1708])).
% 1.34/1.58 tff(1711,plain,(r(s(s(s(elem!1))), elem!1) | b(s(z), s(s(s(z)))) | b(elem!1, s(z)) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(1712,plain,
% 1.34/1.58 (r(s(s(s(elem!1))), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1711, 1057, 221, 10])).
% 1.34/1.58 tff(1713,plain,
% 1.34/1.58 (~r(s(s(s(elem!1))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[842, 1712, 238])).
% 1.34/1.58 tff(1714,plain,
% 1.34/1.58 (b(s(s(s(elem!1))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[856, 1713])).
% 1.34/1.58 tff(1715,plain,
% 1.34/1.58 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1714, 243])).
% 1.34/1.58 tff(1716,plain,
% 1.34/1.58 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[992, 1712, 162])).
% 1.34/1.58 tff(1717,plain,
% 1.34/1.58 (~b(s(z), s(s(z)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1016, 700, 997, 1005, 1007, 701])).
% 1.34/1.58 tff(1718,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[757, 1717, 742])).
% 1.34/1.58 tff(1719,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (s(s(z)) = s(s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(1720,plain,
% 1.34/1.58 (~r(s(s(z)), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1719, 1716, 819, 1715, 229])).
% 1.34/1.58 tff(1721,plain,
% 1.34/1.58 (b(s(s(z)), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[782, 1720, 161])).
% 1.34/1.58 tff(1722,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1723,plain,
% 1.34/1.58 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1724,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1723])).
% 1.34/1.58 tff(1725,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.34/1.58 inference(transitivity,[status(thm)],[1724, 1722])).
% 1.34/1.58 tff(1726,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(1727,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1726, 1725])).
% 1.34/1.58 tff(1728,plain,
% 1.34/1.58 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1727, 453, 1721, 646, 1088])).
% 1.34/1.58 tff(1729,plain,
% 1.34/1.58 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[768, 69, 52, 1728])).
% 1.34/1.58 tff(1730,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1731,plain,
% 1.34/1.58 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1732,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), 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(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1731])).
% 1.34/1.58 tff(1733,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), 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(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.34/1.58 inference(transitivity,[status(thm)],[1732, 1730])).
% 1.34/1.58 tff(1734,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(1735,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 1.34/1.58 tff(1736,plain,
% 1.34/1.58 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1735, 453, 1721, 1088, 299])).
% 1.34/1.58 tff(1737,plain,
% 1.34/1.58 (r(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[795, 69, 153, 1736])).
% 1.34/1.58 tff(1738,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[945, 268, 1082, 1737, 1729])).
% 1.34/1.58 tff(1739,plain,(b(s(s(s(s(z)))), s(z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (elem!1 = s(s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~(s(s(s(z))) = elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(elem!1)) | (~r(elem!1, s(z))) | b(s(z), s(s(s(z)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(1740,plain,
% 1.34/1.58 (b(s(s(s(s(z)))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1739, 255, 905, 9, 1026, 76, 904, 903, 1031, 238, 221, 10])).
% 1.34/1.58 tff(1741,plain,
% 1.34/1.58 (~(s(z) = s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[171, 166])).
% 1.34/1.58 tff(1742,plain,
% 1.34/1.58 (~b(elem!1, s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1079, 910, 629, 909])).
% 1.34/1.58 tff(1743,plain,
% 1.34/1.58 (r(elem!1, s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1069, 1742, 1056])).
% 1.34/1.58 tff(1744,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1745,plain,
% 1.34/1.58 (((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1746,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1745])).
% 1.34/1.58 tff(1747,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))),
% 1.34/1.58 inference(transitivity,[status(thm)],[1746, 1744])).
% 1.34/1.58 tff(1748,plain,
% 1.34/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(1749,plain,
% 1.34/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1748, 1747])).
% 1.34/1.58 tff(1750,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1749, 268, 388, 701, 339])).
% 1.34/1.58 tff(1751,plain,((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(1752,plain,
% 1.34/1.58 (~r(s(z), s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1751, 1743, 701])).
% 1.34/1.58 tff(1753,plain,
% 1.34/1.58 (b(s(z), s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[397, 1752, 1741])).
% 1.34/1.58 tff(1754,plain,
% 1.34/1.58 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(z)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[166])).
% 1.34/1.58 tff(1755,plain,
% 1.34/1.58 (b(s(z), s(s(s(s(z)))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1549, 1754])).
% 1.34/1.58 tff(1756,assumption,(~b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.58 tff(1757,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1756, 1755])).
% 1.34/1.58 tff(1758,plain,((~b(s(z), s(elem!1))) | b(s(z), s(s(s(s(z))))) | (~(s(elem!1) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(1759,plain,
% 1.34/1.58 (b(s(z), s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1758, 1753, 166])).
% 1.34/1.58 tff(1760,plain,
% 1.34/1.58 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[610])).
% 1.34/1.58 tff(1761,plain,
% 1.34/1.58 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[166])).
% 1.34/1.58 tff(1762,plain,
% 1.34/1.58 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[1761, 1760])).
% 1.34/1.58 tff(1763,plain,
% 1.34/1.58 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[910, 1762])).
% 1.34/1.58 tff(1764,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.34/1.58 tff(1765,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1766,plain,
% 1.34/1.58 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(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(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1767,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(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(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1766])).
% 1.34/1.58 tff(1768,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(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(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[1767, 1765])).
% 1.34/1.58 tff(1769,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(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(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(1770,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1769, 1768])).
% 1.34/1.58 tff(1771,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1770, 453, 1764, 1763, 1759, 374])).
% 1.34/1.58 tff(1772,plain,((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (elem!1 = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(1773,plain,
% 1.34/1.58 (~b(s(elem!1), s(s(elem!1)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1772, 1740, 1054, 162, 229, 1031, 904, 903])).
% 1.34/1.58 tff(1774,plain,
% 1.34/1.58 (r(s(elem!1), s(s(elem!1)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[440, 1773, 411])).
% 1.34/1.58 tff(1775,plain,
% 1.34/1.58 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[435, 1774, 76])).
% 1.34/1.58 tff(1776,plain,
% 1.34/1.58 (~r(elem!1, s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[427, 1775, 1026])).
% 1.34/1.58 tff(1777,plain,
% 1.34/1.58 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1776, 897])).
% 1.34/1.58 tff(1778,plain,
% 1.34/1.58 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1656, 1777])).
% 1.34/1.58 tff(1779,assumption,(b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.34/1.58 tff(1780,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.58 tff(1781,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1782,plain,
% 1.34/1.58 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1783,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1782])).
% 1.34/1.58 tff(1784,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[1783, 1781])).
% 1.34/1.58 tff(1785,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(1786,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1785, 1784])).
% 1.34/1.58 tff(1787,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1786, 453, 523, 1633, 1780, 1779])).
% 1.34/1.58 tff(1788,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(1789,plain,
% 1.34/1.58 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1788, 1778, 895, 893])).
% 1.34/1.58 tff(1790,plain,
% 1.34/1.58 (~b(s(s(elem!1)), s(elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1789, 237])).
% 1.34/1.58 tff(1791,plain,
% 1.34/1.58 (b(s(s(s(s(z)))), s(z)) <=> b(s(elem!1), s(z))),
% 1.34/1.58 inference(symmetry,[status(thm)],[1058])).
% 1.34/1.58 tff(1792,plain,
% 1.34/1.58 (b(s(elem!1), s(z))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1764, 1791])).
% 1.34/1.58 tff(1793,assumption,(~b(s(elem!1), s(z))), introduced(assumption)).
% 1.34/1.58 tff(1794,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1793, 1792])).
% 1.34/1.58 tff(1795,plain,((~(s(elem!1) = s(s(s(s(z)))))) | b(s(elem!1), s(z)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(1796,plain,
% 1.34/1.58 (b(s(elem!1), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1795, 1740, 162])).
% 1.34/1.58 tff(1797,assumption,(s(s(s(elem!1))) = s(elem!1)), introduced(assumption)).
% 1.34/1.58 tff(1798,plain,
% 1.34/1.58 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1797])).
% 1.34/1.58 tff(1799,plain,
% 1.34/1.58 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.34/1.58 inference(symmetry,[status(thm)],[1798])).
% 1.34/1.58 tff(1800,plain,
% 1.34/1.58 (elem!1 = s(s(elem!1))),
% 1.34/1.58 inference(transitivity,[status(thm)],[86, 1799, 550])).
% 1.34/1.58 tff(1801,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[216, 1800])).
% 1.34/1.58 tff(1802,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(1803,plain,
% 1.34/1.58 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1802, 209])).
% 1.34/1.58 tff(1804,plain,
% 1.34/1.58 (b(elem!1, s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1087, 1776, 9])).
% 1.34/1.58 tff(1805,plain,
% 1.34/1.58 (r(s(s(s(elem!1))), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[831, 1804, 3, 76, 246, 221, 239])).
% 1.34/1.58 tff(1806,assumption,(~b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.58 tff(1807,plain,
% 1.34/1.58 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.34/1.58 inference(commutativity,[status(thm)],[])).
% 1.34/1.58 tff(1808,plain,
% 1.34/1.58 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.34/1.58 inference(symmetry,[status(thm)],[1807])).
% 1.34/1.58 tff(1809,plain,
% 1.34/1.58 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1808])).
% 1.34/1.58 tff(1810,assumption,(~(s(s(s(elem!1))) = s(elem!1))), introduced(assumption)).
% 1.34/1.58 tff(1811,plain,
% 1.34/1.58 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1810, 1809])).
% 1.34/1.58 tff(1812,plain,
% 1.34/1.58 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(elem!1))))),
% 1.34/1.58 inference(symmetry,[status(thm)],[1470])).
% 1.34/1.58 tff(1813,plain,
% 1.34/1.58 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = s(s(s(elem!1)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1812])).
% 1.34/1.58 tff(1814,plain,
% 1.34/1.58 (~(s(z) = s(s(s(elem!1))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[851, 1813])).
% 1.34/1.58 tff(1815,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1816,plain,
% 1.34/1.58 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1817,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1816])).
% 1.34/1.59 tff(1818,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1817, 1815])).
% 1.34/1.59 tff(1819,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1820,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1)))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1819, 1818])).
% 1.34/1.59 tff(1821,plain,
% 1.34/1.59 (~r(s(z), s(s(s(elem!1))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1820, 268, 701, 833])).
% 1.34/1.59 tff(1822,plain,
% 1.34/1.59 (((~![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)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1823,plain,
% 1.34/1.59 ((~![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)))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1824,plain,
% 1.34/1.59 ((~![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))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1823, 1822])).
% 1.34/1.59 tff(1825,plain,
% 1.34/1.59 ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1824, 69, 1821])).
% 1.34/1.59 tff(1826,plain,
% 1.34/1.59 (b(s(z), s(s(s(elem!1))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1825, 1814])).
% 1.34/1.59 tff(1827,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1828,plain,
% 1.34/1.59 (((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1829,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1828])).
% 1.34/1.59 tff(1830,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1829, 1827])).
% 1.34/1.59 tff(1831,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1832,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1831, 1830])).
% 1.34/1.59 tff(1833,plain,
% 1.34/1.59 (~r(s(s(s(elem!1))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1832, 268, 701, 833])).
% 1.34/1.59 tff(1834,plain,
% 1.34/1.59 (b(s(s(s(elem!1))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[856, 1833])).
% 1.34/1.59 tff(1835,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1836,plain,
% 1.34/1.59 (((~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(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1837,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1836])).
% 1.34/1.59 tff(1838,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1837, 1835])).
% 1.34/1.59 tff(1839,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1840,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1839, 1838])).
% 1.34/1.59 tff(1841,plain,
% 1.34/1.59 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1840, 453, 1059, 1834, 1826])).
% 1.34/1.59 tff(1842,plain,
% 1.34/1.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1843,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1844,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1843, 1842])).
% 1.34/1.59 tff(1845,plain,
% 1.34/1.59 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1844, 69, 1841])).
% 1.34/1.59 tff(1846,plain,
% 1.34/1.59 (r(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1845, 1811])).
% 1.34/1.59 tff(1847,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1848,plain,
% 1.34/1.59 (((~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(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~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(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1849,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1848])).
% 1.34/1.59 tff(1850,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1849, 1847])).
% 1.34/1.59 tff(1851,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1852,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1851, 1850])).
% 1.34/1.59 tff(1853,plain,
% 1.34/1.59 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1852, 453, 1834, 1050, 1826])).
% 1.34/1.59 tff(1854,plain,
% 1.34/1.59 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[675, 1853, 617])).
% 1.34/1.59 tff(1855,plain,
% 1.34/1.59 (~r(s(elem!1), s(s(elem!1)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[668, 268, 1854, 1846])).
% 1.34/1.59 tff(1856,plain,
% 1.34/1.59 (s(elem!1) = s(s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[440, 1855, 1806])).
% 1.34/1.59 tff(1857,assumption,(s(elem!1) = s(s(elem!1))), introduced(assumption)).
% 1.34/1.59 tff(1858,plain,
% 1.34/1.59 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1857])).
% 1.34/1.59 tff(1859,plain,
% 1.34/1.59 (elem!1 = s(s(elem!1))),
% 1.34/1.59 inference(transitivity,[status(thm)],[86, 1858, 194, 1857])).
% 1.34/1.59 tff(1860,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[216, 1859])).
% 1.34/1.59 tff(1861,plain,((~(s(elem!1) = s(s(elem!1)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1862,plain,
% 1.34/1.59 (elem!1 = s(s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1861, 1856])).
% 1.34/1.59 tff(1863,plain,
% 1.34/1.59 (s(s(elem!1)) = elem!1),
% 1.34/1.59 inference(symmetry,[status(thm)],[1862])).
% 1.34/1.59 tff(1864,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1865,plain,
% 1.34/1.59 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1866,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1865])).
% 1.34/1.59 tff(1867,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1866, 1864])).
% 1.34/1.59 tff(1868,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1869,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1868, 1867])).
% 1.34/1.59 tff(1870,plain,
% 1.34/1.59 (~r(s(s(elem!1)), s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1869, 268, 1854, 1846])).
% 1.34/1.59 tff(1871,assumption,(~b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.34/1.59 tff(1872,plain,
% 1.34/1.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1873,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1874,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1873, 1872])).
% 1.34/1.59 tff(1875,plain,
% 1.34/1.59 ((s(s(elem!1)) = s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1874, 69, 1871])).
% 1.34/1.59 tff(1876,plain,
% 1.34/1.59 (s(s(elem!1)) = s(elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1875, 1870])).
% 1.34/1.59 tff(1877,plain,
% 1.34/1.59 (s(elem!1) = s(s(elem!1))),
% 1.34/1.59 inference(symmetry,[status(thm)],[1876])).
% 1.34/1.59 tff(1878,plain,
% 1.34/1.59 (s(elem!1) = elem!1),
% 1.34/1.59 inference(transitivity,[status(thm)],[1877, 1863])).
% 1.34/1.59 tff(1879,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[605, 1878])).
% 1.34/1.59 tff(1880,plain,((~r(s(z), elem!1)) | (s(elem!1) = elem!1) | b(s(elem!1), s(s(elem!1))) | b(s(s(elem!1)), s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1881,plain,
% 1.34/1.59 (b(s(s(elem!1)), s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1880, 1805, 229, 1048, 1803, 608, 1796, 1773, 598])).
% 1.34/1.59 tff(1882,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1881, 1790])).
% 1.34/1.59 tff(1883,plain,(r(s(s(s(s(z)))), elem!1) | (~(s(s(s(z))) = elem!1)) | (s(s(s(s(z)))) = elem!1) | b(s(z), s(s(s(z)))) | (~r(elem!1, s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1884,plain,
% 1.34/1.59 (r(s(s(s(s(z)))), elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1883, 76, 3, 221, 234, 10])).
% 1.34/1.59 tff(1885,plain,
% 1.34/1.59 (r(s(elem!1), elem!1)),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1884, 231])).
% 1.34/1.59 tff(1886,plain,
% 1.34/1.59 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.34/1.59 inference(symmetry,[status(thm)],[570])).
% 1.34/1.59 tff(1887,plain,
% 1.34/1.59 ((s(z) = s(s(s(s(s(s(z))))))) <=> (s(z) = s(s(s(elem!1))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1886])).
% 1.34/1.59 tff(1888,plain,
% 1.34/1.59 ((s(z) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = s(z))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1887, 1470])).
% 1.34/1.59 tff(1889,plain,
% 1.34/1.59 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(s(s(s(z)))))))),
% 1.34/1.59 inference(symmetry,[status(thm)],[1888])).
% 1.34/1.59 tff(1890,plain,
% 1.34/1.59 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = s(s(s(s(s(s(z))))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1889])).
% 1.34/1.59 tff(1891,plain,
% 1.34/1.59 (~(s(z) = s(s(s(s(s(s(z)))))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[851, 1890])).
% 1.34/1.59 tff(1892,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 1.34/1.59 tff(1893,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1894,plain,
% 1.34/1.59 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1895,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1894])).
% 1.34/1.59 tff(1896,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1895, 1893])).
% 1.34/1.59 tff(1897,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1898,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1897, 1896])).
% 1.34/1.59 tff(1899,plain,
% 1.34/1.59 ((~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1898, 268, 1892])).
% 1.34/1.59 tff(1900,plain,
% 1.34/1.59 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1899, 997])).
% 1.34/1.59 tff(1901,plain,
% 1.34/1.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1)) | r(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1)) | r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1902,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1)) | r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1903,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1)) | r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1902, 1901])).
% 1.34/1.59 tff(1904,plain,
% 1.34/1.59 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1903, 69, 955, 1900])).
% 1.34/1.59 tff(1905,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1906,plain,
% 1.34/1.59 (((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1907,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1906])).
% 1.34/1.59 tff(1908,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1907, 1905])).
% 1.34/1.59 tff(1909,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1910,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1909, 1908])).
% 1.34/1.59 tff(1911,plain,
% 1.34/1.60 ($false),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[1910, 268, 388, 701, 1892])).
% 1.34/1.60 tff(1912,plain,((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.60 tff(1913,plain,
% 1.34/1.60 (~r(s(z), s(elem!1))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[1912, 701, 1892])).
% 1.34/1.60 tff(1914,plain,
% 1.34/1.60 (b(s(z), s(elem!1))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[397, 1913, 172])).
% 1.34/1.60 tff(1915,plain,
% 1.34/1.60 ((s(z) = s(s(s(s(z))))) <=> (s(z) = s(elem!1))),
% 1.34/1.60 inference(monotonicity,[status(thm)],[77])).
% 1.34/1.60 tff(1916,plain,
% 1.34/1.60 ((s(z) = s(s(s(s(z))))) <=> (s(elem!1) = s(z))),
% 1.34/1.60 inference(transitivity,[status(thm)],[1915, 173])).
% 1.34/1.60 tff(1917,plain,
% 1.34/1.60 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(z)))),
% 1.34/1.60 inference(monotonicity,[status(thm)],[1916])).
% 1.34/1.60 tff(1918,plain,
% 1.34/1.60 (~(s(elem!1) = s(z))),
% 1.34/1.60 inference(modus_ponens,[status(thm)],[50, 1917])).
% 1.34/1.60 tff(1919,plain,
% 1.34/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)))),
% 1.34/1.60 inference(rewrite,[status(thm)],[])).
% 1.34/1.60 tff(1920,plain,
% 1.34/1.60 (((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)))),
% 1.34/1.60 inference(rewrite,[status(thm)],[])).
% 1.34/1.60 tff(1921,plain,
% 1.34/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1))))),
% 1.34/1.60 inference(monotonicity,[status(thm)],[1920])).
% 1.34/1.60 tff(1922,plain,
% 1.34/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)))),
% 1.34/1.60 inference(transitivity,[status(thm)],[1921, 1919])).
% 1.34/1.60 tff(1923,plain,
% 1.34/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.34/1.60 inference(quant_inst,[status(thm)],[])).
% 1.34/1.60 tff(1924,plain,
% 1.34/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1))),
% 1.34/1.60 inference(modus_ponens,[status(thm)],[1923, 1922])).
% 1.34/1.60 tff(1925,plain,
% 1.34/1.60 (~r(s(elem!1), s(z))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[1924, 268, 701, 1892])).
% 1.34/1.60 tff(1926,plain,
% 1.34/1.60 (b(s(elem!1), s(z))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[353, 1925, 1918])).
% 1.34/1.60 tff(1927,plain,
% 1.34/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.34/1.60 inference(rewrite,[status(thm)],[])).
% 1.34/1.60 tff(1928,plain,
% 1.34/1.60 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1929,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(z))))))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1928])).
% 1.44/1.60 tff(1930,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[1929, 1927])).
% 1.44/1.60 tff(1931,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(1932,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1931, 1930])).
% 1.44/1.60 tff(1933,plain,
% 1.44/1.60 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1932, 453, 1926, 1914, 1904])).
% 1.44/1.60 tff(1934,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1935,plain,
% 1.44/1.60 (((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1936,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1935])).
% 1.44/1.60 tff(1937,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[1936, 1934])).
% 1.44/1.60 tff(1938,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(1939,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1938, 1937])).
% 1.44/1.60 tff(1940,plain,
% 1.44/1.60 ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1939, 268, 701])).
% 1.44/1.60 tff(1941,plain,
% 1.44/1.60 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1940, 997])).
% 1.44/1.60 tff(1942,plain,
% 1.44/1.60 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z))))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1943,plain,
% 1.44/1.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z))))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(1944,plain,
% 1.44/1.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z)))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1943, 1942])).
% 1.44/1.60 tff(1945,plain,
% 1.44/1.60 ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z)))))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1944, 69, 1941])).
% 1.44/1.60 tff(1946,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1945, 1933, 1891])).
% 1.44/1.60 tff(1947,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~(s(s(s(z))) = elem!1)) | (s(s(s(s(s(s(z)))))) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(1948,plain,
% 1.44/1.60 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1947, 1885, 76, 229, 219])).
% 1.44/1.60 tff(1949,plain,
% 1.44/1.60 (~r(s(s(s(elem!1))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[992, 1948, 162])).
% 1.44/1.60 tff(1950,plain,
% 1.44/1.60 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[567, 1949, 200])).
% 1.44/1.60 tff(1951,plain,
% 1.44/1.60 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[576, 1950, 76])).
% 1.44/1.60 tff(1952,plain,
% 1.44/1.60 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.44/1.60 inference(monotonicity,[status(thm)],[76])).
% 1.44/1.60 tff(1953,plain,
% 1.44/1.60 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.60 inference(symmetry,[status(thm)],[1952])).
% 1.44/1.60 tff(1954,plain,
% 1.44/1.60 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1884, 1953])).
% 1.44/1.60 tff(1955,plain,
% 1.44/1.60 (~r(s(s(s(s(z)))), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1167, 1884, 229])).
% 1.44/1.60 tff(1956,plain,
% 1.44/1.60 (b(s(s(s(s(z)))), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1098, 1955])).
% 1.44/1.60 tff(1957,plain,
% 1.44/1.60 (~r(s(z), s(elem!1))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1912, 1885, 229])).
% 1.44/1.60 tff(1958,plain,
% 1.44/1.60 (b(s(z), s(elem!1))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[397, 1957, 172])).
% 1.44/1.60 tff(1959,plain,
% 1.44/1.60 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1758, 1958, 162])).
% 1.44/1.60 tff(1960,plain,
% 1.44/1.60 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[610, 494])).
% 1.44/1.60 tff(1961,plain,
% 1.44/1.60 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(elem!1)), elem!1)),
% 1.44/1.60 inference(symmetry,[status(thm)],[1960])).
% 1.44/1.60 tff(1962,plain,
% 1.44/1.60 (r(s(s(elem!1)), elem!1)),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[256, 1961])).
% 1.44/1.60 tff(1963,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1964,plain,
% 1.44/1.60 (((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1965,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1964])).
% 1.44/1.60 tff(1966,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 1.44/1.60 inference(transitivity,[status(thm)],[1965, 1963])).
% 1.44/1.60 tff(1967,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(1968,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1967, 1966])).
% 1.44/1.60 tff(1969,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1968, 268, 238, 1033, 869])).
% 1.44/1.60 tff(1970,plain,((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(1971,plain,
% 1.44/1.60 (~r(s(s(elem!1)), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1970, 1962, 238])).
% 1.44/1.60 tff(1972,plain,
% 1.44/1.60 (b(s(s(elem!1)), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1047, 1971])).
% 1.44/1.60 tff(1973,plain,
% 1.44/1.60 (b(s(s(s(s(s(z))))), s(z))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1972, 1049])).
% 1.44/1.60 tff(1974,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.44/1.60 tff(1975,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(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(s(z)))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1976,plain,
% 1.44/1.60 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), 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(s(z)))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1977,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), 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(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(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(s(z))))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1976])).
% 1.44/1.60 tff(1978,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), 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(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(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(s(z)))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[1977, 1975])).
% 1.44/1.60 tff(1979,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), 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(s(z)))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(1980,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1979, 1978])).
% 1.44/1.60 tff(1981,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1980, 268, 11, 256, 301])).
% 1.44/1.60 tff(1982,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(1983,plain,
% 1.44/1.60 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1982, 256, 11])).
% 1.44/1.60 tff(1984,plain,
% 1.44/1.60 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[328, 1983])).
% 1.44/1.60 tff(1985,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1986,plain,
% 1.44/1.60 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(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(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1987,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(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(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1986])).
% 1.44/1.60 tff(1988,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(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(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[1987, 1985])).
% 1.44/1.60 tff(1989,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(1990,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1989, 1988])).
% 1.44/1.60 tff(1991,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1990, 453, 1764, 1984, 1974, 1973])).
% 1.44/1.60 tff(1992,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(1993,plain,
% 1.44/1.60 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1992, 1959, 162, 234, 1956, 1954])).
% 1.44/1.60 tff(1994,plain,
% 1.44/1.60 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[687, 1993])).
% 1.44/1.60 tff(1995,plain,
% 1.44/1.60 (b(s(s(s(s(s(z))))), elem!1)),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1994, 901])).
% 1.44/1.60 tff(1996,plain,
% 1.44/1.60 (b(s(elem!1), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1795, 1956, 162])).
% 1.44/1.60 tff(1997,assumption,(~(s(elem!1) = s(s(elem!1)))), introduced(assumption)).
% 1.44/1.60 tff(1998,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(1999,plain,
% 1.44/1.60 (((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2000,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1999])).
% 1.44/1.60 tff(2001,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[2000, 1998])).
% 1.44/1.60 tff(2002,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2003,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2002, 2001])).
% 1.44/1.60 tff(2004,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2003, 268, 1892, 1032, 431])).
% 1.44/1.60 tff(2005,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(2006,plain,
% 1.44/1.60 (~r(s(elem!1), s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2005, 1032, 1892])).
% 1.44/1.60 tff(2007,plain,
% 1.44/1.60 (b(s(elem!1), s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[440, 2006, 1997])).
% 1.44/1.60 tff(2008,plain,
% 1.44/1.60 (~r(s(s(elem!1)), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1041, 1032, 238])).
% 1.44/1.60 tff(2009,plain,
% 1.44/1.60 (b(s(s(elem!1)), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1047, 2008])).
% 1.44/1.60 tff(2010,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2011,plain,
% 1.44/1.61 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2012,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2011])).
% 1.44/1.61 tff(2013,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2012, 2010])).
% 1.44/1.61 tff(2014,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2015,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2014, 2013])).
% 1.44/1.61 tff(2016,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2015, 453, 1059, 1549, 2009, 2007])).
% 1.44/1.61 tff(2017,plain,((~r(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(2018,plain,
% 1.44/1.61 (~r(elem!1, s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2017, 1958, 234, 1996, 411, 1885])).
% 1.44/1.61 tff(2019,plain,
% 1.44/1.61 (b(elem!1, s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1024, 2018, 209])).
% 1.44/1.61 tff(2020,plain,
% 1.44/1.61 (b(elem!1, s(s(s(s(s(z))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2019, 906])).
% 1.44/1.61 tff(2021,plain,
% 1.44/1.61 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[241])).
% 1.44/1.61 tff(2022,plain,
% 1.44/1.61 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.44/1.61 inference(symmetry,[status(thm)],[2021])).
% 1.44/1.61 tff(2023,plain,
% 1.44/1.61 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[201])).
% 1.44/1.61 tff(2024,plain,
% 1.44/1.61 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2023, 2022])).
% 1.44/1.61 tff(2025,plain,
% 1.44/1.61 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.61 inference(symmetry,[status(thm)],[863])).
% 1.44/1.61 tff(2026,plain,
% 1.44/1.61 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[861, 2025])).
% 1.44/1.61 tff(2027,plain,
% 1.44/1.61 ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2026])).
% 1.44/1.61 tff(2028,plain,
% 1.44/1.61 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[969, 453, 2020, 1995, 1951])).
% 1.44/1.61 tff(2029,plain,
% 1.44/1.61 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2028, 2027])).
% 1.44/1.61 tff(2030,plain,
% 1.44/1.61 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[675, 2029, 608])).
% 1.44/1.61 tff(2031,plain,
% 1.44/1.61 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2030, 2024])).
% 1.44/1.61 tff(2032,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2033,plain,
% 1.44/1.61 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2034,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2033])).
% 1.44/1.61 tff(2035,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2034, 2032])).
% 1.44/1.61 tff(2036,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2037,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2036, 2035])).
% 1.44/1.61 tff(2038,plain,
% 1.44/1.61 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2037, 453, 923, 922, 963])).
% 1.44/1.61 tff(2039,plain,
% 1.44/1.61 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[822, 69, 1005, 2038])).
% 1.44/1.61 tff(2040,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.44/1.61 tff(2041,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2042,plain,
% 1.44/1.61 (((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2043,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2042])).
% 1.44/1.61 tff(2044,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2043, 2041])).
% 1.44/1.61 tff(2045,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2046,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2045, 2044])).
% 1.44/1.61 tff(2047,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2046, 268, 2040, 2039, 931])).
% 1.44/1.61 tff(2048,plain,((~b(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (s(s(z)) = s(s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(2049,plain,
% 1.44/1.61 (~b(s(s(z)), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2048, 2031, 819, 2020, 1995, 1951])).
% 1.44/1.61 tff(2050,plain,
% 1.44/1.61 (r(s(s(z)), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[782, 2049, 161])).
% 1.44/1.61 tff(2051,plain,
% 1.44/1.61 (~r(s(s(z)), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[707, 268, 229, 2050])).
% 1.44/1.61 tff(2052,plain,
% 1.44/1.61 (b(s(s(z)), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[720, 69, 717, 2051])).
% 1.44/1.61 tff(2053,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2054,plain,
% 1.44/1.61 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2055,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2054])).
% 1.44/1.61 tff(2056,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2055, 2053])).
% 1.44/1.61 tff(2057,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2058,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2057, 2056])).
% 1.44/1.61 tff(2059,plain,
% 1.44/1.61 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2058, 268, 2050, 1884])).
% 1.44/1.61 tff(2060,plain,
% 1.44/1.61 (b(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[795, 69, 153, 2059])).
% 1.44/1.61 tff(2061,plain,
% 1.44/1.61 (~r(s(z), s(s(z)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[741, 2050, 229])).
% 1.44/1.61 tff(2062,plain,
% 1.44/1.61 (b(s(z), s(s(z)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[757, 2061])).
% 1.44/1.61 tff(2063,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2064,plain,
% 1.44/1.61 (((~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(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2065,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(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(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2064])).
% 1.44/1.61 tff(2066,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(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(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2065, 2063])).
% 1.44/1.61 tff(2067,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(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)))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2068,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2067, 2066])).
% 1.44/1.61 tff(2069,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2068, 453, 1959, 2062, 2060, 2052])).
% 1.44/1.61 tff(2070,plain,((~(s(s(s(z))) = elem!1)) | (s(s(s(s(z)))) = elem!1) | b(s(z), s(s(s(z)))) | b(elem!1, s(z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(2071,plain,
% 1.44/1.61 (b(s(z), s(s(s(z))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2070, 143, 76, 10, 135])).
% 1.44/1.61 tff(2072,plain,
% 1.44/1.61 (b(s(z), elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2071, 115])).
% 1.44/1.61 tff(2073,assumption,(~(elem!1 = s(s(s(s(s(z))))))), introduced(assumption)).
% 1.44/1.61 tff(2074,plain,
% 1.44/1.61 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[531])).
% 1.44/1.61 tff(2075,plain,
% 1.44/1.61 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 1.44/1.61 inference(symmetry,[status(thm)],[2074])).
% 1.44/1.61 tff(2076,assumption,(~r(elem!1, s(z))), introduced(assumption)).
% 1.44/1.61 tff(2077,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 1.44/1.61 tff(2078,plain,
% 1.44/1.61 (b(s(s(s(z))), s(z))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2077, 117])).
% 1.44/1.61 tff(2079,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[128, 2078])).
% 1.44/1.61 tff(2080,plain,((~(s(s(s(z))) = elem!1)) | b(s(s(s(z))), s(z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(2081,plain,
% 1.44/1.61 (~b(elem!1, s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2080, 76, 128])).
% 1.44/1.61 tff(2082,plain,
% 1.44/1.61 (elem!1 = s(z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1130, 2081, 2076])).
% 1.44/1.61 tff(2083,plain,
% 1.44/1.61 (s(z) = elem!1),
% 1.44/1.61 inference(symmetry,[status(thm)],[2082])).
% 1.44/1.61 tff(2084,plain,
% 1.44/1.61 (s(z) = s(s(s(z)))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2083, 86, 2075, 37])).
% 1.44/1.61 tff(2085,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[109, 2084])).
% 1.44/1.61 tff(2086,plain,((~(s(s(s(z))) = elem!1)) | r(elem!1, s(z)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(2087,plain,
% 1.44/1.61 (r(elem!1, s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2086, 123, 76])).
% 1.44/1.61 tff(2088,plain,
% 1.44/1.61 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[162])).
% 1.44/1.61 tff(2089,plain,
% 1.44/1.61 (~(elem!1 = s(elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[143, 1030])).
% 1.44/1.61 tff(2090,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.44/1.61 tff(2091,plain,
% 1.44/1.61 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.61 inference(symmetry,[status(thm)],[522])).
% 1.44/1.61 tff(2092,plain,
% 1.44/1.61 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[299, 2091])).
% 1.44/1.61 tff(2093,plain,
% 1.44/1.61 (b(s(elem!1), elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[299, 521])).
% 1.44/1.61 tff(2094,plain,
% 1.44/1.61 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[162])).
% 1.44/1.61 tff(2095,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2096,plain,
% 1.44/1.61 (((~b(s(s(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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2097,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2096])).
% 1.44/1.61 tff(2098,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2097, 2095])).
% 1.44/1.61 tff(2099,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2100,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2099, 2098])).
% 1.44/1.61 tff(2101,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2100, 453, 523, 1633, 1764, 2090])).
% 1.44/1.61 tff(2102,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(2103,plain,
% 1.44/1.61 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2102, 1764, 523, 2090])).
% 1.44/1.61 tff(2104,plain,
% 1.44/1.61 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1656, 2103])).
% 1.44/1.61 tff(2105,plain,
% 1.44/1.61 (r(elem!1, s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[337, 2104, 76])).
% 1.44/1.61 tff(2106,plain,
% 1.44/1.61 (r(elem!1, s(s(s(s(z)))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2105, 2094])).
% 1.44/1.61 tff(2107,plain,
% 1.44/1.61 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[162])).
% 1.44/1.61 tff(2108,plain,
% 1.44/1.61 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[162])).
% 1.44/1.61 tff(2109,plain,
% 1.44/1.61 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.44/1.61 inference(symmetry,[status(thm)],[2108])).
% 1.44/1.61 tff(2110,plain,
% 1.44/1.61 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2109])).
% 1.44/1.61 tff(2111,plain,
% 1.44/1.61 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[319, 2110])).
% 1.44/1.61 tff(2112,plain,
% 1.44/1.61 (~(elem!1 = s(s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2073, 204])).
% 1.44/1.62 tff(2113,plain,
% 1.44/1.62 (b(s(elem!1), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1795, 1764, 162])).
% 1.44/1.62 tff(2114,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2115,plain,
% 1.44/1.62 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2116,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2115])).
% 1.44/1.62 tff(2117,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.62 inference(transitivity,[status(thm)],[2116, 2114])).
% 1.44/1.62 tff(2118,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(2119,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2118, 2117])).
% 1.44/1.62 tff(2120,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2119, 453, 1059, 499, 629, 907])).
% 1.44/1.62 tff(2121,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(2122,plain,
% 1.44/1.62 (~b(elem!1, s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2121, 2113, 629, 499])).
% 1.44/1.62 tff(2123,plain,
% 1.44/1.62 (r(elem!1, s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1024, 2122, 2112])).
% 1.44/1.62 tff(2124,plain,
% 1.44/1.62 (~r(s(s(elem!1)), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1041, 2123, 238])).
% 1.44/1.62 tff(2125,plain,
% 1.44/1.62 (b(s(s(elem!1)), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1047, 2124])).
% 1.44/1.62 tff(2126,plain,
% 1.44/1.62 (b(s(s(s(s(s(z))))), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1053, 2125, 162])).
% 1.44/1.62 tff(2127,plain,
% 1.44/1.62 (~r(s(z), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1496, 2105, 238])).
% 1.44/1.62 tff(2128,plain,
% 1.44/1.62 (b(s(z), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[397, 2127, 172])).
% 1.44/1.62 tff(2129,assumption,(b(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 1.44/1.62 tff(2130,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2131,plain,
% 1.44/1.62 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2132,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2131])).
% 1.44/1.62 tff(2133,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[2132, 2130])).
% 1.44/1.62 tff(2134,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(2135,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2134, 2133])).
% 1.44/1.62 tff(2136,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2135, 453, 1549, 629, 374, 2129])).
% 1.44/1.62 tff(2137,plain,((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(2138,plain,
% 1.44/1.62 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2137, 2128, 629, 2126])).
% 1.44/1.62 tff(2139,plain,
% 1.44/1.62 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2140,plain,
% 1.44/1.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(2141,plain,
% 1.44/1.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2140, 2139])).
% 1.44/1.62 tff(2142,plain,
% 1.44/1.62 ((s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2141, 69])).
% 1.44/1.62 tff(2143,plain,
% 1.44/1.62 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2142, 2138, 2111])).
% 1.44/1.62 tff(2144,plain,
% 1.44/1.62 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2143, 2107])).
% 1.44/1.62 tff(2145,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2146,plain,
% 1.44/1.62 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2147,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2146])).
% 1.44/1.62 tff(2148,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[2147, 2145])).
% 1.44/1.62 tff(2149,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(2150,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2149, 2148])).
% 1.44/1.62 tff(2151,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2150, 453, 1549, 499, 629, 923])).
% 1.44/1.62 tff(2152,plain,((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(2153,plain,
% 1.44/1.62 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2152, 2128, 629, 499])).
% 1.44/1.62 tff(2154,plain,
% 1.44/1.62 (r(elem!1, s(s(s(s(s(z))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[466, 2153, 2073])).
% 1.44/1.62 tff(2155,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2156,plain,
% 1.44/1.62 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2157,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2156])).
% 1.44/1.62 tff(2158,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[2157, 2155])).
% 1.44/1.62 tff(2159,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(2160,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2159, 2158])).
% 1.44/1.62 tff(2161,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2160, 268, 2154, 2144, 2106])).
% 1.44/1.62 tff(2162,plain,((~b(s(s(s(s(z)))), s(z))) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~r(elem!1, s(z))) | (~(s(s(s(z))) = elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(2163,plain,
% 1.44/1.62 (~b(s(s(s(s(z)))), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2162, 499, 2093, 2073, 238, 76, 2092, 2090])).
% 1.44/1.62 tff(2164,plain,
% 1.44/1.62 (~b(s(elem!1), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1062, 2163, 162])).
% 1.44/1.62 tff(2165,plain,
% 1.44/1.62 (r(s(elem!1), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[353, 2164, 180])).
% 1.44/1.62 tff(2166,plain,
% 1.44/1.62 (~r(elem!1, s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[348, 2165, 238])).
% 1.44/1.62 tff(2167,plain,
% 1.44/1.62 (b(elem!1, s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1069, 2166, 2089])).
% 1.44/1.62 tff(2168,plain,
% 1.44/1.62 (b(elem!1, s(s(s(s(z)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2167, 2088])).
% 1.44/1.62 tff(2169,plain,
% 1.44/1.62 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.44/1.62 inference(commutativity,[status(thm)],[])).
% 1.44/1.62 tff(2170,plain,
% 1.44/1.62 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 1.44/1.62 inference(symmetry,[status(thm)],[2169])).
% 1.44/1.62 tff(2171,plain,
% 1.44/1.62 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = elem!1)),
% 1.44/1.62 inference(transitivity,[status(thm)],[203, 2170])).
% 1.44/1.62 tff(2172,plain,
% 1.44/1.62 ((~(elem!1 = s(s(s(s(s(z))))))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2171])).
% 1.44/1.62 tff(2173,plain,
% 1.44/1.62 (~(s(s(elem!1)) = elem!1)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2073, 2172])).
% 1.44/1.62 tff(2174,plain,
% 1.44/1.62 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[218, 2112, 76])).
% 1.44/1.62 tff(2175,plain,
% 1.44/1.62 (r(s(s(s(s(z)))), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1098, 2163])).
% 1.44/1.62 tff(2176,plain,
% 1.44/1.62 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[167])).
% 1.44/1.62 tff(2177,plain,
% 1.44/1.62 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.44/1.62 inference(symmetry,[status(thm)],[2176])).
% 1.44/1.62 tff(2178,plain,
% 1.44/1.62 ((~(s(s(s(s(s(s(z)))))) = s(elem!1))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2177])).
% 1.44/1.62 tff(2179,plain,
% 1.44/1.62 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[955, 2178])).
% 1.44/1.62 tff(2180,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(s(z)))))), s(z))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[611])).
% 1.44/1.62 tff(2181,plain,
% 1.44/1.62 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[611])).
% 1.44/1.62 tff(2182,plain,
% 1.44/1.62 (b(s(s(s(s(s(s(z)))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.44/1.62 inference(symmetry,[status(thm)],[2181])).
% 1.44/1.62 tff(2183,plain,
% 1.44/1.62 ((~b(s(s(s(s(s(s(z)))))), s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2182])).
% 1.44/1.62 tff(2184,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2185,plain,
% 1.44/1.62 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2186,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2185])).
% 1.44/1.62 tff(2187,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.44/1.62 inference(transitivity,[status(thm)],[2186, 2184])).
% 1.44/1.62 tff(2188,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(2189,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2188, 2187])).
% 1.44/1.62 tff(2190,plain,
% 1.44/1.62 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2189, 453, 499, 963, 530])).
% 1.44/1.62 tff(2191,plain,
% 1.44/1.62 (~b(s(s(s(elem!1))), s(z))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2190, 2183])).
% 1.44/1.62 tff(2192,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[856, 2191])).
% 1.44/1.62 tff(2193,plain,
% 1.44/1.62 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2192, 2180])).
% 1.44/1.62 tff(2194,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2195,plain,
% 1.44/1.62 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2196,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2195])).
% 1.44/1.62 tff(2197,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[2196, 2194])).
% 1.44/1.62 tff(2198,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(2199,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2198, 2197])).
% 1.44/1.62 tff(2200,plain,
% 1.44/1.62 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2199, 268, 1132, 2193])).
% 1.44/1.62 tff(2201,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2202,plain,
% 1.44/1.62 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2203,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2202])).
% 1.44/1.63 tff(2204,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2203, 2201])).
% 1.44/1.63 tff(2205,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(2206,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2205, 2204])).
% 1.44/1.63 tff(2207,plain,
% 1.44/1.63 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2206, 453, 963, 530, 299])).
% 1.44/1.63 tff(2208,plain,
% 1.44/1.63 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2209,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(2210,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2209, 2208])).
% 1.44/1.63 tff(2211,plain,
% 1.44/1.63 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2210, 69, 2207])).
% 1.44/1.63 tff(2212,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2211, 2200, 2179])).
% 1.44/1.63 tff(2213,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(s(s(s(z)))))) = s(elem!1)) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(2214,plain,
% 1.44/1.63 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2213, 2175, 2174, 162, 2168, 299, 499])).
% 1.44/1.63 tff(2215,plain,
% 1.44/1.63 (~b(s(s(s(elem!1))), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[576, 2214, 76])).
% 1.44/1.63 tff(2216,plain,
% 1.44/1.63 (r(s(s(s(elem!1))), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[567, 2215, 200])).
% 1.44/1.63 tff(2217,plain,
% 1.44/1.63 (~(s(elem!1) = elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[143, 597])).
% 1.44/1.63 tff(2218,plain,
% 1.44/1.63 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[607, 2217])).
% 1.44/1.63 tff(2219,plain,
% 1.44/1.63 (~r(s(s(s(elem!1))), s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[842, 833, 238])).
% 1.44/1.63 tff(2220,plain,
% 1.44/1.63 (b(s(s(s(elem!1))), s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[856, 2219])).
% 1.44/1.63 tff(2221,plain,
% 1.44/1.63 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2220, 2181])).
% 1.44/1.63 tff(2222,plain,
% 1.44/1.63 (~r(s(s(elem!1)), s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1970, 869, 238])).
% 1.44/1.63 tff(2223,plain,
% 1.44/1.63 (b(s(s(elem!1)), s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1047, 2222])).
% 1.44/1.63 tff(2224,plain,
% 1.44/1.63 (b(s(s(s(s(s(z))))), s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1053, 2223, 166])).
% 1.44/1.63 tff(2225,plain,
% 1.44/1.63 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[877, 869, 833])).
% 1.44/1.63 tff(2226,plain,
% 1.44/1.63 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[675, 2225, 617])).
% 1.44/1.63 tff(2227,plain,
% 1.44/1.63 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2226, 616])).
% 1.44/1.63 tff(2228,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(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(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2229,plain,
% 1.44/1.63 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2230,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2229])).
% 1.44/1.63 tff(2231,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2230, 2228])).
% 1.44/1.63 tff(2232,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(2233,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2232, 2231])).
% 1.44/1.63 tff(2234,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2233, 453, 499, 2227, 2224, 2221])).
% 1.44/1.63 tff(2235,plain,((~r(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~(s(elem!1) = s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(2236,plain,
% 1.44/1.63 (~r(s(s(elem!1)), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2235, 499, 162, 2218, 2216, 238])).
% 1.44/1.63 tff(2237,plain,
% 1.44/1.63 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2238,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(2239,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2238, 2237])).
% 1.44/1.63 tff(2240,plain,
% 1.44/1.63 ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2239, 69])).
% 1.44/1.63 tff(2241,plain,
% 1.44/1.63 (b(s(s(elem!1)), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2240, 2236, 2173])).
% 1.44/1.63 tff(2242,plain,
% 1.44/1.63 (b(s(s(s(s(s(z))))), elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2241, 899])).
% 1.44/1.63 tff(2243,plain,
% 1.44/1.63 (~b(s(elem!1), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1079, 2241, 2093, 2167])).
% 1.44/1.63 tff(2244,plain,
% 1.44/1.63 (r(s(elem!1), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[440, 2243, 411])).
% 1.44/1.63 tff(2245,plain,
% 1.44/1.63 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[435, 2244, 76])).
% 1.44/1.63 tff(2246,assumption,(r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.44/1.63 tff(2247,plain,
% 1.44/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2248,plain,
% 1.44/1.63 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2249,plain,
% 1.44/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2248])).
% 1.44/1.63 tff(2250,plain,
% 1.44/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2249, 2247])).
% 1.44/1.63 tff(2251,plain,
% 1.44/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(2252,plain,
% 1.44/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2251, 2250])).
% 1.44/1.63 tff(2253,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2252, 268, 1132, 2246, 418])).
% 1.44/1.63 tff(2254,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(2255,plain,
% 1.44/1.63 (~r(s(z), s(s(s(s(s(z))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2254, 2245, 2175])).
% 1.44/1.63 tff(2256,plain,
% 1.44/1.63 (b(s(z), s(s(s(s(s(z))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[372, 2255])).
% 1.44/1.63 tff(2257,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2258,plain,
% 1.44/1.63 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2259,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2258])).
% 1.44/1.63 tff(2260,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2259, 2257])).
% 1.44/1.63 tff(2261,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(2262,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2261, 2260])).
% 1.44/1.63 tff(2263,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2262, 453, 499, 2256, 2242, 2168])).
% 1.44/1.63 tff(2264,plain,((~b(s(z), elem!1)) | (~(s(s(s(z))) = elem!1)) | (~r(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(2265,plain,
% 1.44/1.63 (~b(s(z), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2264, 76, 2087, 299, 2073, 2071])).
% 1.44/1.63 tff(2266,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2265, 2072])).
% 1.44/1.63 tff(2267,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(2268,plain,
% 1.44/1.63 (~b(s(s(s(s(z)))), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2267, 114, 75, 10])).
% 1.44/1.63 tff(2269,plain,
% 1.44/1.63 (s(s(z)) = s(elem!1)),
% 1.44/1.63 inference(symmetry,[status(thm)],[1103])).
% 1.44/1.63 tff(2270,plain,
% 1.44/1.63 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2269])).
% 1.44/1.63 tff(2271,plain,
% 1.44/1.63 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[2270])).
% 1.44/1.63 tff(2272,plain,
% 1.44/1.63 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2269])).
% 1.44/1.63 tff(2273,plain,
% 1.44/1.63 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2272, 624])).
% 1.44/1.63 tff(2274,plain,
% 1.44/1.63 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(s(s(z)))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2273])).
% 1.44/1.63 tff(2275,plain,
% 1.44/1.63 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[52, 2274])).
% 1.44/1.63 tff(2276,plain,
% 1.44/1.63 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(z)), s(s(s(z))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1103, 1104])).
% 1.44/1.63 tff(2277,plain,
% 1.44/1.63 (s(z) = elem!1),
% 1.44/1.63 inference(symmetry,[status(thm)],[1100])).
% 1.44/1.63 tff(2278,plain,
% 1.44/1.63 (s(s(z)) = s(elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2277])).
% 1.44/1.63 tff(2279,plain,
% 1.44/1.63 (s(elem!1) = s(s(z))),
% 1.44/1.63 inference(symmetry,[status(thm)],[2278])).
% 1.44/1.63 tff(2280,plain,
% 1.44/1.63 (s(s(elem!1)) = s(s(s(z)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2279])).
% 1.44/1.63 tff(2281,plain,
% 1.44/1.63 (s(s(z)) = s(s(s(z)))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2278, 1857, 2280])).
% 1.44/1.63 tff(2282,plain,
% 1.44/1.63 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2281])).
% 1.44/1.63 tff(2283,plain,
% 1.44/1.63 (inj_0(s(s(s(z)))) = inj_0(s(s(z)))),
% 1.44/1.63 inference(symmetry,[status(thm)],[2282])).
% 1.44/1.63 tff(2284,plain,
% 1.44/1.63 (s(s(elem!1)) = s(elem!1)),
% 1.44/1.63 inference(symmetry,[status(thm)],[1857])).
% 1.44/1.63 tff(2285,plain,
% 1.44/1.63 (s(s(elem!1)) = s(z)),
% 1.44/1.63 inference(transitivity,[status(thm)],[2284, 2279, 98, 2283, 28])).
% 1.44/1.63 tff(2286,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[816, 2285])).
% 1.44/1.63 tff(2287,plain,((~(s(elem!1) = s(s(elem!1)))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(2288,plain,
% 1.44/1.63 (~(s(elem!1) = s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2287, 1100])).
% 1.44/1.63 tff(2289,plain,
% 1.44/1.63 ((s(z) = s(s(z))) <=> (s(z) = s(elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2269])).
% 1.44/1.63 tff(2290,plain,
% 1.44/1.63 ((s(z) = s(s(z))) <=> (s(elem!1) = s(z))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2289, 173])).
% 1.44/1.63 tff(2291,plain,
% 1.44/1.63 ((s(z) = s(s(z))) <=> (s(z) = s(elem!1))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2290, 174])).
% 1.44/1.63 tff(2292,plain,
% 1.44/1.63 ((~(s(z) = s(s(z)))) <=> (~(s(z) = s(elem!1)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2291])).
% 1.44/1.63 tff(2293,plain,
% 1.44/1.63 (~(s(z) = s(elem!1))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[752, 2292])).
% 1.44/1.63 tff(2294,plain,
% 1.44/1.63 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1100])).
% 1.44/1.63 tff(2295,plain,
% 1.44/1.63 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 1.44/1.63 inference(symmetry,[status(thm)],[2294])).
% 1.44/1.63 tff(2296,plain,
% 1.44/1.63 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1103])).
% 1.44/1.63 tff(2297,plain,
% 1.44/1.63 (r(s(s(z)), s(z)) <=> r(s(elem!1), s(z))),
% 1.44/1.63 inference(symmetry,[status(thm)],[2296])).
% 1.44/1.63 tff(2298,plain,
% 1.44/1.63 (r(s(s(z)), s(z)) <=> r(s(elem!1), elem!1)),
% 1.44/1.63 inference(transitivity,[status(thm)],[2297, 2295])).
% 1.44/1.63 tff(2299,plain,
% 1.44/1.63 ((~r(s(s(z)), s(z))) <=> (~r(s(elem!1), elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2298])).
% 1.44/1.63 tff(2300,plain,
% 1.44/1.63 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1100])).
% 1.44/1.63 tff(2301,plain,
% 1.44/1.63 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(s(z)))), s(z)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2300])).
% 1.44/1.63 tff(2302,plain,
% 1.44/1.63 (~b(s(s(s(s(z)))), s(z))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[249, 2301])).
% 1.44/1.63 tff(2303,plain,
% 1.44/1.63 (r(s(s(s(s(z)))), s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1096, 69, 2302, 1092])).
% 1.44/1.63 tff(2304,plain,
% 1.44/1.63 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1100])).
% 1.44/1.63 tff(2305,plain,
% 1.44/1.63 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(z)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2304])).
% 1.44/1.63 tff(2306,plain,
% 1.44/1.63 (~r(s(s(s(z))), s(z))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2, 2305])).
% 1.44/1.63 tff(2307,plain,
% 1.44/1.63 (b(s(s(s(z))), s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[132, 69, 2306, 127])).
% 1.44/1.63 tff(2308,plain,
% 1.44/1.63 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.44/1.63 inference(commutativity,[status(thm)],[])).
% 1.44/1.63 tff(2309,plain,
% 1.44/1.63 ((elem!1 = s(s(elem!1))) <=> (s(z) = s(s(elem!1)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1100])).
% 1.44/1.63 tff(2310,plain,
% 1.44/1.63 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2309, 2308])).
% 1.44/1.63 tff(2311,plain,
% 1.44/1.63 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 1.44/1.63 inference(symmetry,[status(thm)],[2310])).
% 1.44/1.63 tff(2312,plain,
% 1.44/1.63 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.44/1.63 inference(transitivity,[status(thm)],[2311, 2170])).
% 1.44/1.63 tff(2313,plain,
% 1.44/1.63 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2312])).
% 1.44/1.63 tff(2314,plain,
% 1.44/1.63 (~(s(s(elem!1)) = elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[816, 2313])).
% 1.44/1.63 tff(2315,plain,
% 1.44/1.63 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(z))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1100])).
% 1.44/1.63 tff(2316,plain,
% 1.44/1.63 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 1.44/1.63 inference(symmetry,[status(thm)],[2315])).
% 1.44/1.63 tff(2317,plain,
% 1.44/1.63 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(z))), s(z))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1104])).
% 1.44/1.63 tff(2318,plain,
% 1.44/1.63 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.44/1.63 inference(symmetry,[status(thm)],[2317])).
% 1.44/1.63 tff(2319,plain,
% 1.44/1.63 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 1.44/1.63 inference(transitivity,[status(thm)],[2318, 2316])).
% 1.44/1.63 tff(2320,plain,
% 1.44/1.63 ((~r(s(s(s(z))), s(z))) <=> (~r(s(s(elem!1)), elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2319])).
% 1.44/1.63 tff(2321,plain,
% 1.44/1.63 (~r(s(s(elem!1)), elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2306, 2320])).
% 1.44/1.63 tff(2322,plain,
% 1.44/1.63 (b(s(s(elem!1)), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2240, 2321, 2314])).
% 1.44/1.63 tff(2323,plain,
% 1.44/1.63 ((s(s(s(z))) = s(z)) <=> (s(z) = s(s(s(z))))),
% 1.44/1.63 inference(commutativity,[status(thm)],[])).
% 1.44/1.63 tff(2324,plain,
% 1.44/1.63 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(z))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1100])).
% 1.44/1.63 tff(2325,plain,
% 1.44/1.63 ((s(s(s(z))) = elem!1) <=> (s(z) = s(s(s(z))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2324, 2323])).
% 1.44/1.63 tff(2326,plain,
% 1.44/1.63 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.44/1.63 inference(symmetry,[status(thm)],[2325])).
% 1.44/1.63 tff(2327,plain,
% 1.44/1.63 ((~(s(z) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2326])).
% 1.44/1.63 tff(2328,plain,
% 1.44/1.63 (~(s(s(s(z))) = elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[109, 2327])).
% 1.44/1.63 tff(2329,plain,
% 1.44/1.63 (b(s(s(s(z))), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[74, 2328, 2])).
% 1.44/1.63 tff(2330,assumption,(s(elem!1) = s(s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.44/1.63 tff(2331,plain,
% 1.44/1.63 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 1.44/1.63 inference(symmetry,[status(thm)],[2330])).
% 1.44/1.63 tff(2332,plain,
% 1.44/1.63 (s(s(s(s(s(s(s(s(z)))))))) = s(s(z))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2331, 1103])).
% 1.44/1.63 tff(2333,plain,
% 1.44/1.63 (inj_0(s(s(s(s(s(s(s(s(z))))))))) = inj_0(s(s(z)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2332])).
% 1.44/1.63 tff(2334,plain,
% 1.44/1.63 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(s(s(s(s(z))))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2335,plain,
% 1.44/1.64 (inj_0(s(s(s(s(s(s(s(s(z))))))))) = s(s(s(s(s(s(s(z)))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2334, 21])).
% 1.44/1.64 tff(2336,plain,
% 1.44/1.64 (s(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(s(s(s(s(z)))))))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[2335])).
% 1.44/1.64 tff(2337,plain,
% 1.44/1.64 (s(s(s(s(s(s(s(z))))))) = s(z)),
% 1.44/1.64 inference(transitivity,[status(thm)],[2336, 2333, 28])).
% 1.44/1.64 tff(2338,plain,
% 1.44/1.64 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(z))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2337])).
% 1.44/1.64 tff(2339,plain,
% 1.44/1.64 (s(s(s(s(s(s(z)))))) = z),
% 1.44/1.64 inference(transitivity,[status(thm)],[1375, 2338, 32])).
% 1.44/1.64 tff(2340,plain,
% 1.44/1.64 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2341,plain,
% 1.44/1.64 (~(s(s(s(s(s(s(z)))))) = z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2340, 46])).
% 1.44/1.64 tff(2342,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2341, 2339])).
% 1.44/1.64 tff(2343,plain,((~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(2344,plain,
% 1.44/1.64 (~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2343, 1100])).
% 1.44/1.64 tff(2345,plain,
% 1.44/1.64 (r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2269])).
% 1.44/1.64 tff(2346,plain,
% 1.44/1.64 ((~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) <=> (~r(s(elem!1), s(s(s(s(s(s(s(s(z))))))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2345])).
% 1.44/1.64 tff(2347,plain,
% 1.44/1.64 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1103])).
% 1.44/1.64 tff(2348,plain,
% 1.44/1.64 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[2347])).
% 1.44/1.64 tff(2349,plain,
% 1.44/1.64 ((~r(s(s(z)), s(s(s(s(s(z))))))) <=> (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2348])).
% 1.44/1.64 tff(2350,plain,
% 1.44/1.64 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(z))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1100])).
% 1.44/1.64 tff(2351,plain,
% 1.44/1.64 ((s(elem!1) = s(z)) <=> (s(elem!1) = elem!1)),
% 1.44/1.64 inference(symmetry,[status(thm)],[2350])).
% 1.44/1.64 tff(2352,plain,
% 1.44/1.64 ((s(z) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 1.44/1.64 inference(transitivity,[status(thm)],[2290, 2351])).
% 1.44/1.64 tff(2353,plain,
% 1.44/1.64 ((~(s(z) = s(s(z)))) <=> (~(s(elem!1) = elem!1))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2352])).
% 1.44/1.64 tff(2354,plain,
% 1.44/1.64 (~(s(elem!1) = elem!1)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[752, 2353])).
% 1.44/1.64 tff(2355,plain,
% 1.44/1.64 ((~b(s(s(z)), s(s(s(s(s(z))))))) <=> (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2270])).
% 1.44/1.64 tff(2356,assumption,(s(s(z)) = s(s(s(s(z))))), introduced(assumption)).
% 1.44/1.64 tff(2357,plain,
% 1.44/1.64 (s(s(s(s(z)))) = s(s(z))),
% 1.44/1.64 inference(symmetry,[status(thm)],[2356])).
% 1.44/1.64 tff(2358,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[153, 2357])).
% 1.44/1.64 tff(2359,plain,(~(s(s(z)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(2360,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 1.44/1.64 tff(2361,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2362,plain,
% 1.44/1.64 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2363,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2362])).
% 1.44/1.64 tff(2364,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2363, 2361])).
% 1.44/1.64 tff(2365,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2366,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2365, 2364])).
% 1.44/1.64 tff(2367,plain,
% 1.44/1.64 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2366, 268, 1132, 2360])).
% 1.44/1.64 tff(2368,plain,
% 1.44/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2369,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2370,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2369, 2368])).
% 1.44/1.64 tff(2371,plain,
% 1.44/1.64 (b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2370, 69, 2367, 2359])).
% 1.44/1.64 tff(2372,plain,
% 1.44/1.64 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 1.44/1.64 inference(commutativity,[status(thm)],[])).
% 1.44/1.64 tff(2373,plain,
% 1.44/1.64 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.44/1.64 inference(symmetry,[status(thm)],[2372])).
% 1.44/1.64 tff(2374,plain,
% 1.44/1.64 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1103])).
% 1.44/1.64 tff(2375,plain,
% 1.44/1.64 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2374, 1])).
% 1.44/1.64 tff(2376,plain,
% 1.44/1.64 ((s(s(s(s(z)))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[2375])).
% 1.44/1.64 tff(2377,plain,
% 1.44/1.64 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2376, 2373])).
% 1.44/1.64 tff(2378,plain,
% 1.44/1.64 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2377])).
% 1.44/1.64 tff(2379,plain,
% 1.44/1.64 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[153, 2378])).
% 1.44/1.64 tff(2380,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2381,plain,
% 1.44/1.64 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2382,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2381])).
% 1.44/1.64 tff(2383,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2382, 2380])).
% 1.44/1.64 tff(2384,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2385,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2384, 2383])).
% 1.44/1.64 tff(2386,plain,
% 1.44/1.64 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2385, 268, 1132, 2360])).
% 1.44/1.64 tff(2387,plain,
% 1.44/1.64 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2269])).
% 1.44/1.64 tff(2388,plain,
% 1.44/1.64 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.64 inference(symmetry,[status(thm)],[2387])).
% 1.44/1.64 tff(2389,assumption,(r(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 1.44/1.64 tff(2390,plain,
% 1.44/1.64 (r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2389, 2388])).
% 1.44/1.64 tff(2391,assumption,(~r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.44/1.64 tff(2392,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2391, 2390])).
% 1.44/1.64 tff(2393,plain,(r(s(s(s(s(z)))), s(s(z))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(2394,plain,
% 1.44/1.64 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2393, 2386, 1100])).
% 1.44/1.64 tff(2395,plain,
% 1.44/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2396,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2397,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2396, 2395])).
% 1.44/1.64 tff(2398,plain,
% 1.44/1.64 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2397, 69])).
% 1.44/1.64 tff(2399,plain,
% 1.44/1.64 (b(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2398, 2394, 2379])).
% 1.44/1.64 tff(2400,plain,
% 1.44/1.64 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1103])).
% 1.44/1.64 tff(2401,assumption,(b(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 1.44/1.64 tff(2402,plain,
% 1.44/1.64 (b(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2401, 2400])).
% 1.44/1.64 tff(2403,assumption,(~b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.44/1.64 tff(2404,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2403, 2402])).
% 1.44/1.64 tff(2405,plain,((~b(s(s(s(s(z)))), s(elem!1))) | b(s(s(s(s(z)))), s(s(z))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(2406,plain,
% 1.44/1.64 (b(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2405, 2399, 1100])).
% 1.44/1.64 tff(2407,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2408,plain,
% 1.44/1.64 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2409,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2408])).
% 1.44/1.64 tff(2410,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2409, 2407])).
% 1.44/1.64 tff(2411,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2412,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2411, 2410])).
% 1.44/1.64 tff(2413,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2412, 268, 1132, 301, 258])).
% 1.44/1.64 tff(2414,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(2415,plain,
% 1.44/1.64 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2414, 258, 1132])).
% 1.44/1.64 tff(2416,plain,
% 1.44/1.64 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[328, 2415])).
% 1.44/1.64 tff(2417,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(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2418,plain,
% 1.44/1.64 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2419,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(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(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(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2418])).
% 1.44/1.64 tff(2420,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(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(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(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2419, 2417])).
% 1.44/1.64 tff(2421,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(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2422,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(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2421, 2420])).
% 1.44/1.64 tff(2423,plain,
% 1.44/1.64 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2422, 453, 2416, 2406, 2371])).
% 1.44/1.64 tff(2424,plain,
% 1.44/1.64 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2423, 2355])).
% 1.44/1.64 tff(2425,plain,
% 1.44/1.64 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[659, 2424, 2275])).
% 1.44/1.64 tff(2426,plain,
% 1.44/1.64 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2425, 2347])).
% 1.44/1.64 tff(2427,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2428,plain,
% 1.44/1.64 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2429,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2428])).
% 1.44/1.64 tff(2430,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2429, 2427])).
% 1.44/1.64 tff(2431,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2432,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2431, 2430])).
% 1.44/1.64 tff(2433,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2432, 268, 258, 2360, 2426])).
% 1.44/1.64 tff(2434,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~(elem!1 = s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(2435,plain,
% 1.44/1.64 (~r(s(s(z)), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2434, 258, 1100, 1132])).
% 1.44/1.64 tff(2436,plain,
% 1.44/1.64 (~r(s(elem!1), elem!1)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2435, 2299])).
% 1.44/1.64 tff(2437,plain,
% 1.44/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2438,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2439,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2438, 2437])).
% 1.44/1.64 tff(2440,plain,
% 1.44/1.64 ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2439, 69])).
% 1.44/1.64 tff(2441,plain,
% 1.44/1.64 (b(s(elem!1), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2440, 2436, 2354])).
% 1.44/1.64 tff(2442,plain,
% 1.44/1.64 ((s(z) = s(s(z))) <=> (elem!1 = s(elem!1))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2290, 2351, 1028])).
% 1.44/1.64 tff(2443,plain,
% 1.44/1.64 ((~(s(z) = s(s(z)))) <=> (~(elem!1 = s(elem!1)))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2442])).
% 1.44/1.64 tff(2444,plain,
% 1.44/1.64 (~(elem!1 = s(elem!1))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[752, 2443])).
% 1.44/1.64 tff(2445,plain,
% 1.44/1.64 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1100])).
% 1.44/1.64 tff(2446,plain,
% 1.44/1.64 (r(s(z), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.44/1.64 inference(symmetry,[status(thm)],[2445])).
% 1.44/1.64 tff(2447,plain,
% 1.44/1.64 (r(s(z), s(s(z))) <=> r(s(z), s(elem!1))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2269])).
% 1.44/1.64 tff(2448,plain,
% 1.44/1.64 (r(s(z), s(s(z))) <=> r(elem!1, s(elem!1))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2447, 2446])).
% 1.44/1.64 tff(2449,plain,
% 1.44/1.64 ((~r(s(z), s(s(z)))) <=> (~r(elem!1, s(elem!1)))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2448])).
% 1.44/1.64 tff(2450,assumption,(s(s(s(s(z)))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.44/1.64 tff(2451,plain,
% 1.44/1.64 (s(s(s(s(s(z))))) = s(s(s(s(z))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[2450])).
% 1.44/1.64 tff(2452,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[319, 2451])).
% 1.44/1.64 tff(2453,plain,(~(s(s(s(s(z)))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(2454,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2455,plain,
% 1.44/1.64 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2456,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2455])).
% 1.44/1.65 tff(2457,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[2456, 2454])).
% 1.44/1.65 tff(2458,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2459,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2458, 2457])).
% 1.44/1.65 tff(2460,plain,
% 1.44/1.65 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2459, 268, 1132, 258])).
% 1.44/1.65 tff(2461,plain,
% 1.44/1.65 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2462,plain,
% 1.44/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2463,plain,
% 1.44/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2462, 2461])).
% 1.44/1.65 tff(2464,plain,
% 1.44/1.65 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2463, 69, 2460, 2453])).
% 1.44/1.65 tff(2465,plain,
% 1.44/1.65 (b(s(s(z)), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[720, 69, 717, 2435])).
% 1.44/1.65 tff(2466,plain,
% 1.44/1.65 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2272])).
% 1.44/1.65 tff(2467,plain,
% 1.44/1.65 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[52, 2466])).
% 1.44/1.65 tff(2468,assumption,(r(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 1.44/1.65 tff(2469,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2470,plain,
% 1.44/1.65 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(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(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2471,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2470])).
% 1.44/1.65 tff(2472,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[2471, 2469])).
% 1.44/1.65 tff(2473,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2474,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2473, 2472])).
% 1.44/1.65 tff(2475,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2474, 268, 258, 733, 2468])).
% 1.44/1.65 tff(2476,plain,((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(2477,plain,
% 1.44/1.65 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2476, 733, 258])).
% 1.44/1.65 tff(2478,plain,
% 1.44/1.65 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2269])).
% 1.44/1.65 tff(2479,plain,
% 1.44/1.65 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 1.44/1.65 inference(symmetry,[status(thm)],[2478])).
% 1.44/1.65 tff(2480,assumption,(r(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 1.44/1.65 tff(2481,plain,
% 1.44/1.65 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2480, 2479])).
% 1.44/1.65 tff(2482,assumption,(~r(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 1.44/1.65 tff(2483,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2482, 2481])).
% 1.44/1.65 tff(2484,plain,(r(s(s(s(s(s(z))))), s(s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(2485,plain,
% 1.44/1.65 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2484, 2477, 1100])).
% 1.44/1.65 tff(2486,plain,
% 1.44/1.65 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2142, 2485, 2467])).
% 1.44/1.65 tff(2487,plain,
% 1.44/1.65 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2269])).
% 1.44/1.65 tff(2488,plain,
% 1.44/1.65 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 1.44/1.65 inference(symmetry,[status(thm)],[2487])).
% 1.44/1.65 tff(2489,plain,
% 1.44/1.65 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2129, 2488])).
% 1.44/1.65 tff(2490,assumption,(~b(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 1.44/1.65 tff(2491,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2490, 2489])).
% 1.44/1.65 tff(2492,plain,(b(s(s(s(s(s(z))))), s(s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(2493,plain,
% 1.44/1.65 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2492, 2486, 1100])).
% 1.44/1.65 tff(2494,assumption,(b(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 1.44/1.65 tff(2495,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 1.44/1.65 tff(2496,assumption,(b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.44/1.65 tff(2497,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.44/1.65 tff(2498,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(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2499,plain,
% 1.44/1.65 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2500,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(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(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(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2499])).
% 1.44/1.65 tff(2501,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(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(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(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[2500, 2498])).
% 1.44/1.65 tff(2502,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(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2503,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2502, 2501])).
% 1.44/1.65 tff(2504,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2503, 453, 2497, 2496, 2495, 2494])).
% 1.44/1.65 tff(2505,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(2506,plain,
% 1.44/1.65 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2505, 2493, 2465, 2464])).
% 1.44/1.65 tff(2507,plain,
% 1.44/1.65 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2405, 2506, 1100])).
% 1.44/1.65 tff(2508,plain,
% 1.44/1.65 (r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2398, 2507, 2379])).
% 1.44/1.65 tff(2509,plain,
% 1.44/1.65 (r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2393, 2508, 1100])).
% 1.44/1.65 tff(2510,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2511,plain,
% 1.44/1.65 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2512,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2511])).
% 1.44/1.65 tff(2513,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[2512, 2510])).
% 1.44/1.65 tff(2514,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2515,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2514, 2513])).
% 1.44/1.65 tff(2516,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2515, 268, 1132, 733, 2509])).
% 1.44/1.65 tff(2517,plain,((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~(elem!1 = s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(2518,plain,
% 1.44/1.65 (~r(s(z), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2517, 258, 1100, 1132])).
% 1.44/1.65 tff(2519,plain,
% 1.44/1.65 (~r(elem!1, s(elem!1))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2518, 2449])).
% 1.44/1.65 tff(2520,plain,
% 1.44/1.65 (b(elem!1, s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1069, 2519, 2444])).
% 1.44/1.65 tff(2521,plain,
% 1.44/1.65 (~b(s(elem!1), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1079, 2520, 909, 2441])).
% 1.44/1.65 tff(2522,plain,
% 1.44/1.65 (r(s(elem!1), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[440, 2521, 2288])).
% 1.44/1.65 tff(2523,plain,
% 1.44/1.65 (r(s(s(z)), s(s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2522, 2276])).
% 1.44/1.65 tff(2524,plain,
% 1.44/1.65 (b(s(z), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[757, 2518])).
% 1.44/1.65 tff(2525,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(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2526,plain,
% 1.44/1.65 (((~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(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2527,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(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(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2526])).
% 1.44/1.65 tff(2528,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(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(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[2527, 2525])).
% 1.44/1.65 tff(2529,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(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2530,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(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2529, 2528])).
% 1.44/1.65 tff(2531,plain,
% 1.44/1.65 (~b(s(s(s(z))), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2530, 453, 2524, 120, 2465])).
% 1.44/1.65 tff(2532,plain,
% 1.44/1.65 (((~![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))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2533,plain,
% 1.44/1.65 ((~![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))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2534,plain,
% 1.44/1.65 ((~![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)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2533, 2532])).
% 1.44/1.65 tff(2535,plain,
% 1.44/1.65 (r(s(s(s(z))), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2534, 69, 160, 2531])).
% 1.44/1.65 tff(2536,plain,
% 1.44/1.65 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2269])).
% 1.44/1.65 tff(2537,plain,
% 1.44/1.65 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[2536, 1307])).
% 1.44/1.65 tff(2538,plain,
% 1.44/1.65 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(z)))),
% 1.44/1.65 inference(symmetry,[status(thm)],[2537])).
% 1.44/1.65 tff(2539,plain,
% 1.44/1.65 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(z))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2538])).
% 1.44/1.65 tff(2540,plain,
% 1.44/1.65 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 1.44/1.65 inference(symmetry,[status(thm)],[1433])).
% 1.44/1.65 tff(2541,plain,
% 1.44/1.65 (s(s(s(s(s(s(s(z))))))) = s(s(z))),
% 1.44/1.65 inference(transitivity,[status(thm)],[2540, 1103])).
% 1.44/1.65 tff(2542,plain,
% 1.44/1.65 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(z)))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2541])).
% 1.44/1.65 tff(2543,plain,
% 1.44/1.65 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.44/1.65 inference(symmetry,[status(thm)],[2542])).
% 1.44/1.65 tff(2544,plain,
% 1.44/1.65 (s(z) = s(s(s(s(s(s(z))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[29, 2543, 1174])).
% 1.44/1.65 tff(2545,plain,
% 1.44/1.65 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2544])).
% 1.44/1.65 tff(2546,plain,
% 1.44/1.65 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 1.44/1.65 inference(symmetry,[status(thm)],[2545])).
% 1.44/1.65 tff(2547,plain,
% 1.44/1.65 (s(s(s(s(s(z))))) = z),
% 1.44/1.65 inference(transitivity,[status(thm)],[808, 2546, 32])).
% 1.44/1.65 tff(2548,plain,
% 1.44/1.65 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2549,plain,
% 1.44/1.65 (~(s(s(s(s(s(z))))) = z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2548, 46])).
% 1.44/1.65 tff(2550,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2549, 2547])).
% 1.44/1.65 tff(2551,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(2552,plain,
% 1.44/1.65 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2551, 1100])).
% 1.44/1.65 tff(2553,plain,
% 1.44/1.65 (~(s(s(s(s(s(s(s(z))))))) = s(s(z)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2552, 2539])).
% 1.44/1.65 tff(2554,plain,
% 1.44/1.65 (~b(s(s(s(z))), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2530, 453, 1008, 120, 2495])).
% 1.44/1.65 tff(2555,plain,
% 1.44/1.65 (r(s(s(s(z))), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2534, 69, 160, 2554])).
% 1.44/1.65 tff(2556,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2557,plain,
% 1.44/1.65 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2558,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2557])).
% 1.44/1.65 tff(2559,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[2558, 2556])).
% 1.44/1.65 tff(2560,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2561,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2560, 2559])).
% 1.44/1.65 tff(2562,plain,
% 1.44/1.65 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2561, 268, 2468, 2555])).
% 1.44/1.65 tff(2563,plain,
% 1.44/1.65 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.44/1.65 inference(symmetry,[status(thm)],[57])).
% 1.44/1.65 tff(2564,plain,
% 1.44/1.65 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(s(z)))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2563])).
% 1.44/1.65 tff(2565,plain,
% 1.44/1.65 (~(s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[111, 2564])).
% 1.44/1.65 tff(2566,plain,
% 1.44/1.65 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2567,plain,
% 1.44/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2568,plain,
% 1.44/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2567, 2566])).
% 1.44/1.66 tff(2569,plain,
% 1.44/1.66 ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2568, 69])).
% 1.44/1.66 tff(2570,plain,
% 1.44/1.66 (b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2569, 2565])).
% 1.44/1.66 tff(2571,plain,
% 1.44/1.66 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2570, 2562])).
% 1.44/1.66 tff(2572,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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2573,plain,
% 1.44/1.66 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2574,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[2573])).
% 1.44/1.66 tff(2575,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[2574, 2572])).
% 1.44/1.66 tff(2576,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(2577,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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2576, 2575])).
% 1.44/1.66 tff(2578,plain,
% 1.44/1.66 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2577, 453, 1780, 2497, 2571])).
% 1.44/1.66 tff(2579,plain,
% 1.44/1.66 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1656, 2578])).
% 1.44/1.66 tff(2580,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.44/1.66 tff(2581,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), 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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2582,plain,
% 1.44/1.66 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(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))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2583,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), 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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[2582])).
% 1.44/1.66 tff(2584,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), 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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[2583, 2581])).
% 1.44/1.66 tff(2585,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(2586,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2585, 2584])).
% 1.44/1.66 tff(2587,plain,
% 1.44/1.66 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2586, 268, 2468, 2555])).
% 1.44/1.66 tff(2588,plain,
% 1.44/1.66 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[687, 2587])).
% 1.44/1.66 tff(2589,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(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2590,plain,
% 1.44/1.66 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2591,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(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[2590])).
% 1.44/1.66 tff(2592,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(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[2591, 2589])).
% 1.44/1.66 tff(2593,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(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(2594,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2593, 2592])).
% 1.44/1.66 tff(2595,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2594, 453, 523, 1291, 1779, 2497])).
% 1.44/1.66 tff(2596,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(2597,plain,
% 1.44/1.66 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2596, 2588, 1291, 2497])).
% 1.44/1.66 tff(2598,plain,
% 1.44/1.66 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[518, 2597])).
% 1.44/1.66 tff(2599,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2600,plain,
% 1.44/1.66 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2601,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[2600])).
% 1.44/1.66 tff(2602,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[2601, 2599])).
% 1.44/1.66 tff(2603,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(2604,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2603, 2602])).
% 1.44/1.66 tff(2605,plain,
% 1.44/1.66 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2604, 268, 2598, 2580])).
% 1.44/1.66 tff(2606,plain,
% 1.44/1.66 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2393, 2605, 1100])).
% 1.44/1.66 tff(2607,plain,
% 1.44/1.66 (b(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2398, 2606, 2379])).
% 1.44/1.66 tff(2608,plain,
% 1.44/1.66 (b(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2405, 2607, 1100])).
% 1.44/1.66 tff(2609,plain,
% 1.44/1.66 (~b(s(z), s(s(s(s(z)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2068, 453, 1008, 2608, 2495])).
% 1.44/1.66 tff(2610,plain,
% 1.44/1.66 (r(s(z), s(s(s(s(z)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1677, 69, 50, 2609])).
% 1.44/1.66 tff(2611,assumption,(b(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.44/1.66 tff(2612,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(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2613,plain,
% 1.44/1.66 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2614,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[2613])).
% 1.44/1.66 tff(2615,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[2614, 2612])).
% 1.44/1.66 tff(2616,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(2617,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2616, 2615])).
% 1.44/1.66 tff(2618,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2617, 453, 443, 1779, 2611, 120])).
% 1.44/1.66 tff(2619,plain,((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(2620,plain,
% 1.44/1.66 (~b(s(z), s(s(s(s(s(z))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2619, 2571, 120, 2588])).
% 1.44/1.66 tff(2621,plain,
% 1.44/1.66 (r(s(z), s(s(s(s(s(z))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[372, 2620])).
% 1.44/1.66 tff(2622,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2623,plain,
% 1.44/1.66 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2624,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[2623])).
% 1.44/1.66 tff(2625,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[2624, 2622])).
% 1.44/1.66 tff(2626,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(2627,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2626, 2625])).
% 1.44/1.66 tff(2628,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2627, 268, 11, 1132, 2246, 257])).
% 1.44/1.66 tff(2629,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(2630,plain,
% 1.44/1.66 (~r(s(z), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2629, 2621, 1132, 2598])).
% 1.44/1.66 tff(2631,plain,
% 1.44/1.66 (b(s(z), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[227, 2630])).
% 1.44/1.66 tff(2632,assumption,(s(s(s(s(s(s(s(z))))))) = s(z)), introduced(assumption)).
% 1.44/1.66 tff(2633,plain,
% 1.44/1.67 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(z))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2632])).
% 1.44/1.67 tff(2634,plain,
% 1.44/1.67 (s(s(s(s(s(s(z)))))) = z),
% 1.44/1.67 inference(transitivity,[status(thm)],[1375, 2633, 32])).
% 1.44/1.67 tff(2635,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2341, 2634])).
% 1.44/1.67 tff(2636,plain,(~(s(s(s(s(s(s(s(z))))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2637,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.44/1.67 tff(2638,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2639,plain,
% 1.44/1.67 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2640,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2639])).
% 1.44/1.67 tff(2641,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[2640, 2638])).
% 1.44/1.67 tff(2642,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(2643,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[2642, 2641])).
% 1.44/1.67 tff(2644,plain,
% 1.44/1.67 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2643, 268, 2246, 376, 2637])).
% 1.44/1.67 tff(2645,plain,
% 1.44/1.67 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2646,plain,
% 1.44/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(2647,plain,
% 1.44/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[2646, 2645])).
% 1.44/1.67 tff(2648,plain,
% 1.44/1.67 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2647, 69, 2644, 2636])).
% 1.44/1.67 tff(2649,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2650,plain,
% 1.44/1.67 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2651,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2650])).
% 1.44/1.67 tff(2652,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[2651, 2649])).
% 1.44/1.67 tff(2653,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(2654,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[2653, 2652])).
% 1.44/1.67 tff(2655,plain,
% 1.44/1.67 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2654, 268, 300, 2637])).
% 1.44/1.67 tff(2656,plain,
% 1.44/1.67 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(z))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[1175])).
% 1.44/1.67 tff(2657,plain,
% 1.44/1.67 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.44/1.67 inference(symmetry,[status(thm)],[2656])).
% 1.44/1.67 tff(2658,plain,
% 1.44/1.67 (s(s(z)) = s(s(s(s(s(s(z))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[98, 2657, 1174])).
% 1.44/1.67 tff(2659,plain,
% 1.44/1.67 (s(z) = s(s(s(s(s(z)))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[29, 806, 183])).
% 1.44/1.67 tff(2660,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[289, 2659])).
% 1.44/1.67 tff(2661,plain,(~(s(s(z)) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2662,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2661, 2658])).
% 1.44/1.67 tff(2663,plain,(~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2664,plain,
% 1.44/1.67 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1238, 69, 2663, 2655])).
% 1.44/1.67 tff(2665,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(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(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(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2666,plain,
% 1.44/1.67 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2667,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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(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(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2666])).
% 1.44/1.67 tff(2668,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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(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(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[2667, 2665])).
% 1.44/1.67 tff(2669,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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(2670,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[2669, 2668])).
% 1.44/1.67 tff(2671,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2670, 453, 2611, 2090, 2664, 2648])).
% 1.44/1.67 tff(2672,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2673,plain,
% 1.44/1.67 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2672, 2571, 2631, 2621, 2610, 2579])).
% 1.44/1.67 tff(2674,plain,
% 1.44/1.67 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 1.44/1.67 inference(commutativity,[status(thm)],[])).
% 1.44/1.67 tff(2675,plain,
% 1.44/1.67 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 1.44/1.67 inference(symmetry,[status(thm)],[2674])).
% 1.44/1.67 tff(2676,plain,
% 1.44/1.67 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2675])).
% 1.44/1.67 tff(2677,assumption,(s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.44/1.67 tff(2678,plain,
% 1.44/1.67 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(s(z))))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2677])).
% 1.44/1.67 tff(2679,plain,
% 1.44/1.67 (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(z)))))),
% 1.44/1.67 inference(symmetry,[status(thm)],[2678])).
% 1.44/1.67 tff(2680,assumption,(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.44/1.67 tff(2681,plain,
% 1.44/1.67 (inj_0(s(s(s(s(s(s(s(s(z))))))))) = inj_0(s(s(s(s(s(z))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2680])).
% 1.44/1.67 tff(2682,plain,
% 1.44/1.67 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[2336, 2681, 23])).
% 1.44/1.67 tff(2683,plain,
% 1.44/1.67 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2682])).
% 1.44/1.67 tff(2684,plain,
% 1.44/1.67 (s(s(s(s(s(s(z)))))) = s(s(s(z)))),
% 1.44/1.67 inference(transitivity,[status(thm)],[1375, 2683, 37])).
% 1.44/1.67 tff(2685,plain,
% 1.44/1.67 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(z))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2684])).
% 1.44/1.67 tff(2686,plain,
% 1.44/1.67 (s(s(s(s(s(z))))) = s(s(z))),
% 1.44/1.67 inference(transitivity,[status(thm)],[808, 2685, 97])).
% 1.44/1.67 tff(2687,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[52, 2686])).
% 1.44/1.67 tff(2688,plain,(~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2689,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2688, 2679])).
% 1.44/1.67 tff(2690,plain,(~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2691,plain,
% 1.44/1.67 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[2690, 2676])).
% 1.44/1.67 tff(2692,plain,
% 1.44/1.67 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2693,plain,
% 1.44/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(2694,plain,
% 1.44/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[2693, 2692])).
% 1.44/1.67 tff(2695,plain,
% 1.44/1.67 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2694, 69])).
% 1.44/1.67 tff(2696,plain,
% 1.44/1.67 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2695, 2691])).
% 1.44/1.67 tff(2697,plain,
% 1.44/1.67 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2696, 2673])).
% 1.44/1.67 tff(2698,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(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2699,plain,
% 1.44/1.67 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2700,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(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2699])).
% 1.44/1.67 tff(2701,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(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[2700, 2698])).
% 1.44/1.67 tff(2702,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(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(2703,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(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[2702, 2701])).
% 1.44/1.67 tff(2704,plain,
% 1.44/1.67 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2703, 453, 1780, 2497, 2697])).
% 1.44/1.67 tff(2705,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.44/1.67 tff(2706,plain,
% 1.44/1.67 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(s(s(z))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2705])).
% 1.44/1.67 tff(2707,plain,
% 1.44/1.67 (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2705])).
% 1.44/1.67 tff(2708,plain,
% 1.44/1.67 (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(z))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[2707, 1375, 2706, 23])).
% 1.44/1.67 tff(2709,assumption,(s(s(s(s(z)))) = s(s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.44/1.67 tff(2710,plain,
% 1.44/1.67 (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(z))))),
% 1.44/1.67 inference(symmetry,[status(thm)],[2709])).
% 1.44/1.67 tff(2711,plain,
% 1.44/1.67 (inj_0(s(s(s(s(s(s(s(s(z))))))))) = inj_0(s(s(s(s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2710])).
% 1.44/1.67 tff(2712,plain,
% 1.44/1.67 (s(s(s(s(s(s(s(z))))))) = s(s(s(z)))),
% 1.44/1.67 inference(transitivity,[status(thm)],[2336, 2711, 37])).
% 1.44/1.67 tff(2713,plain,
% 1.44/1.67 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(z))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2712])).
% 1.44/1.67 tff(2714,plain,
% 1.44/1.67 (s(s(s(s(s(s(z)))))) = s(s(z))),
% 1.44/1.67 inference(transitivity,[status(thm)],[1375, 2713, 97])).
% 1.44/1.67 tff(2715,plain,
% 1.44/1.67 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(z)))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2714])).
% 1.44/1.67 tff(2716,plain,
% 1.44/1.67 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.44/1.67 inference(symmetry,[status(thm)],[2715])).
% 1.44/1.67 tff(2717,plain,
% 1.44/1.67 (s(z) = s(s(s(s(s(z)))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[29, 2716, 183])).
% 1.44/1.67 tff(2718,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[289, 2717])).
% 1.44/1.67 tff(2719,plain,(~(s(s(s(s(z)))) = s(s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2720,plain,
% 1.44/1.67 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(z)))))),
% 1.44/1.67 inference(commutativity,[status(thm)],[])).
% 1.44/1.67 tff(2721,plain,
% 1.44/1.67 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(s(z)))))))))),
% 1.44/1.67 inference(symmetry,[status(thm)],[2720])).
% 1.44/1.67 tff(2722,assumption,(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(z))))), introduced(assumption)).
% 1.44/1.67 tff(2723,plain,
% 1.44/1.67 (s(s(s(s(z)))) = s(s(s(s(s(s(s(s(z))))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[2722, 2721])).
% 1.44/1.67 tff(2724,assumption,(~(s(s(s(s(z)))) = s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 1.44/1.67 tff(2725,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2724, 2723])).
% 1.44/1.67 tff(2726,plain,((~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2727,plain,
% 1.44/1.67 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2726, 2719])).
% 1.44/1.67 tff(2728,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2727, 2708])).
% 1.44/1.67 tff(2729,plain,(~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(2730,plain,
% 1.44/1.67 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(2731,plain,
% 1.44/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(2732,plain,
% 1.44/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[2731, 2730])).
% 1.44/1.67 tff(2733,plain,
% 1.44/1.67 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2732, 69, 2729, 2704])).
% 1.44/1.67 tff(2734,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(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(2735,plain,
% 1.44/1.67 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(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(2736,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2735])).
% 1.44/1.67 tff(2737,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[2736, 2734])).
% 1.44/1.68 tff(2738,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(2739,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2738, 2737])).
% 1.44/1.68 tff(2740,plain,
% 1.44/1.68 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2739, 268, 2598, 2580])).
% 1.44/1.68 tff(2741,plain,
% 1.44/1.68 (b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2370, 69, 2740, 2359])).
% 1.44/1.68 tff(2742,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(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(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2743,plain,
% 1.44/1.68 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2744,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(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(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2743])).
% 1.44/1.68 tff(2745,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(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(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[2744, 2742])).
% 1.44/1.68 tff(2746,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(2747,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2746, 2745])).
% 1.44/1.68 tff(2748,plain,
% 1.44/1.68 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2747, 453, 1780, 2497, 2741])).
% 1.44/1.68 tff(2749,plain,
% 1.44/1.68 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2748, 2355])).
% 1.44/1.68 tff(2750,plain,
% 1.44/1.68 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[659, 2749, 2275])).
% 1.44/1.68 tff(2751,plain,
% 1.44/1.68 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2750, 2347])).
% 1.44/1.68 tff(2752,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2753,plain,
% 1.44/1.68 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2754,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2753])).
% 1.44/1.68 tff(2755,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[2754, 2752])).
% 1.44/1.68 tff(2756,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(2757,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2756, 2755])).
% 1.44/1.68 tff(2758,plain,
% 1.44/1.68 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2757, 268, 2580, 2751, 2733])).
% 1.44/1.68 tff(2759,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2760,plain,
% 1.44/1.68 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2761,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2760])).
% 1.44/1.68 tff(2762,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[2761, 2759])).
% 1.44/1.68 tff(2763,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(2764,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2763, 2762])).
% 1.44/1.68 tff(2765,plain,
% 1.44/1.68 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2764, 453, 2497, 2697, 2741])).
% 1.44/1.68 tff(2766,plain,
% 1.44/1.68 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1369, 69, 2765])).
% 1.44/1.68 tff(2767,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2766, 2758, 2553])).
% 1.44/1.68 tff(2768,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~(elem!1 = s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(2769,plain,
% 1.44/1.68 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2768, 2523, 1100, 2464, 2416, 2524, 2465, 1132, 1291, 120])).
% 1.44/1.68 tff(2770,plain,
% 1.44/1.68 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2484, 2769, 1100])).
% 1.44/1.68 tff(2771,plain,
% 1.44/1.68 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2142, 2770, 2467])).
% 1.44/1.68 tff(2772,plain,
% 1.44/1.68 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2492, 2771, 1100])).
% 1.44/1.68 tff(2773,plain,
% 1.44/1.68 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2505, 2772, 2465, 2464])).
% 1.44/1.68 tff(2774,plain,
% 1.44/1.68 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2405, 2773, 1100])).
% 1.44/1.68 tff(2775,plain,
% 1.44/1.68 (r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2398, 2774, 2379])).
% 1.44/1.68 tff(2776,plain,
% 1.44/1.68 (r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2393, 2775, 1100])).
% 1.44/1.68 tff(2777,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2778,plain,
% 1.44/1.68 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2779,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2778])).
% 1.44/1.68 tff(2780,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[2779, 2777])).
% 1.44/1.68 tff(2781,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(2782,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2781, 2780])).
% 1.44/1.68 tff(2783,plain,
% 1.44/1.68 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2782, 268, 2776, 2535])).
% 1.44/1.68 tff(2784,plain,
% 1.44/1.68 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[518, 2783])).
% 1.44/1.68 tff(2785,plain,
% 1.44/1.68 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2596, 2784, 1291, 2464])).
% 1.44/1.68 tff(2786,plain,
% 1.44/1.68 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[687, 2785])).
% 1.44/1.68 tff(2787,assumption,(r(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.44/1.68 tff(2788,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2789,plain,
% 1.44/1.68 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2790,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(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(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2789])).
% 1.44/1.68 tff(2791,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(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(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[2790, 2788])).
% 1.44/1.68 tff(2792,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(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(z)), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(2793,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2792, 2791])).
% 1.44/1.68 tff(2794,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2793, 268, 256, 2580, 2787])).
% 1.44/1.68 tff(2795,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(2796,plain,
% 1.44/1.68 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2795, 2786, 2523])).
% 1.44/1.68 tff(2797,plain,
% 1.44/1.68 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2796, 2349])).
% 1.44/1.68 tff(2798,plain,
% 1.44/1.68 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[659, 2797, 2275])).
% 1.44/1.68 tff(2799,plain,
% 1.44/1.68 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2798, 2271])).
% 1.44/1.68 tff(2800,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2801,plain,
% 1.44/1.68 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2802,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2801])).
% 1.44/1.68 tff(2803,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[2802, 2800])).
% 1.44/1.68 tff(2804,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(2805,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2804, 2803])).
% 1.44/1.68 tff(2806,plain,
% 1.44/1.68 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2805, 268, 2776, 2535])).
% 1.44/1.68 tff(2807,plain,
% 1.44/1.68 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1656, 2806])).
% 1.44/1.68 tff(2808,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2809,plain,
% 1.44/1.68 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(2810,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[2809])).
% 1.44/1.68 tff(2811,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[2810, 2808])).
% 1.44/1.68 tff(2812,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2813,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2812, 2811])).
% 1.44/1.69 tff(2814,plain,
% 1.44/1.69 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2813, 453, 2784, 2807, 2416, 2464, 2799])).
% 1.44/1.69 tff(2815,plain,
% 1.44/1.69 (r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2370, 69, 2359, 2814])).
% 1.44/1.69 tff(2816,assumption,(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))), introduced(assumption)).
% 1.44/1.69 tff(2817,plain,
% 1.44/1.69 (inj_0(s(s(s(s(s(s(s(s(z))))))))) = inj_0(s(s(s(z))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2816])).
% 1.44/1.69 tff(2818,plain,
% 1.44/1.69 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(s(s(z)))))))))),
% 1.44/1.69 inference(symmetry,[status(thm)],[2817])).
% 1.44/1.69 tff(2819,plain,
% 1.44/1.69 (s(elem!1) = s(s(s(s(s(s(s(z)))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[1103, 98, 2818, 2335])).
% 1.44/1.69 tff(2820,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1442, 2819])).
% 1.44/1.69 tff(2821,plain,((~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(2822,plain,
% 1.44/1.69 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2821, 1100, 2552])).
% 1.44/1.69 tff(2823,assumption,(b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.44/1.69 tff(2824,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(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2825,plain,
% 1.44/1.69 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2826,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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2825])).
% 1.44/1.69 tff(2827,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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[2826, 2824])).
% 1.44/1.69 tff(2828,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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2829,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(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2828, 2827])).
% 1.44/1.69 tff(2830,plain,
% 1.44/1.69 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2829, 453, 523, 1780, 2823])).
% 1.44/1.69 tff(2831,plain,
% 1.44/1.69 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2832,plain,
% 1.44/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2833,plain,
% 1.44/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2832, 2831])).
% 1.44/1.69 tff(2834,plain,
% 1.44/1.69 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2833, 69, 2688, 2830])).
% 1.44/1.69 tff(2835,assumption,(~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))), introduced(assumption)).
% 1.44/1.69 tff(2836,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(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2837,plain,
% 1.44/1.69 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2838,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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2837])).
% 1.44/1.69 tff(2839,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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[2838, 2836])).
% 1.44/1.69 tff(2840,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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2841,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(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2840, 2839])).
% 1.44/1.69 tff(2842,plain,
% 1.44/1.69 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2841, 453, 523, 1633, 2823])).
% 1.44/1.69 tff(2843,plain,
% 1.44/1.69 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2844,plain,
% 1.44/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2845,plain,
% 1.44/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2844, 2843])).
% 1.44/1.69 tff(2846,plain,
% 1.44/1.69 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2845, 69])).
% 1.44/1.69 tff(2847,plain,
% 1.44/1.69 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2846, 2842, 2835])).
% 1.44/1.69 tff(2848,plain,
% 1.44/1.69 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1788, 1780, 523, 1633])).
% 1.44/1.69 tff(2849,plain,
% 1.44/1.69 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[687, 2848])).
% 1.44/1.69 tff(2850,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2851,plain,
% 1.44/1.69 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2852,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2851])).
% 1.44/1.69 tff(2853,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[2852, 2850])).
% 1.44/1.69 tff(2854,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2855,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2854, 2853])).
% 1.44/1.69 tff(2856,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2855, 268, 2849, 2847, 2834])).
% 1.44/1.69 tff(2857,plain,((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(2858,plain,
% 1.44/1.69 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2857, 2807, 2416, 2784, 2822])).
% 1.44/1.69 tff(2859,plain,
% 1.44/1.69 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2860,plain,
% 1.44/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2861,plain,
% 1.44/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2860, 2859])).
% 1.44/1.69 tff(2862,plain,
% 1.44/1.69 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2861, 69])).
% 1.44/1.69 tff(2863,plain,
% 1.44/1.69 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2862, 2727])).
% 1.44/1.69 tff(2864,plain,
% 1.44/1.69 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2863, 2858])).
% 1.44/1.69 tff(2865,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2866,plain,
% 1.44/1.69 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(2867,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2866])).
% 1.44/1.69 tff(2868,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[2867, 2865])).
% 1.44/1.69 tff(2869,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(2870,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2869, 2868])).
% 1.44/1.69 tff(2871,plain,
% 1.44/1.69 (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2870, 268, 2864, 2815])).
% 1.44/1.69 tff(2872,plain,
% 1.44/1.69 (~r(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2871, 2346])).
% 1.44/1.69 tff(2873,plain,
% 1.44/1.69 (b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2269])).
% 1.44/1.69 tff(2874,plain,
% 1.44/1.69 ((~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) <=> (~b(s(elem!1), s(s(s(s(s(s(s(s(z))))))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2873])).
% 1.44/1.69 tff(2875,assumption,(s(s(s(s(s(s(s(s(z)))))))) = s(z)), introduced(assumption)).
% 1.44/1.69 tff(2876,plain,
% 1.44/1.69 (s(z) = s(s(s(s(s(s(s(s(z))))))))),
% 1.44/1.69 inference(symmetry,[status(thm)],[2875])).
% 1.44/1.69 tff(2877,assumption,(s(z) = s(s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.44/1.69 tff(2878,plain,
% 1.44/1.69 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(s(s(z)))))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[2877])).
% 1.44/1.69 tff(2879,plain,
% 1.44/1.69 (inj_0(s(s(s(s(s(s(s(s(z))))))))) = inj_0(s(z))),
% 1.44/1.69 inference(symmetry,[status(thm)],[2878])).
% 1.44/1.69 tff(2880,plain,
% 1.44/1.69 (s(s(s(s(s(s(s(z))))))) = z),
% 1.44/1.70 inference(transitivity,[status(thm)],[2336, 2879, 32])).
% 1.44/1.70 tff(2881,plain,
% 1.44/1.70 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(s(z))))))) = z))),
% 1.44/1.70 inference(quant_inst,[status(thm)],[])).
% 1.44/1.70 tff(2882,plain,
% 1.44/1.70 (~(s(s(s(s(s(s(s(z))))))) = z)),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[2881, 46])).
% 1.44/1.70 tff(2883,plain,
% 1.44/1.70 ($false),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[2882, 2880])).
% 1.44/1.70 tff(2884,plain,(~(s(z) = s(s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.70 tff(2885,plain,
% 1.44/1.70 ($false),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[2884, 2876])).
% 1.44/1.70 tff(2886,plain,(~(s(s(s(s(s(s(s(s(z)))))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.70 tff(2887,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(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2888,plain,
% 1.54/1.70 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2889,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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2888])).
% 1.54/1.70 tff(2890,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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[2889, 2887])).
% 1.54/1.70 tff(2891,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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(2892,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2891, 2890])).
% 1.54/1.70 tff(2893,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2892, 453, 523, 1633, 1974, 120])).
% 1.54/1.70 tff(2894,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(2895,plain,
% 1.54/1.70 (~b(s(z), s(s(s(s(z)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2894, 2807, 120, 2784])).
% 1.54/1.70 tff(2896,plain,
% 1.54/1.70 (r(s(z), s(s(s(s(z)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1677, 69, 50, 2895])).
% 1.54/1.70 tff(2897,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2898,plain,
% 1.54/1.70 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2899,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2898])).
% 1.54/1.70 tff(2900,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[2899, 2897])).
% 1.54/1.70 tff(2901,plain,
% 1.54/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(2902,plain,
% 1.54/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2901, 2900])).
% 1.54/1.70 tff(2903,plain,
% 1.54/1.70 (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2902, 268, 2896, 2864])).
% 1.54/1.70 tff(2904,plain,
% 1.54/1.70 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = s(z)) | b(s(s(s(s(s(s(s(s(z)))))))), s(z)) | r(s(s(s(s(s(s(s(s(z)))))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = s(z)) | b(s(s(s(s(s(s(s(s(z)))))))), s(z)) | r(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2905,plain,
% 1.54/1.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = s(z)) | b(s(s(s(s(s(s(s(s(z)))))))), s(z)) | r(s(s(s(s(s(s(s(s(z)))))))), s(z)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(2906,plain,
% 1.54/1.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = s(z)) | b(s(s(s(s(s(s(s(s(z)))))))), s(z)) | r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2905, 2904])).
% 1.54/1.70 tff(2907,plain,
% 1.54/1.70 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2906, 69, 2903, 2886])).
% 1.54/1.70 tff(2908,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(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(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(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2909,plain,
% 1.54/1.70 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2910,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(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(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(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2909])).
% 1.54/1.70 tff(2911,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(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(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(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[2910, 2908])).
% 1.54/1.70 tff(2912,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(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(2913,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(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2912, 2911])).
% 1.54/1.70 tff(2914,plain,
% 1.54/1.70 (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2913, 453, 2524, 2465, 2907])).
% 1.54/1.70 tff(2915,plain,
% 1.54/1.70 (~b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2914, 2874])).
% 1.54/1.70 tff(2916,plain,
% 1.54/1.70 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(s(s(s(z))))))))) | b(s(elem!1), s(s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))) | b(s(elem!1), s(s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(s(s(s(s(s(z))))))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2917,plain,
% 1.54/1.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(s(s(s(z))))))))) | b(s(elem!1), s(s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(s(s(s(s(s(z))))))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(2918,plain,
% 1.54/1.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))) | b(s(elem!1), s(s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2917, 2916])).
% 1.54/1.70 tff(2919,plain,
% 1.54/1.70 ((s(elem!1) = s(s(s(s(s(s(s(s(z))))))))) | b(s(elem!1), s(s(s(s(s(s(s(s(z))))))))) | r(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2918, 69])).
% 1.54/1.70 tff(2920,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2919, 2915, 2872, 2344])).
% 1.54/1.70 tff(2921,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~(elem!1 = s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(2922,plain,
% 1.54/1.70 (~r(s(s(s(s(s(z))))), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2921, 1100, 2329, 2307, 2303, 2322])).
% 1.54/1.70 tff(2923,plain,
% 1.54/1.70 (b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[297, 2922])).
% 1.54/1.70 tff(2924,plain,
% 1.54/1.70 ((~(s(s(s(s(s(z))))) = elem!1)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[55])).
% 1.54/1.70 tff(2925,plain,
% 1.54/1.70 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[637, 2924])).
% 1.54/1.70 tff(2926,plain,
% 1.54/1.70 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[1100])).
% 1.54/1.70 tff(2927,plain,
% 1.54/1.70 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.70 inference(symmetry,[status(thm)],[2926])).
% 1.54/1.70 tff(2928,plain,
% 1.54/1.70 ((~r(s(s(s(s(s(z))))), s(z))) <=> (~r(s(s(s(s(s(z))))), elem!1))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2927])).
% 1.54/1.70 tff(2929,plain,
% 1.54/1.70 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2922, 2928])).
% 1.54/1.70 tff(2930,plain,
% 1.54/1.70 (b(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[643, 2929, 637])).
% 1.54/1.70 tff(2931,plain,
% 1.54/1.70 ((~r(s(s(s(z))), s(z))) <=> (~r(s(s(elem!1)), s(z)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2318])).
% 1.54/1.70 tff(2932,plain,
% 1.54/1.70 (~r(s(s(elem!1)), s(z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2306, 2931])).
% 1.54/1.70 tff(2933,plain,
% 1.54/1.70 (b(s(s(elem!1)), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1047, 2932])).
% 1.54/1.70 tff(2934,plain,
% 1.54/1.70 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2596, 1779, 1291, 523])).
% 1.54/1.70 tff(2935,plain,
% 1.54/1.70 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2463, 69, 2934, 2453])).
% 1.54/1.70 tff(2936,plain,
% 1.54/1.70 (~r(s(z), s(s(s(s(s(z))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2254, 2935, 1132])).
% 1.54/1.70 tff(2937,plain,
% 1.54/1.70 (b(s(z), s(s(s(s(s(z))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[372, 2936])).
% 1.54/1.70 tff(2938,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(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2939,plain,
% 1.54/1.70 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2940,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(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2939])).
% 1.54/1.70 tff(2941,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(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[2940, 2938])).
% 1.54/1.70 tff(2942,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(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(2943,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2942, 2941])).
% 1.54/1.70 tff(2944,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2943, 453, 2937, 1779, 374, 120])).
% 1.54/1.70 tff(2945,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(2946,plain,
% 1.54/1.70 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2945, 523, 120, 1132, 1291, 374])).
% 1.54/1.70 tff(2947,plain,
% 1.54/1.70 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[687, 2946])).
% 1.54/1.70 tff(2948,plain,
% 1.54/1.70 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[1103, 1104])).
% 1.54/1.70 tff(2949,plain,
% 1.54/1.70 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.54/1.70 inference(symmetry,[status(thm)],[2948])).
% 1.54/1.70 tff(2950,plain,
% 1.54/1.70 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[2949])).
% 1.54/1.70 tff(2951,plain,
% 1.54/1.70 (r(s(elem!1), elem!1) <=> r(s(s(z)), s(z))),
% 1.54/1.70 inference(transitivity,[status(thm)],[2294, 2296])).
% 1.54/1.70 tff(2952,plain,
% 1.54/1.70 (r(s(elem!1), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2440, 526, 2354])).
% 1.54/1.70 tff(2953,plain,
% 1.54/1.70 (r(s(s(z)), s(z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2952, 2951])).
% 1.54/1.70 tff(2954,plain,
% 1.54/1.70 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2366, 268, 1132, 2953])).
% 1.54/1.70 tff(2955,plain,
% 1.54/1.70 (b(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2370, 69, 2954, 2359])).
% 1.54/1.70 tff(2956,assumption,(b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.70 tff(2957,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.54/1.70 tff(2958,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(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2959,plain,
% 1.54/1.70 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(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(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(2960,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(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2959])).
% 1.54/1.71 tff(2961,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(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(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(z))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2960, 2958])).
% 1.54/1.71 tff(2962,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(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(2963,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2962, 2961])).
% 1.54/1.71 tff(2964,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2963, 453, 523, 120, 2957, 2956])).
% 1.54/1.71 tff(2965,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(2966,plain,
% 1.54/1.71 (~b(s(s(z)), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2965, 2955, 120, 523])).
% 1.54/1.71 tff(2967,plain,
% 1.54/1.71 (~b(s(elem!1), s(s(elem!1)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2966, 2950])).
% 1.54/1.71 tff(2968,plain,
% 1.54/1.71 (r(s(elem!1), s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[440, 2967, 2288])).
% 1.54/1.71 tff(2969,plain,
% 1.54/1.71 (r(s(s(z)), s(s(s(z))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2968, 2276])).
% 1.54/1.71 tff(2970,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2971,plain,
% 1.54/1.71 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2972,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2971])).
% 1.54/1.71 tff(2973,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2972, 2970])).
% 1.54/1.71 tff(2974,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(2975,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2974, 2973])).
% 1.54/1.71 tff(2976,plain,
% 1.54/1.71 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2975, 268, 256, 2969])).
% 1.54/1.71 tff(2977,plain,
% 1.54/1.71 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2484, 2976, 1100])).
% 1.54/1.71 tff(2978,plain,
% 1.54/1.71 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2142, 2977, 2467])).
% 1.54/1.71 tff(2979,plain,
% 1.54/1.71 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2492, 2978, 1100])).
% 1.54/1.71 tff(2980,plain,
% 1.54/1.71 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2385, 268, 1132, 2953])).
% 1.54/1.71 tff(2981,plain,
% 1.54/1.71 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2393, 2980, 1100])).
% 1.54/1.71 tff(2982,plain,
% 1.54/1.71 (b(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2398, 2981, 2379])).
% 1.54/1.71 tff(2983,plain,
% 1.54/1.71 (b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2405, 2982, 1100])).
% 1.54/1.71 tff(2984,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(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(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(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2985,plain,
% 1.54/1.71 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2986,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(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2985])).
% 1.54/1.71 tff(2987,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(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2986, 2984])).
% 1.54/1.71 tff(2988,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(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(2989,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(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2988, 2987])).
% 1.54/1.71 tff(2990,plain,
% 1.54/1.71 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2989, 453, 2983, 2955, 2979])).
% 1.54/1.71 tff(2991,plain,
% 1.54/1.71 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[328, 2990])).
% 1.54/1.71 tff(2992,plain,
% 1.54/1.71 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[309, 2991, 256])).
% 1.54/1.71 tff(2993,plain,
% 1.54/1.71 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1656, 2992])).
% 1.54/1.71 tff(2994,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.71 tff(2995,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(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2996,plain,
% 1.54/1.71 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(2997,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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2996])).
% 1.54/1.71 tff(2998,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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[2997, 2995])).
% 1.54/1.71 tff(2999,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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3000,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(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2999, 2998])).
% 1.54/1.71 tff(3001,plain,
% 1.54/1.71 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3000, 453, 523, 1633, 2994])).
% 1.54/1.71 tff(3002,plain,
% 1.54/1.71 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1238, 69, 2663, 3001])).
% 1.54/1.71 tff(3003,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3004,plain,
% 1.54/1.71 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3005,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3004])).
% 1.54/1.71 tff(3006,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3005, 3003])).
% 1.54/1.71 tff(3007,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3008,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3007, 3006])).
% 1.54/1.71 tff(3009,plain,
% 1.54/1.71 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3008, 268, 2360, 2580, 3002])).
% 1.54/1.71 tff(3010,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(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3011,plain,
% 1.54/1.71 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3012,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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3011])).
% 1.54/1.71 tff(3013,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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3012, 3010])).
% 1.54/1.71 tff(3014,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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3015,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3014, 3013])).
% 1.54/1.71 tff(3016,plain,
% 1.54/1.71 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3015, 453, 523, 2994, 2956])).
% 1.54/1.71 tff(3017,plain,
% 1.54/1.71 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1369, 69, 3016])).
% 1.54/1.71 tff(3018,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3017, 3009, 2553])).
% 1.54/1.71 tff(3019,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~(elem!1 = s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(3020,plain,
% 1.54/1.71 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3019, 2953, 2969, 1100, 523, 2955, 2993])).
% 1.54/1.71 tff(3021,plain,
% 1.54/1.71 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2696, 3020])).
% 1.54/1.71 tff(3022,plain,
% 1.54/1.71 ((~(s(z) = s(s(z)))) <=> (~(s(elem!1) = s(z)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2290])).
% 1.54/1.71 tff(3023,plain,
% 1.54/1.71 (~(s(elem!1) = s(z))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[752, 3022])).
% 1.54/1.71 tff(3024,plain,
% 1.54/1.71 (s(s(s(z))) = s(s(elem!1))),
% 1.54/1.71 inference(symmetry,[status(thm)],[1104])).
% 1.54/1.71 tff(3025,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[555, 3024])).
% 1.54/1.71 tff(3026,plain,((~(elem!1 = s(z))) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(3027,plain,
% 1.54/1.71 (s(s(s(z))) = s(s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3026, 1100])).
% 1.54/1.71 tff(3028,plain,
% 1.54/1.71 (s(z) = elem!1),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[547, 3027])).
% 1.54/1.71 tff(3029,plain,
% 1.54/1.71 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[1121])).
% 1.54/1.71 tff(3030,plain,
% 1.54/1.71 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 1.54/1.71 inference(symmetry,[status(thm)],[3029])).
% 1.54/1.71 tff(3031,plain,
% 1.54/1.71 ((~b(s(elem!1), elem!1)) <=> (~b(s(elem!1), s(z)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3030])).
% 1.54/1.71 tff(3032,plain,
% 1.54/1.71 (~b(s(elem!1), s(z))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[526, 3031])).
% 1.54/1.71 tff(3033,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1059, 3032])).
% 1.54/1.71 tff(3034,plain,((~(s(z) = elem!1)) | (~b(s(elem!1), s(z))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(3035,plain,
% 1.54/1.71 (~b(s(elem!1), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3034, 526, 3028])).
% 1.54/1.71 tff(3036,plain,
% 1.54/1.71 (r(s(elem!1), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[353, 3035, 3023])).
% 1.54/1.71 tff(3037,plain,
% 1.54/1.71 ((s(elem!1) = s(s(s(z)))) <=> (s(s(z)) = s(s(s(z))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[1103])).
% 1.54/1.71 tff(3038,plain,
% 1.54/1.71 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3037, 486])).
% 1.54/1.71 tff(3039,plain,
% 1.54/1.71 ((s(s(s(z))) = s(s(z))) <=> (s(elem!1) = s(s(s(z))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[3038])).
% 1.54/1.71 tff(3040,plain,
% 1.54/1.71 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3039])).
% 1.54/1.71 tff(3041,plain,
% 1.54/1.71 (~(s(elem!1) = s(s(s(z))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[160, 3040])).
% 1.54/1.71 tff(3042,plain,
% 1.54/1.71 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[1103])).
% 1.54/1.71 tff(3043,plain,
% 1.54/1.71 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[3042])).
% 1.54/1.71 tff(3044,plain,
% 1.54/1.71 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3043])).
% 1.54/1.71 tff(3045,plain,
% 1.54/1.71 (~b(s(elem!1), s(s(s(z))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2966, 3044])).
% 1.54/1.71 tff(3046,plain,
% 1.54/1.71 (r(s(elem!1), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1305, 3045, 3041])).
% 1.54/1.71 tff(3047,assumption,(r(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.54/1.71 tff(3048,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3049,plain,
% 1.54/1.71 (((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3050,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3049])).
% 1.54/1.71 tff(3051,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3050, 3048])).
% 1.54/1.72 tff(3052,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3053,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3052, 3051])).
% 1.54/1.72 tff(3054,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3053, 268, 340, 257, 3047])).
% 1.54/1.72 tff(3055,plain,((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(3056,plain,
% 1.54/1.72 (~r(s(z), s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3055, 3046, 3036])).
% 1.54/1.72 tff(3057,plain,
% 1.54/1.72 (b(s(z), s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[227, 3056])).
% 1.54/1.72 tff(3058,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3059,plain,
% 1.54/1.72 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3060,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3059])).
% 1.54/1.72 tff(3061,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3060, 3058])).
% 1.54/1.72 tff(3062,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3063,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3062, 3061])).
% 1.54/1.72 tff(3064,plain,
% 1.54/1.72 (~b(s(z), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3063, 453, 523, 120, 3057])).
% 1.54/1.72 tff(3065,plain,
% 1.54/1.72 (r(s(z), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1677, 69, 50, 3064])).
% 1.54/1.72 tff(3066,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3067,plain,
% 1.54/1.72 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3068,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3067])).
% 1.54/1.72 tff(3069,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3068, 3066])).
% 1.54/1.72 tff(3070,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3071,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3070, 3069])).
% 1.54/1.72 tff(3072,plain,
% 1.54/1.72 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3071, 268, 3065, 3021])).
% 1.54/1.72 tff(3073,plain,
% 1.54/1.72 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2647, 69, 3072, 2636])).
% 1.54/1.72 tff(3074,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3075,plain,
% 1.54/1.72 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(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(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3076,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(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(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3075])).
% 1.54/1.72 tff(3077,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(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(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3076, 3074])).
% 1.54/1.72 tff(3078,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(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(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3079,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3078, 3077])).
% 1.54/1.72 tff(3080,plain,
% 1.54/1.72 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3079, 268, 256, 2991, 3021])).
% 1.54/1.72 tff(3081,plain,
% 1.54/1.72 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2732, 69, 2729, 3080])).
% 1.54/1.72 tff(3082,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(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(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3083,plain,
% 1.54/1.72 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3084,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)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(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(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3083])).
% 1.54/1.72 tff(3085,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)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(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(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3084, 3082])).
% 1.54/1.72 tff(3086,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)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3087,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3086, 3085])).
% 1.54/1.72 tff(3088,plain,
% 1.54/1.72 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3087, 453, 2983, 2955, 2979])).
% 1.54/1.72 tff(3089,plain,
% 1.54/1.72 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2463, 69, 3088, 2453])).
% 1.54/1.72 tff(3090,plain,
% 1.54/1.72 (~r(s(z), s(s(s(s(s(z))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2254, 3089, 1132])).
% 1.54/1.72 tff(3091,plain,
% 1.54/1.72 (b(s(z), s(s(s(s(s(z))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[372, 3090])).
% 1.54/1.72 tff(3092,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3093,plain,
% 1.54/1.72 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3094,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3093])).
% 1.54/1.72 tff(3095,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3094, 3092])).
% 1.54/1.72 tff(3096,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3097,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3096, 3095])).
% 1.54/1.72 tff(3098,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3097, 453, 3091, 374, 3081, 3073])).
% 1.54/1.72 tff(3099,plain,(b(s(elem!1), elem!1) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~(elem!1 = s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(3100,plain,
% 1.54/1.72 (b(s(elem!1), elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3099, 2947, 374, 1100, 523, 1132, 120])).
% 1.54/1.72 tff(3101,plain,
% 1.54/1.72 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2311])).
% 1.54/1.72 tff(3102,plain,
% 1.54/1.72 (~(elem!1 = s(s(elem!1)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[816, 3101])).
% 1.54/1.72 tff(3103,plain,
% 1.54/1.72 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2277])).
% 1.54/1.72 tff(3104,plain,
% 1.54/1.72 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 1.54/1.72 inference(symmetry,[status(thm)],[3103])).
% 1.54/1.72 tff(3105,plain,
% 1.54/1.72 (b(s(s(z)), elem!1) <=> b(s(elem!1), s(z))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2269, 1100])).
% 1.54/1.72 tff(3106,plain,
% 1.54/1.72 (b(s(elem!1), s(z)) <=> b(s(s(z)), elem!1)),
% 1.54/1.72 inference(symmetry,[status(thm)],[3105])).
% 1.54/1.72 tff(3107,plain,
% 1.54/1.72 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[1100])).
% 1.54/1.72 tff(3108,plain,
% 1.54/1.72 (b(s(elem!1), elem!1) <=> b(s(s(z)), s(z))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3107, 3106, 3104])).
% 1.54/1.72 tff(3109,plain,
% 1.54/1.72 (b(s(s(z)), s(z))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[629, 3108])).
% 1.54/1.72 tff(3110,plain,
% 1.54/1.72 (b(s(z), s(s(s(s(s(z))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[372, 367])).
% 1.54/1.72 tff(3111,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3112,plain,
% 1.54/1.72 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(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(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3113,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(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(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z)))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3112])).
% 1.54/1.73 tff(3114,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(s(s(z))))))) | (~b(s(z), s(s(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(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3113, 3111])).
% 1.54/1.73 tff(3115,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(s(s(z))))))) | (~b(s(z), s(s(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)))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3116,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3115, 3114])).
% 1.54/1.73 tff(3117,plain,
% 1.54/1.73 (~b(s(s(s(z))), s(s(z)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3116, 453, 3110, 120, 3109])).
% 1.54/1.73 tff(3118,plain,
% 1.54/1.73 (r(s(s(s(z))), s(s(z)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2534, 69, 160, 3117])).
% 1.54/1.73 tff(3119,plain,
% 1.54/1.73 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[1100])).
% 1.54/1.73 tff(3120,plain,
% 1.54/1.73 (r(s(z), s(s(s(s(s(z))))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[412, 3119])).
% 1.54/1.73 tff(3121,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[367, 3120])).
% 1.54/1.73 tff(3122,plain,((~r(elem!1, s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(z)))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3123,plain,
% 1.54/1.73 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3122, 367, 1100])).
% 1.54/1.73 tff(3124,plain,
% 1.54/1.73 (b(elem!1, s(s(s(s(s(z))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[466, 3123, 2073])).
% 1.54/1.73 tff(3125,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(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3126,plain,
% 1.54/1.73 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3127,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(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3126])).
% 1.54/1.73 tff(3128,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(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3127, 3125])).
% 1.54/1.73 tff(3129,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(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3130,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3129, 3128])).
% 1.54/1.73 tff(3131,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3130, 453, 629, 923, 646, 645])).
% 1.54/1.73 tff(3132,plain,((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3133,plain,
% 1.54/1.73 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3132, 3124, 646, 629])).
% 1.54/1.73 tff(3134,plain,
% 1.54/1.73 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[659, 3133, 2275])).
% 1.54/1.73 tff(3135,plain,
% 1.54/1.73 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3134, 2347])).
% 1.54/1.73 tff(3136,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3137,plain,
% 1.54/1.73 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3138,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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3137])).
% 1.54/1.73 tff(3139,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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3138, 3136])).
% 1.54/1.73 tff(3140,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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3141,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3140, 3139])).
% 1.54/1.73 tff(3142,plain,
% 1.54/1.73 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3141, 453, 3110, 374, 120])).
% 1.54/1.73 tff(3143,plain,
% 1.54/1.73 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2570, 3142])).
% 1.54/1.73 tff(3144,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3145,plain,
% 1.54/1.73 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3146,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3145])).
% 1.54/1.73 tff(3147,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3146, 3144])).
% 1.54/1.73 tff(3148,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3149,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3148, 3147])).
% 1.54/1.73 tff(3150,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3149, 268, 3143, 3135, 3118])).
% 1.54/1.73 tff(3151,plain,(r(s(z), s(s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~(elem!1 = s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (elem!1 = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3152,plain,
% 1.54/1.73 (r(s(z), s(s(s(s(s(z))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3151, 3100, 374, 1100, 646, 120, 2073])).
% 1.54/1.73 tff(3153,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3154,plain,
% 1.54/1.73 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3155,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3154])).
% 1.54/1.73 tff(3156,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3155, 3153])).
% 1.54/1.73 tff(3157,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3158,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3157, 3156])).
% 1.54/1.73 tff(3159,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3158, 268, 256, 2246, 257])).
% 1.54/1.73 tff(3160,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3161,plain,
% 1.54/1.73 (~r(s(z), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3160, 2947, 3152])).
% 1.54/1.73 tff(3162,plain,
% 1.54/1.73 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[1121])).
% 1.54/1.73 tff(3163,plain,
% 1.54/1.73 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 1.54/1.73 inference(symmetry,[status(thm)],[3162])).
% 1.54/1.73 tff(3164,plain,
% 1.54/1.73 (s(s(z)) = s(elem!1)),
% 1.54/1.73 inference(monotonicity,[status(thm)],[1121])).
% 1.54/1.73 tff(3165,plain,
% 1.54/1.73 (s(s(s(z))) = s(s(elem!1))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3164])).
% 1.54/1.73 tff(3166,plain,
% 1.54/1.73 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3165])).
% 1.54/1.73 tff(3167,plain,
% 1.54/1.73 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(z))))),
% 1.54/1.73 inference(symmetry,[status(thm)],[3166])).
% 1.54/1.73 tff(3168,plain,
% 1.54/1.73 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3167, 3163])).
% 1.54/1.73 tff(3169,plain,
% 1.54/1.73 (r(s(z), s(s(s(z))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[1032, 3168])).
% 1.54/1.73 tff(3170,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[222, 3169])).
% 1.54/1.73 tff(3171,plain,((~r(elem!1, s(s(elem!1)))) | r(s(z), s(s(s(z)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3172,plain,
% 1.54/1.73 (~r(elem!1, s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3171, 3161, 3028])).
% 1.54/1.73 tff(3173,plain,
% 1.54/1.73 (b(elem!1, s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1024, 3172, 3102])).
% 1.54/1.73 tff(3174,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(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3175,plain,
% 1.54/1.73 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3176,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3175])).
% 1.54/1.73 tff(3177,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3176, 3174])).
% 1.54/1.73 tff(3178,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3179,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3178, 3177])).
% 1.54/1.73 tff(3180,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3179, 453, 629, 1050, 907, 910])).
% 1.54/1.73 tff(3181,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3182,plain,
% 1.54/1.73 (~b(s(elem!1), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3181, 3173, 3100, 1050])).
% 1.54/1.73 tff(3183,plain,
% 1.54/1.73 (r(s(elem!1), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[440, 3182, 2288])).
% 1.54/1.73 tff(3184,plain,
% 1.54/1.73 (r(s(s(z)), s(s(s(z))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3183, 2276])).
% 1.54/1.73 tff(3185,plain,
% 1.54/1.73 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2975, 268, 2947, 3184])).
% 1.54/1.73 tff(3186,plain,
% 1.54/1.73 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2484, 3185, 1100])).
% 1.54/1.73 tff(3187,plain,
% 1.54/1.73 (b(s(s(z)), s(z))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3100, 3108])).
% 1.54/1.73 tff(3188,plain,
% 1.54/1.73 (b(s(z), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[227, 3161])).
% 1.54/1.73 tff(3189,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(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), 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(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3190,plain,
% 1.54/1.73 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), 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(s(z))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3191,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(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), 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(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z)))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3190])).
% 1.54/1.73 tff(3192,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(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), 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(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3191, 3189])).
% 1.54/1.73 tff(3193,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(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), 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(s(z)))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3194,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3193, 3192])).
% 1.54/1.73 tff(3195,plain,
% 1.54/1.73 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3194, 453, 374, 3188, 3187])).
% 1.54/1.73 tff(3196,plain,
% 1.54/1.73 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2492, 3195, 1100])).
% 1.54/1.73 tff(3197,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2142, 3196, 3186, 2467])).
% 1.54/1.73 tff(3198,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~(elem!1 = s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(z))) | (elem!1 = s(s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3199,plain,
% 1.54/1.73 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3198, 1100, 2923, 2933, 2930, 2307, 2925, 2303, 2329])).
% 1.54/1.73 tff(3200,plain,
% 1.54/1.73 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[518, 3199])).
% 1.54/1.73 tff(3201,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3202,plain,
% 1.54/1.74 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3203,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3202])).
% 1.54/1.74 tff(3204,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3203, 3201])).
% 1.54/1.74 tff(3205,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3206,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3205, 3204])).
% 1.54/1.74 tff(3207,plain,
% 1.54/1.74 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3206, 268, 11, 1132, 2360])).
% 1.54/1.74 tff(3208,plain,
% 1.54/1.74 (b(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2370, 69, 3207, 2359])).
% 1.54/1.74 tff(3209,plain,
% 1.54/1.74 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2943, 453, 443, 374, 120])).
% 1.54/1.74 tff(3210,plain,
% 1.54/1.74 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[687, 3209])).
% 1.54/1.74 tff(3211,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3212,plain,
% 1.54/1.74 (((~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(s(z)))), s(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(z)))), s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3213,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3212])).
% 1.54/1.74 tff(3214,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3213, 3211])).
% 1.54/1.74 tff(3215,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(z)))), s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3216,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3215, 3214])).
% 1.54/1.74 tff(3217,plain,
% 1.54/1.74 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3216, 268, 11, 3210])).
% 1.54/1.74 tff(3218,plain,
% 1.54/1.74 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2463, 69, 3217, 2453])).
% 1.54/1.74 tff(3219,plain,
% 1.54/1.74 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1982, 3210, 11])).
% 1.54/1.74 tff(3220,plain,
% 1.54/1.74 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[328, 3219])).
% 1.54/1.74 tff(3221,plain,
% 1.54/1.74 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2747, 453, 3220, 3218, 2956])).
% 1.54/1.74 tff(3222,plain,
% 1.54/1.74 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3221, 2355])).
% 1.54/1.74 tff(3223,plain,
% 1.54/1.74 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[659, 3222, 2275])).
% 1.54/1.74 tff(3224,assumption,(r(s(elem!1), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.54/1.74 tff(3225,plain,
% 1.54/1.74 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3224, 2347])).
% 1.54/1.74 tff(3226,assumption,(~r(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.54/1.74 tff(3227,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3226, 3225])).
% 1.54/1.74 tff(3228,plain,((~r(s(elem!1), s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(z)))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3229,plain,
% 1.54/1.74 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3228, 3223, 1100])).
% 1.54/1.74 tff(3230,plain,
% 1.54/1.74 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3141, 453, 443, 374, 120])).
% 1.54/1.74 tff(3231,plain,
% 1.54/1.74 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2570, 3230])).
% 1.54/1.74 tff(3232,plain,
% 1.54/1.74 (~r(s(s(s(z))), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3149, 268, 3231, 3229])).
% 1.54/1.74 tff(3233,plain,
% 1.54/1.74 (b(s(s(s(z))), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2534, 69, 160, 3232])).
% 1.54/1.74 tff(3234,plain,
% 1.54/1.74 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.54/1.74 inference(symmetry,[status(thm)],[2276])).
% 1.54/1.74 tff(3235,plain,
% 1.54/1.74 ((~r(s(s(z)), s(s(s(z))))) <=> (~r(s(elem!1), s(s(elem!1))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3234])).
% 1.54/1.74 tff(3236,plain,
% 1.54/1.74 (~r(s(s(z)), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2795, 3229, 3210])).
% 1.54/1.74 tff(3237,plain,
% 1.54/1.74 (~r(s(elem!1), s(s(elem!1)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3236, 3235])).
% 1.54/1.74 tff(3238,plain,
% 1.54/1.74 (b(s(elem!1), s(s(elem!1)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[440, 3237, 2288])).
% 1.54/1.74 tff(3239,plain,
% 1.54/1.74 (b(s(s(z)), s(s(s(z))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3238, 2948])).
% 1.54/1.74 tff(3240,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3241,plain,
% 1.54/1.74 (((~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(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(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(z))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3242,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(z)))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3241])).
% 1.54/1.74 tff(3243,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), 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(z))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3242, 3240])).
% 1.54/1.74 tff(3244,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3245,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), 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(z)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3244, 3243])).
% 1.54/1.74 tff(3246,plain,
% 1.54/1.74 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3245, 453, 2496, 3239, 3233])).
% 1.54/1.74 tff(3247,plain,
% 1.54/1.74 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1656, 3246])).
% 1.54/1.74 tff(3248,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(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(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3249,plain,
% 1.54/1.74 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3250,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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3249])).
% 1.54/1.74 tff(3251,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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3250, 3248])).
% 1.54/1.74 tff(3252,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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3253,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3252, 3251])).
% 1.54/1.74 tff(3254,plain,
% 1.54/1.74 (~b(s(z), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3253, 453, 443, 3220, 3218])).
% 1.54/1.74 tff(3255,plain,
% 1.54/1.74 (r(s(z), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1677, 69, 50, 3254])).
% 1.54/1.74 tff(3256,plain,
% 1.54/1.74 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3071, 268, 376, 2637])).
% 1.54/1.74 tff(3257,plain,
% 1.54/1.74 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2647, 69, 3256, 2636])).
% 1.54/1.74 tff(3258,plain,
% 1.54/1.74 (~r(s(z), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[384, 300, 376])).
% 1.54/1.74 tff(3259,plain,
% 1.54/1.74 (b(s(z), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[227, 3258])).
% 1.54/1.74 tff(3260,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(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(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3261,plain,
% 1.54/1.74 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3262,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3261])).
% 1.54/1.74 tff(3263,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3262, 3260])).
% 1.54/1.74 tff(3264,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3265,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3264, 3263])).
% 1.54/1.74 tff(3266,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3265, 453, 443, 374, 120, 3259, 2664, 3257])).
% 1.54/1.74 tff(3267,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3268,plain,
% 1.54/1.74 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3267, 443, 374, 120, 3255, 3247])).
% 1.54/1.74 tff(3269,plain,
% 1.54/1.74 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2696, 3268])).
% 1.54/1.74 tff(3270,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3271,plain,
% 1.54/1.74 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3272,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(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3271])).
% 1.54/1.74 tff(3273,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(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3272, 3270])).
% 1.54/1.74 tff(3274,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(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3275,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3274, 3273])).
% 1.54/1.74 tff(3276,plain,
% 1.54/1.74 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3275, 453, 443, 3220, 3218, 374, 3269])).
% 1.54/1.74 tff(3277,plain,
% 1.54/1.74 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2732, 69, 2729, 3276])).
% 1.54/1.74 tff(3278,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3279,plain,
% 1.54/1.74 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3280,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3279])).
% 1.54/1.75 tff(3281,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3280, 3278])).
% 1.54/1.75 tff(3282,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3283,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3282, 3281])).
% 1.54/1.75 tff(3284,plain,
% 1.54/1.75 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3283, 268, 2360, 3229, 3277])).
% 1.54/1.75 tff(3285,plain,
% 1.54/1.75 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2764, 453, 3218, 3269, 2956])).
% 1.54/1.75 tff(3286,plain,
% 1.54/1.75 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1369, 69, 3285])).
% 1.54/1.75 tff(3287,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3286, 3284, 2553])).
% 1.54/1.75 tff(3288,plain,((~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~(elem!1 = s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3289,plain,
% 1.54/1.75 (~b(s(z), s(s(s(s(s(z))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3288, 2360, 1100, 3208, 374, 120, 2406, 11])).
% 1.54/1.75 tff(3290,plain,
% 1.54/1.75 (r(s(z), s(s(s(s(s(z))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[372, 3289])).
% 1.54/1.75 tff(3291,plain,
% 1.54/1.75 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2254, 3290, 1132])).
% 1.54/1.75 tff(3292,plain,
% 1.54/1.75 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2463, 69, 3291, 2453])).
% 1.54/1.75 tff(3293,plain,
% 1.54/1.75 (~r(s(z), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2629, 3290, 1132, 11])).
% 1.54/1.75 tff(3294,plain,
% 1.54/1.75 (b(s(z), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[227, 3293])).
% 1.54/1.75 tff(3295,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3296,plain,
% 1.54/1.75 (((~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))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3297,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(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)))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3296])).
% 1.54/1.75 tff(3298,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(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))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3297, 3295])).
% 1.54/1.75 tff(3299,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(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))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3300,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3299, 3298])).
% 1.54/1.75 tff(3301,plain,
% 1.54/1.75 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3300, 453, 374, 120, 3294])).
% 1.54/1.75 tff(3302,plain,
% 1.54/1.75 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[687, 3301])).
% 1.54/1.75 tff(3303,plain,
% 1.54/1.75 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1982, 3302, 11])).
% 1.54/1.75 tff(3304,plain,
% 1.54/1.75 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[328, 3303])).
% 1.54/1.75 tff(3305,plain,
% 1.54/1.75 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2747, 453, 3304, 3292, 3208])).
% 1.54/1.75 tff(3306,plain,
% 1.54/1.75 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3305, 2355])).
% 1.54/1.75 tff(3307,plain,
% 1.54/1.75 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[659, 3306, 2275])).
% 1.54/1.75 tff(3308,plain,
% 1.54/1.75 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3228, 3307, 1100])).
% 1.54/1.75 tff(3309,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3310,plain,
% 1.54/1.75 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3311,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3310])).
% 1.54/1.75 tff(3312,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3311, 3309])).
% 1.54/1.75 tff(3313,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3314,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3313, 3312])).
% 1.54/1.75 tff(3315,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3314, 268, 3290, 2360, 3308])).
% 1.54/1.75 tff(3316,plain,((~r(s(s(z)), s(z))) | (~(elem!1 = s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3317,plain,
% 1.54/1.75 (~r(s(s(z)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3316, 1100, 3200, 2923, 2307, 2303])).
% 1.54/1.75 tff(3318,plain,
% 1.54/1.75 (~r(s(elem!1), elem!1)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3317, 2299])).
% 1.54/1.75 tff(3319,plain,
% 1.54/1.75 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[1100])).
% 1.54/1.75 tff(3320,plain,
% 1.54/1.75 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.54/1.75 inference(symmetry,[status(thm)],[3319])).
% 1.54/1.75 tff(3321,plain,
% 1.54/1.75 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.54/1.75 inference(transitivity,[status(thm)],[1107, 3320])).
% 1.54/1.75 tff(3322,plain,
% 1.54/1.75 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3321])).
% 1.54/1.75 tff(3323,plain,
% 1.54/1.75 (~b(s(s(s(elem!1))), elem!1)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[2302, 3322])).
% 1.54/1.75 tff(3324,plain,
% 1.54/1.75 (b(s(elem!1), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2440, 3318, 2354])).
% 1.54/1.75 tff(3325,plain,
% 1.54/1.75 (r(s(z), s(s(s(s(s(z))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3151, 3324, 2923, 1100, 2930, 2307, 2925])).
% 1.54/1.75 tff(3326,plain,
% 1.54/1.75 (~r(s(z), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2629, 3325, 2303, 3200])).
% 1.54/1.75 tff(3327,plain,
% 1.54/1.75 (~r(elem!1, s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3171, 3326, 3028])).
% 1.54/1.75 tff(3328,plain,
% 1.54/1.75 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 1.54/1.75 inference(commutativity,[status(thm)],[])).
% 1.54/1.75 tff(3329,plain,
% 1.54/1.75 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.54/1.75 inference(symmetry,[status(thm)],[3328])).
% 1.54/1.75 tff(3330,plain,
% 1.54/1.75 ((~(s(elem!1) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3329])).
% 1.54/1.75 tff(3331,plain,
% 1.54/1.75 (~(s(s(elem!1)) = s(elem!1))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1997, 3330])).
% 1.54/1.75 tff(3332,assumption,(~r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.54/1.75 tff(3333,assumption,(~b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.54/1.75 tff(3334,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 1.54/1.75 tff(3335,plain,
% 1.54/1.75 (s(s(elem!1)) = elem!1),
% 1.54/1.75 inference(symmetry,[status(thm)],[3334])).
% 1.54/1.75 tff(3336,plain,
% 1.54/1.75 (s(s(s(elem!1))) = s(elem!1)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3335])).
% 1.54/1.75 tff(3337,plain,
% 1.54/1.75 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), s(s(elem!1)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3336, 3334])).
% 1.54/1.75 tff(3338,plain,
% 1.54/1.75 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), elem!1)),
% 1.54/1.75 inference(symmetry,[status(thm)],[3337])).
% 1.54/1.75 tff(3339,plain,
% 1.54/1.75 (b(s(s(s(elem!1))), elem!1)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[910, 3338])).
% 1.54/1.75 tff(3340,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3333, 3339])).
% 1.54/1.75 tff(3341,plain,((~(elem!1 = s(s(elem!1)))) | b(s(s(s(elem!1))), elem!1) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3342,plain,
% 1.54/1.75 (~(elem!1 = s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3341, 3333, 910])).
% 1.54/1.75 tff(3343,plain,
% 1.54/1.75 (b(elem!1, s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1024, 3342, 3332])).
% 1.54/1.75 tff(3344,assumption,(~r(s(elem!1), elem!1)), introduced(assumption)).
% 1.54/1.75 tff(3345,assumption,(s(elem!1) = elem!1), introduced(assumption)).
% 1.54/1.75 tff(3346,plain,
% 1.54/1.75 (s(s(elem!1)) = s(elem!1)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3345])).
% 1.54/1.75 tff(3347,plain,
% 1.54/1.75 (s(elem!1) = s(s(elem!1))),
% 1.54/1.75 inference(symmetry,[status(thm)],[3346])).
% 1.54/1.75 tff(3348,plain,
% 1.54/1.75 (elem!1 = s(elem!1)),
% 1.54/1.75 inference(symmetry,[status(thm)],[3345])).
% 1.54/1.75 tff(3349,plain,
% 1.54/1.75 (elem!1 = s(s(elem!1))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3348, 3347])).
% 1.54/1.75 tff(3350,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[216, 3349])).
% 1.54/1.75 tff(3351,plain,((~(s(elem!1) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3352,plain,
% 1.54/1.75 (~(s(elem!1) = elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3351, 3342])).
% 1.54/1.75 tff(3353,plain,
% 1.54/1.75 (b(s(elem!1), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2440, 3352, 3344])).
% 1.54/1.75 tff(3354,plain,
% 1.54/1.75 (~b(s(s(elem!1)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3181, 3353, 3343, 910])).
% 1.54/1.75 tff(3355,plain,
% 1.54/1.75 (r(s(s(elem!1)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1047, 3354])).
% 1.54/1.75 tff(3356,assumption,(s(s(elem!1)) = elem!1), introduced(assumption)).
% 1.54/1.75 tff(3357,plain,
% 1.54/1.75 (elem!1 = s(s(elem!1))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3356, 2169])).
% 1.54/1.75 tff(3358,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[216, 3357])).
% 1.54/1.75 tff(3359,plain,((~(s(s(elem!1)) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3360,plain,
% 1.54/1.75 (~(s(s(elem!1)) = elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3359, 3342])).
% 1.54/1.75 tff(3361,plain,
% 1.54/1.75 (~b(s(s(elem!1)), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[918, 3353, 3343, 910])).
% 1.54/1.75 tff(3362,plain,
% 1.54/1.75 (r(s(s(elem!1)), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2240, 3361, 3360])).
% 1.54/1.75 tff(3363,plain,
% 1.54/1.75 (~r(elem!1, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1970, 3362, 3355])).
% 1.54/1.75 tff(3364,plain,
% 1.54/1.75 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[607, 3352])).
% 1.54/1.75 tff(3365,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.75 tff(3366,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3367,plain,
% 1.54/1.75 (((~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(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3368,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3367])).
% 1.54/1.75 tff(3369,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3368, 3366])).
% 1.54/1.75 tff(3370,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3371,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3370, 3369])).
% 1.54/1.75 tff(3372,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3371, 453, 629, 3365, 907, 910])).
% 1.54/1.75 tff(3373,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3374,plain,
% 1.54/1.75 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3373, 3353, 3343, 910])).
% 1.54/1.75 tff(3375,plain,
% 1.54/1.75 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[675, 3374, 3364])).
% 1.54/1.75 tff(3376,plain,
% 1.54/1.75 (~r(s(s(s(elem!1))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[877, 3362, 3375])).
% 1.54/1.75 tff(3377,plain,
% 1.54/1.75 (s(s(s(elem!1))) = elem!1),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[567, 3376, 3333])).
% 1.54/1.75 tff(3378,plain,
% 1.54/1.75 ((s(s(s(elem!1))) = s(z)) <=> (elem!1 = s(z))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3377])).
% 1.54/1.75 tff(3379,plain,
% 1.54/1.75 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = elem!1)),
% 1.54/1.75 inference(transitivity,[status(thm)],[3378, 1119])).
% 1.54/1.75 tff(3380,plain,
% 1.54/1.75 ((s(s(s(elem!1))) = s(z)) <=> (elem!1 = s(z))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3379, 1120])).
% 1.54/1.75 tff(3381,plain,
% 1.54/1.75 ((~(s(s(s(elem!1))) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3380])).
% 1.54/1.75 tff(3382,plain,
% 1.54/1.75 (~(elem!1 = s(z))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[851, 3381])).
% 1.54/1.75 tff(3383,plain,
% 1.54/1.75 (b(elem!1, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1130, 3382, 3363])).
% 1.54/1.75 tff(3384,plain,
% 1.54/1.75 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3379])).
% 1.54/1.75 tff(3385,plain,
% 1.54/1.75 (~(s(z) = elem!1)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[851, 3384])).
% 1.54/1.75 tff(3386,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3387,plain,
% 1.54/1.75 (((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3388,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3387])).
% 1.54/1.75 tff(3389,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3388, 3386])).
% 1.54/1.75 tff(3390,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3391,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3390, 3389])).
% 1.54/1.75 tff(3392,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3391, 268, 701, 1033, 869])).
% 1.54/1.75 tff(3393,plain,((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3394,plain,
% 1.54/1.75 (~r(s(z), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3393, 3355, 3362])).
% 1.54/1.75 tff(3395,plain,
% 1.54/1.75 (b(s(z), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[506, 3394, 3385])).
% 1.54/1.75 tff(3396,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), 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(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3397,plain,
% 1.54/1.75 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3398,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3397])).
% 1.54/1.75 tff(3399,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3398, 3396])).
% 1.54/1.75 tff(3400,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3401,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3400, 3399])).
% 1.54/1.76 tff(3402,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3401, 453, 1549, 499, 2077, 629])).
% 1.54/1.76 tff(3403,plain,((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(3404,plain,
% 1.54/1.76 (~b(s(z), s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3403, 3395, 3353, 3383])).
% 1.54/1.76 tff(3405,plain,
% 1.54/1.76 (r(s(z), s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[397, 3404, 177])).
% 1.54/1.76 tff(3406,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.54/1.76 tff(3407,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3408,plain,
% 1.54/1.76 (((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3409,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3408])).
% 1.54/1.76 tff(3410,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3409, 3407])).
% 1.54/1.76 tff(3411,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3412,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3411, 3410])).
% 1.54/1.76 tff(3413,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3412, 268, 388, 1033, 3406])).
% 1.54/1.76 tff(3414,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(3415,plain,
% 1.54/1.76 (~r(s(s(elem!1)), s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3414, 3405, 3355])).
% 1.54/1.76 tff(3416,plain,
% 1.54/1.76 ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1874, 69, 3415])).
% 1.54/1.76 tff(3417,plain,
% 1.54/1.76 (b(s(s(elem!1)), s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3416, 3331])).
% 1.54/1.76 tff(3418,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(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3419,plain,
% 1.54/1.76 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3420,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(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(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3419])).
% 1.54/1.76 tff(3421,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(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(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3420, 3418])).
% 1.54/1.76 tff(3422,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3423,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3422, 3421])).
% 1.54/1.76 tff(3424,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3423, 453, 3353, 3343, 910, 3417])).
% 1.54/1.76 tff(3425,plain,(b(s(s(s(elem!1))), elem!1) | (~b(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (s(z) = s(elem!1)) | r(s(elem!1), elem!1) | r(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(3426,plain,
% 1.54/1.76 (~b(s(elem!1), s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3425, 3327, 3323, 2288, 3318, 2293])).
% 1.54/1.76 tff(3427,plain,
% 1.54/1.76 (r(s(elem!1), s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[440, 3426, 2288])).
% 1.54/1.76 tff(3428,plain,
% 1.54/1.76 (r(s(s(z)), s(s(s(z))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3427, 2276])).
% 1.54/1.76 tff(3429,plain,
% 1.54/1.76 (b(s(z), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[227, 3326])).
% 1.54/1.76 tff(3430,plain,
% 1.54/1.76 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3300, 453, 2923, 2307, 3429])).
% 1.54/1.76 tff(3431,plain,
% 1.54/1.76 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[687, 3430])).
% 1.54/1.76 tff(3432,plain,
% 1.54/1.76 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2795, 3431, 3428])).
% 1.54/1.76 tff(3433,plain,
% 1.54/1.76 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3228, 3432, 1100])).
% 1.54/1.76 tff(3434,plain,
% 1.54/1.76 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[659, 3433, 2275])).
% 1.54/1.76 tff(3435,plain,
% 1.54/1.76 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3434, 2271])).
% 1.54/1.76 tff(3436,plain,
% 1.54/1.76 (b(s(s(z)), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[720, 69, 717, 3317])).
% 1.54/1.76 tff(3437,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(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3438,plain,
% 1.54/1.76 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(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(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3439,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(s(z))))) | (~b(s(z), s(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(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3438])).
% 1.54/1.76 tff(3440,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(s(z))))) | (~b(s(z), s(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(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3439, 3437])).
% 1.54/1.76 tff(3441,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(s(z))))) | (~b(s(z), s(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))))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3442,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3441, 3440])).
% 1.54/1.76 tff(3443,plain,
% 1.54/1.76 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3442, 453, 2923, 3429, 3436])).
% 1.54/1.76 tff(3444,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3443, 3435])).
% 1.54/1.76 tff(3445,plain,((~(elem!1 = s(z))) | (s(s(s(s(s(z))))) = elem!1) | r(s(s(s(z))), elem!1) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(3446,plain,
% 1.54/1.76 (~(elem!1 = s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3445, 249, 2, 637])).
% 1.54/1.76 tff(3447,plain,
% 1.54/1.76 (~(s(z) = elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1125, 3446])).
% 1.54/1.76 tff(3448,plain,
% 1.54/1.76 (r(s(s(s(z))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[134, 128])).
% 1.54/1.76 tff(3449,plain,
% 1.54/1.76 (r(elem!1, s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1130, 3446, 10])).
% 1.54/1.76 tff(3450,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3451,plain,
% 1.54/1.76 (((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3452,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z)))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3451])).
% 1.54/1.76 tff(3453,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3452, 3450])).
% 1.54/1.76 tff(3454,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3455,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3454, 3453])).
% 1.54/1.76 tff(3456,plain,
% 1.54/1.76 (~r(elem!1, s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3455, 268, 3449, 3448])).
% 1.54/1.76 tff(3457,plain,
% 1.54/1.76 (r(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[643, 638, 637])).
% 1.54/1.76 tff(3458,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3459,plain,
% 1.54/1.76 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3460,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3459])).
% 1.54/1.76 tff(3461,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3460, 3458])).
% 1.54/1.76 tff(3462,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3463,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3462, 3461])).
% 1.54/1.76 tff(3464,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3463, 268, 238, 412, 258])).
% 1.54/1.76 tff(3465,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(3466,plain,
% 1.54/1.76 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3465, 258, 3449])).
% 1.54/1.76 tff(3467,plain,
% 1.54/1.76 (b(elem!1, s(s(s(s(s(z))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[466, 3466, 2925])).
% 1.54/1.76 tff(3468,assumption,(s(s(z)) = elem!1), introduced(assumption)).
% 1.54/1.76 tff(3469,plain,
% 1.54/1.76 (s(s(s(z))) = s(elem!1)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3468])).
% 1.54/1.76 tff(3470,plain,
% 1.54/1.76 ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3469])).
% 1.54/1.76 tff(3471,plain,
% 1.54/1.76 ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3470, 1432])).
% 1.54/1.76 tff(3472,plain,
% 1.54/1.76 ((~(s(s(s(z))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3471])).
% 1.54/1.76 tff(3473,plain,
% 1.54/1.76 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(commutativity,[status(thm)],[])).
% 1.54/1.76 tff(3474,plain,
% 1.54/1.76 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(s(s(s(z)))))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3473])).
% 1.54/1.76 tff(3475,plain,
% 1.54/1.76 (~(s(s(s(z))) = s(s(s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[2663, 3474])).
% 1.54/1.76 tff(3476,plain,
% 1.54/1.76 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3475, 3472])).
% 1.54/1.76 tff(3477,plain,
% 1.54/1.76 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3469])).
% 1.54/1.76 tff(3478,plain,
% 1.54/1.76 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3477])).
% 1.54/1.76 tff(3479,plain,
% 1.54/1.76 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3478])).
% 1.54/1.76 tff(3480,plain,
% 1.54/1.76 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3479])).
% 1.54/1.76 tff(3481,plain,
% 1.54/1.76 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3478])).
% 1.54/1.76 tff(3482,plain,
% 1.54/1.76 ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3481])).
% 1.54/1.76 tff(3483,plain,
% 1.54/1.76 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.54/1.76 inference(commutativity,[status(thm)],[])).
% 1.54/1.76 tff(3484,plain,
% 1.54/1.76 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3478])).
% 1.54/1.76 tff(3485,plain,
% 1.54/1.76 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.54/1.76 inference(transitivity,[status(thm)],[3484, 3483])).
% 1.54/1.76 tff(3486,plain,
% 1.54/1.76 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3485])).
% 1.54/1.76 tff(3487,plain,
% 1.54/1.76 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3486])).
% 1.54/1.76 tff(3488,plain,
% 1.54/1.76 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3468])).
% 1.54/1.76 tff(3489,plain,
% 1.54/1.76 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3488])).
% 1.54/1.76 tff(3490,plain,
% 1.54/1.76 (~(s(s(s(s(z)))) = elem!1)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[153, 3489])).
% 1.54/1.76 tff(3491,plain,
% 1.54/1.76 (~(elem!1 = s(s(elem!1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3490, 3487])).
% 1.54/1.76 tff(3492,plain,
% 1.54/1.76 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = elem!1)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3356])).
% 1.54/1.76 tff(3493,plain,
% 1.54/1.76 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(elem!1)))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3492])).
% 1.54/1.76 tff(3494,plain,
% 1.54/1.76 (s(s(z)) = s(s(elem!1))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3468, 3493])).
% 1.54/1.76 tff(3495,plain,
% 1.54/1.76 (s(s(s(elem!1))) = s(elem!1)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3356])).
% 1.54/1.76 tff(3496,plain,
% 1.54/1.76 ((s(s(s(elem!1))) = s(z)) <=> (s(elem!1) = s(z))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3495])).
% 1.54/1.76 tff(3497,plain,
% 1.54/1.76 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3496])).
% 1.54/1.76 tff(3498,plain,
% 1.54/1.76 (~(s(elem!1) = s(z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[851, 3497])).
% 1.54/1.76 tff(3499,plain,
% 1.54/1.76 (~(s(s(z)) = s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1188, 3498])).
% 1.54/1.76 tff(3500,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3499, 3494])).
% 1.54/1.76 tff(3501,plain,((~(s(s(z)) = elem!1)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(3502,plain,
% 1.54/1.76 (~(s(s(elem!1)) = elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3501, 3468])).
% 1.54/1.76 tff(3503,plain,
% 1.54/1.76 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3478])).
% 1.54/1.76 tff(3504,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.54/1.76 inference(symmetry,[status(thm)],[3503])).
% 1.54/1.76 tff(3505,plain,
% 1.54/1.76 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3504])).
% 1.54/1.76 tff(3506,plain,
% 1.54/1.76 (~b(s(s(elem!1)), elem!1)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[249, 3505])).
% 1.54/1.76 tff(3507,plain,
% 1.54/1.76 (r(s(s(elem!1)), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2240, 3506, 3502])).
% 1.54/1.76 tff(3508,plain,
% 1.54/1.76 ((s(z) = s(s(z))) <=> (s(z) = elem!1)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3468])).
% 1.54/1.76 tff(3509,plain,
% 1.54/1.76 ((s(z) = s(s(z))) <=> (elem!1 = s(z))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3508, 1120])).
% 1.54/1.76 tff(3510,plain,
% 1.54/1.76 ((~(s(z) = s(s(z)))) <=> (~(elem!1 = s(z)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3509])).
% 1.54/1.76 tff(3511,plain,
% 1.54/1.76 (~(elem!1 = s(z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[752, 3510])).
% 1.54/1.76 tff(3512,plain,
% 1.54/1.76 (r(elem!1, s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1130, 3511, 10])).
% 1.54/1.76 tff(3513,plain,
% 1.54/1.76 (~r(s(s(elem!1)), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1970, 3512, 3507])).
% 1.54/1.76 tff(3514,plain,
% 1.54/1.76 (b(s(s(elem!1)), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1047, 3513])).
% 1.54/1.76 tff(3515,plain,
% 1.54/1.76 (s(elem!1) = s(s(s(z)))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3469])).
% 1.54/1.76 tff(3516,plain,
% 1.54/1.76 ((s(elem!1) = elem!1) <=> (s(s(s(z))) = elem!1)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3515])).
% 1.54/1.76 tff(3517,plain,
% 1.54/1.76 ((s(s(s(z))) = elem!1) <=> (s(elem!1) = elem!1)),
% 1.54/1.76 inference(symmetry,[status(thm)],[3516])).
% 1.54/1.76 tff(3518,plain,
% 1.54/1.76 ((~(s(s(s(z))) = elem!1)) <=> (~(s(elem!1) = elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3517])).
% 1.54/1.76 tff(3519,plain,
% 1.54/1.76 ((s(s(s(z))) = s(s(z))) <=> (s(s(s(z))) = elem!1)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3468])).
% 1.54/1.76 tff(3520,plain,
% 1.54/1.76 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(s(z))) = elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3519])).
% 1.54/1.76 tff(3521,plain,
% 1.54/1.76 (~(s(s(s(z))) = elem!1)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[160, 3520])).
% 1.54/1.76 tff(3522,plain,
% 1.54/1.76 (~(s(elem!1) = elem!1)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3521, 3518])).
% 1.54/1.76 tff(3523,plain,
% 1.54/1.76 (r(s(s(s(z))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3469])).
% 1.54/1.76 tff(3524,plain,
% 1.54/1.76 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(elem!1), elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3523])).
% 1.54/1.76 tff(3525,plain,
% 1.54/1.76 (~r(s(elem!1), elem!1)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[2, 3524])).
% 1.54/1.76 tff(3526,plain,
% 1.54/1.76 (b(s(elem!1), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2440, 3525, 3522])).
% 1.54/1.76 tff(3527,plain,
% 1.54/1.76 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3478])).
% 1.54/1.76 tff(3528,plain,
% 1.54/1.76 ((s(elem!1) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3527])).
% 1.54/1.76 tff(3529,plain,
% 1.54/1.76 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3528])).
% 1.54/1.76 tff(3530,plain,
% 1.54/1.76 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3469])).
% 1.54/1.76 tff(3531,plain,
% 1.54/1.76 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3530, 2372])).
% 1.54/1.76 tff(3532,plain,
% 1.54/1.76 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3531])).
% 1.54/1.76 tff(3533,plain,
% 1.54/1.76 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[142, 3532])).
% 1.54/1.76 tff(3534,plain,
% 1.54/1.76 (~(s(elem!1) = s(s(elem!1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3533, 3529])).
% 1.54/1.76 tff(3535,plain,
% 1.54/1.76 (r(s(s(elem!1)), s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3478])).
% 1.54/1.76 tff(3536,plain,
% 1.54/1.76 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3535])).
% 1.54/1.76 tff(3537,plain,
% 1.54/1.76 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3478])).
% 1.54/1.76 tff(3538,plain,
% 1.54/1.76 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3478, 3537])).
% 1.54/1.76 tff(3539,plain,
% 1.54/1.76 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.54/1.76 inference(commutativity,[status(thm)],[])).
% 1.54/1.76 tff(3540,plain,
% 1.54/1.76 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3478, 3537])).
% 1.54/1.76 tff(3541,plain,
% 1.54/1.76 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3540, 3539])).
% 1.54/1.76 tff(3542,plain,
% 1.54/1.76 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3541])).
% 1.54/1.76 tff(3543,plain,
% 1.54/1.76 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3542])).
% 1.54/1.76 tff(3544,plain,
% 1.54/1.76 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[319, 3543])).
% 1.54/1.76 tff(3545,plain,
% 1.54/1.76 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3537])).
% 1.54/1.76 tff(3546,plain,
% 1.54/1.76 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3545])).
% 1.54/1.76 tff(3547,plain,
% 1.54/1.76 ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3546])).
% 1.54/1.76 tff(3548,plain,
% 1.54/1.76 ((s(s(elem!1)) = s(z)) <=> (s(z) = s(s(elem!1)))),
% 1.54/1.76 inference(symmetry,[status(thm)],[2308])).
% 1.54/1.76 tff(3549,plain,
% 1.54/1.76 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = s(s(elem!1))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3548])).
% 1.54/1.76 tff(3550,plain,
% 1.54/1.76 (~(s(z) = s(s(elem!1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[816, 3549])).
% 1.54/1.76 tff(3551,plain,
% 1.54/1.76 ((~(s(z) = s(s(z)))) <=> (~(s(z) = elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3508])).
% 1.54/1.76 tff(3552,plain,
% 1.54/1.76 (~(s(z) = elem!1)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[752, 3551])).
% 1.54/1.76 tff(3553,plain,
% 1.54/1.76 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3469])).
% 1.54/1.76 tff(3554,plain,
% 1.54/1.76 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3553])).
% 1.54/1.76 tff(3555,plain,
% 1.54/1.76 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3554])).
% 1.54/1.76 tff(3556,plain,
% 1.54/1.77 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3537])).
% 1.54/1.77 tff(3557,plain,
% 1.54/1.77 (b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[2220, 3556])).
% 1.54/1.77 tff(3558,plain,
% 1.54/1.77 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[877, 833, 869])).
% 1.54/1.77 tff(3559,plain,
% 1.54/1.77 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[675, 3558, 3544])).
% 1.54/1.77 tff(3560,plain,
% 1.54/1.77 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3559, 3545])).
% 1.54/1.77 tff(3561,plain,
% 1.54/1.77 (~r(s(s(elem!1)), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1970, 238, 869])).
% 1.54/1.77 tff(3562,plain,
% 1.54/1.77 (b(s(s(elem!1)), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1047, 3561])).
% 1.54/1.77 tff(3563,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), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3564,plain,
% 1.54/1.77 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3565,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), 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(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3564])).
% 1.54/1.77 tff(3566,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), 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(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3565, 3563])).
% 1.54/1.77 tff(3567,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3568,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3567, 3566])).
% 1.54/1.77 tff(3569,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3568, 453, 499, 3562, 3560, 3557])).
% 1.54/1.77 tff(3570,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~(s(s(z)) = elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(3571,plain,
% 1.54/1.77 (~r(s(s(s(elem!1))), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3570, 499, 3468, 238, 869])).
% 1.54/1.77 tff(3572,plain,
% 1.54/1.77 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3537])).
% 1.54/1.77 tff(3573,plain,
% 1.54/1.77 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.54/1.77 inference(symmetry,[status(thm)],[3572])).
% 1.54/1.77 tff(3574,plain,
% 1.54/1.77 (r(s(s(s(elem!1))), elem!1)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[722, 3573])).
% 1.54/1.77 tff(3575,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[563, 3574])).
% 1.54/1.77 tff(3576,plain,((~(s(s(z)) = elem!1)) | r(s(s(s(elem!1))), elem!1) | (~r(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(3577,plain,
% 1.54/1.77 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3576, 3571, 3468])).
% 1.54/1.77 tff(3578,plain,
% 1.54/1.77 (b(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[643, 3577, 637])).
% 1.54/1.77 tff(3579,plain,
% 1.54/1.77 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3517, 1028])).
% 1.54/1.77 tff(3580,plain,
% 1.54/1.77 ((~(s(s(s(z))) = elem!1)) <=> (~(elem!1 = s(elem!1)))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3579])).
% 1.54/1.77 tff(3581,plain,
% 1.54/1.77 (~(elem!1 = s(elem!1))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3521, 3580])).
% 1.54/1.77 tff(3582,plain,
% 1.54/1.77 ((s(z) = s(s(s(z)))) <=> (s(z) = s(elem!1))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3469])).
% 1.54/1.77 tff(3583,plain,
% 1.54/1.77 ((s(z) = s(s(s(z)))) <=> (s(elem!1) = s(z))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3582, 173])).
% 1.54/1.77 tff(3584,plain,
% 1.54/1.77 ((s(z) = s(s(s(z)))) <=> (s(z) = s(elem!1))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3583, 174])).
% 1.54/1.77 tff(3585,plain,
% 1.54/1.77 ((~(s(z) = s(s(s(z))))) <=> (~(s(z) = s(elem!1)))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3584])).
% 1.54/1.77 tff(3586,plain,
% 1.54/1.77 (~(s(z) = s(elem!1))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[109, 3585])).
% 1.54/1.77 tff(3587,plain,
% 1.54/1.77 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3537])).
% 1.54/1.77 tff(3588,plain,
% 1.54/1.77 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[3587])).
% 1.54/1.77 tff(3589,plain,
% 1.54/1.77 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3468])).
% 1.54/1.77 tff(3590,plain,
% 1.54/1.77 ((s(s(s(s(s(z))))) = s(s(z))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3589, 55])).
% 1.54/1.77 tff(3591,plain,
% 1.54/1.77 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3590])).
% 1.54/1.77 tff(3592,plain,
% 1.54/1.77 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[52, 3591])).
% 1.54/1.77 tff(3593,plain,
% 1.54/1.77 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2152, 1549, 499, 629])).
% 1.54/1.77 tff(3594,plain,
% 1.54/1.77 (r(elem!1, s(s(s(s(s(z))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[466, 3593, 3592])).
% 1.54/1.77 tff(3595,plain,
% 1.54/1.77 (r(elem!1, s(s(s(elem!1))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3594, 3588])).
% 1.54/1.77 tff(3596,plain,
% 1.54/1.77 (~r(s(s(s(elem!1))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1423, 3595, 238])).
% 1.54/1.77 tff(3597,plain,
% 1.54/1.77 (b(s(s(s(elem!1))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[856, 3596])).
% 1.54/1.77 tff(3598,plain,
% 1.54/1.77 (b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3597, 3556])).
% 1.54/1.77 tff(3599,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(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3600,plain,
% 1.54/1.77 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3601,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(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), 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(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3600])).
% 1.54/1.77 tff(3602,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(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), 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(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3601, 3599])).
% 1.54/1.77 tff(3603,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(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3604,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(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3603, 3602])).
% 1.54/1.77 tff(3605,plain,
% 1.54/1.77 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3604, 453, 1549, 1050, 3598])).
% 1.54/1.77 tff(3606,plain,
% 1.54/1.77 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3605, 3547])).
% 1.54/1.77 tff(3607,plain,
% 1.54/1.77 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[675, 3606, 3544])).
% 1.54/1.77 tff(3608,plain,
% 1.54/1.77 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3607, 3538])).
% 1.54/1.77 tff(3609,plain,
% 1.54/1.77 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[3483])).
% 1.54/1.77 tff(3610,plain,
% 1.54/1.77 ((s(s(s(s(z)))) = s(s(z))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3488, 3609])).
% 1.54/1.77 tff(3611,plain,
% 1.54/1.77 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3610])).
% 1.54/1.77 tff(3612,plain,
% 1.54/1.77 (~(elem!1 = s(s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[153, 3611])).
% 1.54/1.77 tff(3613,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), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3614,plain,
% 1.54/1.77 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3615,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3614])).
% 1.54/1.77 tff(3616,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3615, 3613])).
% 1.54/1.77 tff(3617,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3618,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3617, 3616])).
% 1.54/1.77 tff(3619,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3618, 453, 499, 646, 530, 374])).
% 1.54/1.77 tff(3620,plain,((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(3621,plain,
% 1.54/1.77 (~b(elem!1, s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3620, 3598, 499, 646])).
% 1.54/1.77 tff(3622,plain,
% 1.54/1.77 (r(elem!1, s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1087, 3621, 3612])).
% 1.54/1.77 tff(3623,plain,
% 1.54/1.77 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[427, 3622, 3594])).
% 1.54/1.77 tff(3624,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3623, 3608])).
% 1.54/1.77 tff(3625,plain,((~b(s(z), s(elem!1))) | (~(s(s(z)) = elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(3626,plain,
% 1.54/1.77 (~b(s(z), s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3625, 499, 3468, 3578, 3562, 238, 629])).
% 1.54/1.77 tff(3627,plain,
% 1.54/1.77 (r(s(z), s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[397, 3626, 3586])).
% 1.54/1.77 tff(3628,plain,
% 1.54/1.77 (~r(elem!1, s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1496, 3627, 238])).
% 1.54/1.77 tff(3629,plain,
% 1.54/1.77 (b(elem!1, s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1069, 3628, 3581])).
% 1.54/1.77 tff(3630,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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3631,plain,
% 1.54/1.77 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3632,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3631])).
% 1.54/1.77 tff(3633,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3632, 3630])).
% 1.54/1.77 tff(3634,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3635,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3634, 3633])).
% 1.54/1.77 tff(3636,plain,
% 1.54/1.77 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3635, 453, 629, 3629, 3578])).
% 1.54/1.77 tff(3637,plain,
% 1.54/1.77 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3636, 3555])).
% 1.54/1.77 tff(3638,plain,
% 1.54/1.77 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3469])).
% 1.54/1.77 tff(3639,plain,
% 1.54/1.77 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(z))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[3638])).
% 1.54/1.77 tff(3640,plain,
% 1.54/1.77 ((~b(s(z), s(elem!1))) <=> (~b(s(z), s(s(s(z)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3639])).
% 1.54/1.77 tff(3641,assumption,(~b(s(z), s(elem!1))), introduced(assumption)).
% 1.54/1.77 tff(3642,plain,
% 1.54/1.77 (~b(s(z), s(s(s(z))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3641, 3640])).
% 1.54/1.77 tff(3643,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2090, 3642])).
% 1.54/1.77 tff(3644,plain,(b(s(z), s(elem!1)) | (~b(s(z), s(s(s(z))))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(3645,plain,
% 1.54/1.77 (~b(s(z), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3644, 3626, 3468])).
% 1.54/1.77 tff(3646,plain,
% 1.54/1.77 (r(s(z), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[227, 3645])).
% 1.54/1.77 tff(3647,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(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3648,plain,
% 1.54/1.77 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3649,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3648])).
% 1.54/1.77 tff(3650,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3649, 3647])).
% 1.54/1.77 tff(3651,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3652,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3651, 3650])).
% 1.54/1.77 tff(3653,plain,
% 1.54/1.77 (~b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3652, 453, 499, 3629, 3578])).
% 1.54/1.77 tff(3654,plain,
% 1.54/1.77 (r(s(s(s(s(s(z))))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[297, 3653])).
% 1.54/1.77 tff(3655,plain,
% 1.54/1.77 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[276, 3654, 3646])).
% 1.54/1.77 tff(3656,plain,
% 1.54/1.77 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[687, 3655])).
% 1.54/1.77 tff(3657,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3656, 3637])).
% 1.54/1.77 tff(3658,plain,((~b(s(z), elem!1)) | (~(s(s(z)) = elem!1)) | (~b(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(3659,plain,
% 1.54/1.77 (~b(s(z), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3658, 3468, 3526, 3512, 637, 3507])).
% 1.54/1.78 tff(3660,plain,
% 1.54/1.78 (r(s(z), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[506, 3659, 3552])).
% 1.54/1.78 tff(3661,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3662,plain,
% 1.54/1.78 (((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3663,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3662])).
% 1.54/1.78 tff(3664,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.54/1.78 inference(transitivity,[status(thm)],[3663, 3661])).
% 1.54/1.78 tff(3665,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(3666,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3665, 3664])).
% 1.54/1.78 tff(3667,plain,
% 1.54/1.78 (~r(s(z), s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3666, 268, 3660, 3507])).
% 1.54/1.78 tff(3668,plain,
% 1.54/1.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3669,plain,
% 1.54/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(3670,plain,
% 1.54/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3669, 3668])).
% 1.54/1.78 tff(3671,plain,
% 1.54/1.78 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3670, 69, 3667])).
% 1.54/1.78 tff(3672,plain,
% 1.54/1.78 (b(s(z), s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3671, 3550])).
% 1.54/1.78 tff(3673,plain,
% 1.54/1.78 (~r(s(z), s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3666, 268, 701, 869])).
% 1.54/1.78 tff(3674,plain,
% 1.54/1.78 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3670, 69, 3673])).
% 1.54/1.78 tff(3675,plain,
% 1.54/1.78 (b(s(z), s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3674, 3550])).
% 1.54/1.78 tff(3676,plain,
% 1.54/1.78 (~r(s(s(s(s(s(z))))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[730, 722, 701])).
% 1.54/1.78 tff(3677,plain,
% 1.54/1.78 (b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[297, 3676])).
% 1.54/1.78 tff(3678,plain,
% 1.54/1.78 (r(s(s(s(elem!1))), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3576, 722, 3468])).
% 1.54/1.78 tff(3679,plain,
% 1.54/1.78 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[877, 3678, 869])).
% 1.54/1.78 tff(3680,plain,
% 1.54/1.78 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[675, 3679, 3544])).
% 1.54/1.78 tff(3681,plain,
% 1.54/1.78 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3680, 3545])).
% 1.54/1.78 tff(3682,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(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3683,plain,
% 1.54/1.78 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3684,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(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), 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(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3683])).
% 1.54/1.78 tff(3685,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(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), 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(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[3684, 3682])).
% 1.54/1.78 tff(3686,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(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(3687,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3686, 3685])).
% 1.54/1.78 tff(3688,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3687, 453, 1050, 3681, 3677, 3675])).
% 1.54/1.78 tff(3689,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~(s(s(z)) = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(3690,plain,
% 1.54/1.78 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3689, 3514, 3468, 3507, 3660])).
% 1.54/1.78 tff(3691,plain,
% 1.54/1.78 (b(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[643, 3690, 637])).
% 1.54/1.78 tff(3692,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.54/1.78 tff(3693,plain,
% 1.54/1.78 ((~(s(z) = s(s(s(z))))) <=> (~(s(elem!1) = s(z)))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3583])).
% 1.54/1.78 tff(3694,plain,
% 1.54/1.78 (~(s(elem!1) = s(z))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[109, 3693])).
% 1.54/1.78 tff(3695,plain,
% 1.54/1.78 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3469])).
% 1.54/1.78 tff(3696,plain,
% 1.54/1.78 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[3695, 624])).
% 1.54/1.78 tff(3697,plain,
% 1.54/1.78 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(s(s(z)))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3696])).
% 1.54/1.78 tff(3698,plain,
% 1.54/1.78 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[111, 3697])).
% 1.54/1.78 tff(3699,plain,
% 1.54/1.78 (r(s(s(s(s(s(z))))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[297, 278])).
% 1.54/1.78 tff(3700,assumption,(~(s(elem!1) = s(s(s(s(s(z))))))), introduced(assumption)).
% 1.54/1.78 tff(3701,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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3702,plain,
% 1.54/1.78 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3703,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3702])).
% 1.54/1.78 tff(3704,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.54/1.78 inference(transitivity,[status(thm)],[3703, 3701])).
% 1.54/1.78 tff(3705,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(3706,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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3705, 3704])).
% 1.54/1.78 tff(3707,plain,
% 1.54/1.78 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3706, 453, 629, 1445, 646])).
% 1.54/1.78 tff(3708,plain,
% 1.54/1.78 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[659, 3707, 3700])).
% 1.54/1.78 tff(3709,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3710,plain,
% 1.54/1.78 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3711,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3710])).
% 1.54/1.78 tff(3712,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[3711, 3709])).
% 1.54/1.78 tff(3713,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(3714,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3713, 3712])).
% 1.54/1.78 tff(3715,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3714, 268, 340, 258, 3708])).
% 1.54/1.78 tff(3716,plain,((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (s(elem!1) = s(s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (elem!1 = s(elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(3717,plain,
% 1.54/1.78 (~r(s(elem!1), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3716, 3699, 3698, 629, 646, 3581, 238])).
% 1.54/1.78 tff(3718,plain,
% 1.54/1.78 (b(s(elem!1), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[353, 3717, 3694])).
% 1.54/1.78 tff(3719,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(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3720,plain,
% 1.54/1.78 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3721,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(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3720])).
% 1.54/1.78 tff(3722,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(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[3721, 3719])).
% 1.54/1.78 tff(3723,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(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(3724,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(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3723, 3722])).
% 1.54/1.78 tff(3725,plain,
% 1.54/1.78 (~b(s(elem!1), s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3724, 453, 3718, 1050, 3692])).
% 1.54/1.78 tff(3726,plain,
% 1.54/1.78 (r(s(elem!1), s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[440, 3725, 3534])).
% 1.54/1.78 tff(3727,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.78 inference(symmetry,[status(thm)],[3538])).
% 1.54/1.78 tff(3728,plain,
% 1.54/1.78 (r(s(s(elem!1)), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[3535, 3727])).
% 1.54/1.78 tff(3729,plain,
% 1.54/1.78 ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3728])).
% 1.54/1.78 tff(3730,plain,
% 1.54/1.78 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3695])).
% 1.54/1.78 tff(3731,plain,
% 1.54/1.78 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[111, 3730])).
% 1.54/1.78 tff(3732,plain,
% 1.54/1.78 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3537])).
% 1.54/1.78 tff(3733,plain,
% 1.54/1.78 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3537])).
% 1.54/1.78 tff(3734,plain,
% 1.54/1.78 ((elem!1 = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.54/1.78 inference(symmetry,[status(thm)],[3733])).
% 1.54/1.78 tff(3735,plain,
% 1.54/1.78 ((~(elem!1 = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3734])).
% 1.54/1.78 tff(3736,plain,
% 1.54/1.78 (~(elem!1 = s(s(s(elem!1))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3592, 3735])).
% 1.54/1.78 tff(3737,plain,
% 1.54/1.78 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.54/1.78 inference(symmetry,[status(thm)],[3556])).
% 1.54/1.78 tff(3738,plain,
% 1.54/1.78 ((~b(s(s(s(s(s(z))))), s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3737])).
% 1.54/1.78 tff(3739,plain,
% 1.54/1.78 (~b(s(s(s(elem!1))), s(z))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[278, 3738])).
% 1.54/1.78 tff(3740,plain,
% 1.54/1.78 (r(s(s(s(elem!1))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[856, 3739])).
% 1.54/1.78 tff(3741,plain,
% 1.54/1.78 (~r(elem!1, s(s(s(elem!1))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1423, 3740, 238])).
% 1.54/1.78 tff(3742,plain,
% 1.54/1.78 (b(elem!1, s(s(s(elem!1))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1428, 3741, 3736])).
% 1.54/1.78 tff(3743,plain,
% 1.54/1.78 (b(elem!1, s(s(s(s(s(z))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3742, 3732])).
% 1.54/1.78 tff(3744,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(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3745,plain,
% 1.54/1.78 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3746,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(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3745])).
% 1.54/1.78 tff(3747,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(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3746, 3744])).
% 1.54/1.79 tff(3748,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(3749,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3748, 3747])).
% 1.54/1.79 tff(3750,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3749, 453, 629, 3743, 646, 2129])).
% 1.54/1.79 tff(3751,plain,((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~(s(s(z)) = elem!1)) | (~r(elem!1, s(z))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(3752,plain,
% 1.54/1.79 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3751, 278, 646, 3468, 238, 629])).
% 1.54/1.79 tff(3753,plain,
% 1.54/1.79 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2142, 3752, 3731])).
% 1.54/1.79 tff(3754,plain,
% 1.54/1.79 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3478])).
% 1.54/1.79 tff(3755,plain,
% 1.54/1.79 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3754])).
% 1.54/1.79 tff(3756,plain,
% 1.54/1.79 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3469])).
% 1.54/1.79 tff(3757,plain,
% 1.54/1.79 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3756, 3755])).
% 1.54/1.79 tff(3758,plain,
% 1.54/1.79 (r(s(s(s(z))), s(z)) <=> r(s(elem!1), s(z))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3469])).
% 1.54/1.79 tff(3759,plain,
% 1.54/1.79 (r(s(elem!1), s(z)) <=> r(s(s(s(z))), s(z))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3758])).
% 1.54/1.79 tff(3760,plain,
% 1.54/1.79 ((~r(s(elem!1), s(z))) <=> (~r(s(s(s(z))), s(z)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3759])).
% 1.54/1.79 tff(3761,assumption,(~r(s(elem!1), s(z))), introduced(assumption)).
% 1.54/1.79 tff(3762,plain,
% 1.54/1.79 (~r(s(s(s(z))), s(z))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3761, 3760])).
% 1.54/1.79 tff(3763,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[233, 3762])).
% 1.54/1.79 tff(3764,plain,(r(s(elem!1), s(z)) | (~r(s(s(s(z))), s(z))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(3765,plain,
% 1.54/1.79 (~r(s(s(s(z))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3764, 3717, 3468])).
% 1.54/1.79 tff(3766,plain,
% 1.54/1.79 (b(s(s(s(z))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[134, 3765])).
% 1.54/1.79 tff(3767,plain,
% 1.54/1.79 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3477])).
% 1.54/1.79 tff(3768,plain,
% 1.54/1.79 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3767])).
% 1.54/1.79 tff(3769,plain,
% 1.54/1.79 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1050, 3768])).
% 1.54/1.79 tff(3770,plain,
% 1.54/1.79 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3469])).
% 1.54/1.79 tff(3771,plain,
% 1.54/1.79 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3770])).
% 1.54/1.79 tff(3772,plain,
% 1.54/1.79 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3753, 3771])).
% 1.54/1.79 tff(3773,plain,
% 1.54/1.79 (~r(s(z), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[276, 3772, 3699])).
% 1.54/1.79 tff(3774,plain,
% 1.54/1.79 (b(s(z), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[227, 3773])).
% 1.54/1.79 tff(3775,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(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3776,plain,
% 1.54/1.79 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(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(z)))), s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3777,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(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(z)))), s(z)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3776])).
% 1.54/1.79 tff(3778,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(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(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(z)))), s(z))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3777, 3775])).
% 1.54/1.79 tff(3779,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(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(3780,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3779, 3778])).
% 1.54/1.79 tff(3781,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3780, 453, 523, 1764, 120, 2090])).
% 1.54/1.79 tff(3782,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(3783,plain,
% 1.54/1.79 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3782, 3774, 3769, 3766])).
% 1.54/1.79 tff(3784,plain,
% 1.54/1.79 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[518, 3783])).
% 1.54/1.79 tff(3785,plain,
% 1.54/1.79 (r(s(s(elem!1)), s(elem!1))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3784, 3757])).
% 1.54/1.79 tff(3786,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3787,plain,
% 1.54/1.79 (((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3788,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3787])).
% 1.54/1.79 tff(3789,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3788, 3786])).
% 1.54/1.79 tff(3790,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(3791,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3790, 3789])).
% 1.54/1.79 tff(3792,plain,
% 1.54/1.79 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3791, 268, 3785, 3753])).
% 1.54/1.79 tff(3793,plain,
% 1.54/1.79 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3792, 3729])).
% 1.54/1.79 tff(3794,plain,
% 1.54/1.79 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[675, 3793, 3544])).
% 1.54/1.79 tff(3795,plain,
% 1.54/1.79 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3794, 3545])).
% 1.54/1.79 tff(3796,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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3797,plain,
% 1.54/1.79 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3798,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(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3797])).
% 1.54/1.79 tff(3799,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(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3798, 3796])).
% 1.54/1.79 tff(3800,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(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(elem!1)))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(3801,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3800, 3799])).
% 1.54/1.79 tff(3802,plain,
% 1.54/1.79 (~b(elem!1, s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3801, 453, 3743, 646, 3795])).
% 1.54/1.79 tff(3803,plain,
% 1.54/1.79 (r(elem!1, s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1024, 3802, 3491])).
% 1.54/1.79 tff(3804,plain,
% 1.54/1.79 (elem!1 = s(s(z))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3468])).
% 1.54/1.79 tff(3805,plain,
% 1.54/1.79 (inj_0(s(s(s(s(s(s(s(s(z))))))))) = inj_0(s(elem!1))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[2331])).
% 1.54/1.79 tff(3806,plain,
% 1.54/1.79 (s(s(s(s(s(s(s(z))))))) = s(s(z))),
% 1.54/1.79 inference(transitivity,[status(thm)],[2336, 3805, 85, 3804])).
% 1.54/1.79 tff(3807,plain,
% 1.54/1.79 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(z)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3806])).
% 1.54/1.79 tff(3808,plain,
% 1.54/1.79 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3807])).
% 1.54/1.79 tff(3809,plain,
% 1.54/1.79 (s(z) = s(s(s(s(s(s(z))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[29, 3808, 1174])).
% 1.54/1.79 tff(3810,plain,
% 1.54/1.79 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3809])).
% 1.54/1.79 tff(3811,plain,
% 1.54/1.79 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3810])).
% 1.54/1.79 tff(3812,plain,
% 1.54/1.79 (s(s(s(s(s(z))))) = z),
% 1.54/1.79 inference(transitivity,[status(thm)],[808, 3811, 32])).
% 1.54/1.79 tff(3813,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2549, 3812])).
% 1.54/1.79 tff(3814,plain,((~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(3815,plain,
% 1.54/1.79 (~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3814, 3468])).
% 1.54/1.79 tff(3816,assumption,(elem!1 = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.54/1.79 tff(3817,plain,
% 1.54/1.79 (s(s(s(s(s(s(s(z))))))) = elem!1),
% 1.54/1.79 inference(symmetry,[status(thm)],[3816])).
% 1.54/1.79 tff(3818,plain,
% 1.54/1.79 (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3817])).
% 1.54/1.79 tff(3819,plain,
% 1.54/1.79 (s(elem!1) = s(s(s(s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(symmetry,[status(thm)],[3818])).
% 1.54/1.79 tff(3820,assumption,(~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 1.54/1.79 tff(3821,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3820, 3819])).
% 1.54/1.79 tff(3822,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(3823,plain,
% 1.54/1.79 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3822, 3815])).
% 1.54/1.79 tff(3824,plain,
% 1.54/1.79 ((~(s(s(s(z))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3470])).
% 1.54/1.79 tff(3825,plain,
% 1.54/1.79 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3475, 3824])).
% 1.54/1.79 tff(3826,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3827,plain,
% 1.54/1.79 (((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3828,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3827])).
% 1.54/1.79 tff(3829,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3828, 3826])).
% 1.54/1.79 tff(3830,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(3831,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3830, 3829])).
% 1.54/1.79 tff(3832,plain,
% 1.54/1.79 (~r(elem!1, s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3831, 268, 3803, 3726])).
% 1.54/1.79 tff(3833,plain,
% 1.54/1.79 (b(elem!1, s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1069, 3832, 3581])).
% 1.54/1.79 tff(3834,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))), introduced(assumption)).
% 1.54/1.79 tff(3835,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3836,plain,
% 1.54/1.79 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3837,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3836])).
% 1.54/1.79 tff(3838,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3837, 3835])).
% 1.54/1.79 tff(3839,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(3840,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3839, 3838])).
% 1.54/1.79 tff(3841,plain,
% 1.54/1.79 ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3840, 268, 431])).
% 1.54/1.79 tff(3842,plain,
% 1.54/1.79 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3841, 3834])).
% 1.54/1.79 tff(3843,plain,
% 1.54/1.79 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1320, 3842, 1442])).
% 1.54/1.79 tff(3844,assumption,(~(elem!1 = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.54/1.79 tff(3845,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3846,plain,
% 1.54/1.79 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(3847,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[3846])).
% 1.54/1.79 tff(3848,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3847, 3845])).
% 1.54/1.79 tff(3849,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(3850,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.54/1.80 inference(modus_ponens,[status(thm)],[3849, 3848])).
% 1.54/1.80 tff(3851,plain,
% 1.54/1.80 ((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[3850, 268, 1032])).
% 1.54/1.80 tff(3852,plain,
% 1.54/1.80 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[3851, 3834])).
% 1.54/1.80 tff(3853,plain,
% 1.54/1.80 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.54/1.80 tff(3854,plain,
% 1.54/1.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 1.54/1.80 inference(quant_inst,[status(thm)],[])).
% 1.54/1.80 tff(3855,plain,
% 1.54/1.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.54/1.80 inference(modus_ponens,[status(thm)],[3854, 3853])).
% 1.54/1.80 tff(3856,plain,
% 1.54/1.80 ((elem!1 = s(s(s(s(s(s(s(z)))))))) | b(elem!1, s(s(s(s(s(s(s(z)))))))) | r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[3855, 69])).
% 1.54/1.80 tff(3857,plain,
% 1.54/1.80 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[3856, 3852, 3844])).
% 1.54/1.80 tff(3858,plain,
% 1.54/1.80 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.54/1.80 inference(commutativity,[status(thm)],[])).
% 1.54/1.80 tff(3859,assumption,(s(s(s(s(s(s(s(z))))))) = elem!1), introduced(assumption)).
% 1.54/1.80 tff(3860,plain,
% 1.54/1.80 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 1.54/1.80 inference(modus_ponens,[status(thm)],[3859, 3858])).
% 1.54/1.80 tff(3861,plain,
% 1.54/1.80 ($false),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[3844, 3860])).
% 1.54/1.80 tff(3862,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (elem!1 = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.80 tff(3863,plain,
% 1.54/1.80 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[3862, 3844])).
% 1.54/1.80 tff(3864,plain,
% 1.54/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.54/1.80 tff(3865,plain,
% 1.54/1.80 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.54/1.80 tff(3866,plain,
% 1.54/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.54/1.80 inference(monotonicity,[status(thm)],[3865])).
% 1.54/1.80 tff(3867,plain,
% 1.54/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[3866, 3864])).
% 1.64/1.80 tff(3868,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3869,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3868, 3867])).
% 1.64/1.80 tff(3870,plain,
% 1.64/1.80 ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3869, 268, 238, 1032])).
% 1.64/1.80 tff(3871,plain,
% 1.64/1.80 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3870, 3834])).
% 1.64/1.80 tff(3872,plain,
% 1.64/1.80 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3873,plain,
% 1.64/1.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3874,plain,
% 1.64/1.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3873, 3872])).
% 1.64/1.80 tff(3875,plain,
% 1.64/1.80 ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3874, 69])).
% 1.64/1.80 tff(3876,plain,
% 1.64/1.80 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3875, 3871, 3863])).
% 1.64/1.80 tff(3877,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1454, 3876, 3857, 1071, 3843])).
% 1.64/1.80 tff(3878,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(3879,plain,
% 1.64/1.80 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3878, 3833, 3825, 3823, 238, 3803, 3726])).
% 1.64/1.80 tff(3880,plain,
% 1.64/1.80 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3879, 3482])).
% 1.64/1.80 tff(3881,plain,
% 1.64/1.80 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2696, 3880])).
% 1.64/1.80 tff(3882,plain,
% 1.64/1.80 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3881, 3480])).
% 1.64/1.80 tff(3883,plain,
% 1.64/1.80 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3478])).
% 1.64/1.80 tff(3884,plain,
% 1.64/1.80 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[3883])).
% 1.64/1.80 tff(3885,plain,
% 1.64/1.80 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1982, 3784, 3772])).
% 1.64/1.80 tff(3886,plain,
% 1.64/1.80 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[328, 3885])).
% 1.64/1.80 tff(3887,plain,
% 1.64/1.80 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3886, 3884])).
% 1.64/1.80 tff(3888,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3889,plain,
% 1.64/1.80 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3890,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3889])).
% 1.64/1.80 tff(3891,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[3890, 3888])).
% 1.64/1.80 tff(3892,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3893,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3892, 3891])).
% 1.64/1.80 tff(3894,plain,
% 1.64/1.80 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3893, 453, 1050, 3887])).
% 1.64/1.80 tff(3895,plain,
% 1.64/1.80 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3894, 3882])).
% 1.64/1.80 tff(3896,plain,
% 1.64/1.80 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2732, 69, 2729, 3895])).
% 1.64/1.80 tff(3897,plain,
% 1.64/1.80 (b(s(z), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3644, 3774, 3468])).
% 1.64/1.80 tff(3898,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3899,plain,
% 1.64/1.80 (((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3900,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(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(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3899])).
% 1.64/1.80 tff(3901,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(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(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[3900, 3898])).
% 1.64/1.80 tff(3902,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3903,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3902, 3901])).
% 1.64/1.80 tff(3904,plain,
% 1.64/1.80 ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3903, 453, 3718, 3897, 1050, 3692])).
% 1.64/1.80 tff(3905,plain,
% 1.64/1.80 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3904, 3882])).
% 1.64/1.80 tff(3906,plain,
% 1.64/1.80 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2647, 69, 2636, 3905])).
% 1.64/1.80 tff(3907,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3908,plain,
% 1.64/1.80 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3909,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3908])).
% 1.64/1.80 tff(3910,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[3909, 3907])).
% 1.64/1.80 tff(3911,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3912,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3911, 3910])).
% 1.64/1.80 tff(3913,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3912, 268, 3699, 3906, 3896])).
% 1.64/1.80 tff(3914,plain,(b(s(s(s(s(s(z))))), s(z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~(s(s(z)) = elem!1)) | (~r(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(3915,plain,
% 1.64/1.80 (b(s(s(s(s(s(z))))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3914, 3514, 3672, 3468, 3512, 3691, 3526])).
% 1.64/1.80 tff(3916,plain,
% 1.64/1.80 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3687, 453, 3514, 3915, 3672])).
% 1.64/1.80 tff(3917,plain,
% 1.64/1.80 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3916, 3547])).
% 1.64/1.80 tff(3918,plain,
% 1.64/1.80 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[675, 3917, 3544])).
% 1.64/1.80 tff(3919,plain,
% 1.64/1.80 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3918, 3538])).
% 1.64/1.80 tff(3920,plain,
% 1.64/1.80 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3919, 3536])).
% 1.64/1.80 tff(3921,plain,
% 1.64/1.80 ((~b(s(z), s(s(s(z))))) <=> (~b(s(z), s(elem!1)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3638])).
% 1.64/1.80 tff(3922,plain,
% 1.64/1.80 ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3883])).
% 1.64/1.80 tff(3923,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3924,plain,
% 1.64/1.80 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(3925,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[3924])).
% 1.64/1.80 tff(3926,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[3925, 3923])).
% 1.64/1.80 tff(3927,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(3928,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3927, 3926])).
% 1.64/1.80 tff(3929,plain,
% 1.64/1.80 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3928, 453, 3514, 3915, 3672])).
% 1.64/1.80 tff(3930,plain,
% 1.64/1.80 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3929, 3922])).
% 1.64/1.80 tff(3931,plain,
% 1.64/1.80 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[328, 3930])).
% 1.64/1.80 tff(3932,plain,
% 1.64/1.80 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3514, 3768])).
% 1.64/1.80 tff(3933,plain,
% 1.64/1.80 (b(s(z), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3644, 2090, 3468])).
% 1.64/1.80 tff(3934,plain,
% 1.64/1.80 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2137, 3933, 629, 374])).
% 1.64/1.80 tff(3935,plain,
% 1.64/1.80 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2142, 3934, 3731])).
% 1.64/1.80 tff(3936,plain,
% 1.64/1.80 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3935, 3771])).
% 1.64/1.80 tff(3937,plain,
% 1.64/1.80 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1982, 3936, 301])).
% 1.64/1.80 tff(3938,plain,
% 1.64/1.80 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[518, 3937])).
% 1.64/1.80 tff(3939,plain,
% 1.64/1.80 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[309, 3936, 301])).
% 1.64/1.80 tff(3940,plain,
% 1.64/1.80 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1656, 3939])).
% 1.64/1.80 tff(3941,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2102, 3940, 3938, 2090, 1764])).
% 1.64/1.80 tff(3942,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~(s(s(z)) = elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(3943,plain,
% 1.64/1.80 (~b(s(z), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3942, 3932, 3931, 3468, 3526, 3915])).
% 1.64/1.80 tff(3944,plain,
% 1.64/1.80 (~b(s(z), s(elem!1))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[3943, 3921])).
% 1.64/1.81 tff(3945,plain,
% 1.64/1.81 (r(s(z), s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[397, 3944, 3586])).
% 1.64/1.81 tff(3946,plain,
% 1.64/1.81 (~r(elem!1, s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1496, 3945, 3512])).
% 1.64/1.81 tff(3947,plain,
% 1.64/1.81 (b(elem!1, s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1069, 3946, 3581])).
% 1.64/1.81 tff(3948,plain,
% 1.64/1.81 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3706, 453, 3526, 3947, 3691])).
% 1.64/1.81 tff(3949,plain,
% 1.64/1.81 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[659, 3948, 3698])).
% 1.64/1.81 tff(3950,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3951,plain,
% 1.64/1.81 (((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3952,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3951])).
% 1.64/1.81 tff(3953,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[3952, 3950])).
% 1.64/1.81 tff(3954,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(3955,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3954, 3953])).
% 1.64/1.81 tff(3956,plain,
% 1.64/1.81 (~r(s(elem!1), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3955, 268, 3507, 3949, 3920])).
% 1.64/1.81 tff(3957,plain,
% 1.64/1.81 (b(s(elem!1), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[440, 3956, 3534])).
% 1.64/1.81 tff(3958,plain,
% 1.64/1.81 (~b(elem!1, s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3181, 3957, 3526, 3514])).
% 1.64/1.81 tff(3959,plain,
% 1.64/1.81 (r(elem!1, s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1024, 3958, 3491])).
% 1.64/1.81 tff(3960,plain,
% 1.64/1.81 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3478])).
% 1.64/1.81 tff(3961,plain,
% 1.64/1.81 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.81 inference(symmetry,[status(thm)],[3960])).
% 1.64/1.81 tff(3962,plain,
% 1.64/1.81 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3931, 3961])).
% 1.64/1.81 tff(3963,assumption,(r(s(s(s(s(s(z))))), s(s(elem!1)))), introduced(assumption)).
% 1.64/1.81 tff(3964,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3965,plain,
% 1.64/1.81 (((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3966,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3965])).
% 1.64/1.81 tff(3967,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[3966, 3964])).
% 1.64/1.81 tff(3968,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(3969,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3968, 3967])).
% 1.64/1.81 tff(3970,plain,
% 1.64/1.81 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3969, 268, 3834, 3963])).
% 1.64/1.81 tff(3971,plain,
% 1.64/1.81 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2732, 69, 2729, 3970])).
% 1.64/1.81 tff(3972,plain,
% 1.64/1.81 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3869, 268, 238, 1032, 3834])).
% 1.64/1.81 tff(3973,plain,
% 1.64/1.81 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3875, 3972, 3863])).
% 1.64/1.81 tff(3974,plain,
% 1.64/1.81 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3850, 268, 1032, 3834])).
% 1.64/1.81 tff(3975,plain,
% 1.64/1.81 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3856, 3974, 3844])).
% 1.64/1.81 tff(3976,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(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3977,plain,
% 1.64/1.81 (((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3978,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3977])).
% 1.64/1.81 tff(3979,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[3978, 3976])).
% 1.64/1.81 tff(3980,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(3981,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3980, 3979])).
% 1.64/1.81 tff(3982,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3981, 453, 646, 3975, 3973, 3971])).
% 1.64/1.81 tff(3983,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(3984,plain,
% 1.64/1.81 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3983, 3691, 3823, 3962, 3512, 3959])).
% 1.64/1.81 tff(3985,plain,
% 1.64/1.81 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3984, 3482])).
% 1.64/1.81 tff(3986,plain,
% 1.64/1.81 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2696, 3985])).
% 1.64/1.81 tff(3987,plain,
% 1.64/1.81 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3986, 3480])).
% 1.64/1.81 tff(3988,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(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3989,plain,
% 1.64/1.81 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(3990,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[3989])).
% 1.64/1.81 tff(3991,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[3990, 3988])).
% 1.64/1.81 tff(3992,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(3993,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3992, 3991])).
% 1.64/1.81 tff(3994,plain,
% 1.64/1.81 ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3993, 453, 3514, 3957])).
% 1.64/1.81 tff(3995,plain,
% 1.64/1.81 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3994, 3987])).
% 1.64/1.81 tff(3996,assumption,(~b(s(s(s(s(s(s(s(z))))))), s(elem!1))), introduced(assumption)).
% 1.64/1.81 tff(3997,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(elem!1))), introduced(assumption)).
% 1.64/1.81 tff(3998,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1287, 69, 1284, 3997, 3996])).
% 1.64/1.81 tff(3999,plain,(b(s(s(s(s(s(s(s(z))))))), s(elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(4000,plain,
% 1.64/1.81 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3999, 3995, 3476])).
% 1.64/1.81 tff(4001,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(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4002,plain,
% 1.64/1.81 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4003,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(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(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4002])).
% 1.64/1.81 tff(4004,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(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(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[4003, 4001])).
% 1.64/1.81 tff(4005,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(4006,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(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4005, 4004])).
% 1.64/1.81 tff(4007,plain,
% 1.64/1.81 ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4006, 453, 3514, 3672])).
% 1.64/1.81 tff(4008,plain,
% 1.64/1.81 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4007, 3987])).
% 1.64/1.81 tff(4009,plain,
% 1.64/1.81 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2647, 69, 2636, 4008])).
% 1.64/1.81 tff(4010,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(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4011,plain,
% 1.64/1.81 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4012,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4011])).
% 1.64/1.81 tff(4013,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[4012, 4010])).
% 1.64/1.81 tff(4014,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(4015,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(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4014, 4013])).
% 1.64/1.81 tff(4016,plain,
% 1.64/1.81 ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4015, 453, 3514, 3957])).
% 1.64/1.81 tff(4017,plain,
% 1.64/1.81 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4016, 3987])).
% 1.64/1.81 tff(4018,plain,
% 1.64/1.81 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1320, 4017, 3825])).
% 1.64/1.81 tff(4019,plain,
% 1.64/1.81 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3635, 453, 3526, 3947, 3691])).
% 1.64/1.81 tff(4020,plain,
% 1.64/1.81 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2142, 4019, 3731])).
% 1.64/1.81 tff(4021,plain,
% 1.64/1.81 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4020, 3771])).
% 1.64/1.81 tff(4022,plain,
% 1.64/1.81 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1982, 4021, 3931])).
% 1.64/1.81 tff(4023,plain,
% 1.64/1.81 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[518, 4022])).
% 1.64/1.81 tff(4024,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4025,plain,
% 1.64/1.81 (((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4026,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4025])).
% 1.64/1.82 tff(4027,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4026, 4024])).
% 1.64/1.82 tff(4028,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4029,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4028, 4027])).
% 1.64/1.82 tff(4030,plain,
% 1.64/1.82 (~r(s(z), s(s(s(s(s(z))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4029, 268, 3945, 4020])).
% 1.64/1.82 tff(4031,plain,
% 1.64/1.82 (b(s(z), s(s(s(s(s(z))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[372, 4030])).
% 1.64/1.82 tff(4032,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4033,plain,
% 1.64/1.82 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4034,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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4033])).
% 1.64/1.82 tff(4035,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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4034, 4032])).
% 1.64/1.82 tff(4036,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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4037,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4036, 4035])).
% 1.64/1.82 tff(4038,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4037, 453, 523, 443, 1764, 120])).
% 1.64/1.82 tff(4039,plain,((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4040,plain,
% 1.64/1.82 (~b(s(s(s(z))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4039, 4031, 3932, 4023])).
% 1.64/1.82 tff(4041,plain,
% 1.64/1.82 (r(s(s(s(z))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[134, 4040])).
% 1.64/1.82 tff(4042,plain,
% 1.64/1.82 (r(s(elem!1), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3764, 4041, 3468])).
% 1.64/1.82 tff(4043,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4044,plain,
% 1.64/1.82 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4045,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4044])).
% 1.64/1.82 tff(4046,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4045, 4043])).
% 1.64/1.82 tff(4047,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4048,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4047, 4046])).
% 1.64/1.82 tff(4049,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4048, 268, 4042, 4018, 4009, 4000])).
% 1.64/1.82 tff(4050,plain,((~(s(s(z)) = elem!1)) | (s(s(s(s(s(z))))) = elem!1) | b(elem!1, s(z)) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4051,plain,
% 1.64/1.82 (~(s(s(z)) = elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4050, 249, 10, 637, 2])).
% 1.64/1.82 tff(4052,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4053,plain,
% 1.64/1.82 (((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4054,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4053])).
% 1.64/1.82 tff(4055,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4054, 4052])).
% 1.64/1.82 tff(4056,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4057,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4056, 4055])).
% 1.64/1.82 tff(4058,plain,
% 1.64/1.82 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4057, 268, 3449, 258])).
% 1.64/1.82 tff(4059,plain,
% 1.64/1.82 (b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[643, 4058, 637])).
% 1.64/1.82 tff(4060,assumption,(~(s(s(z)) = elem!1)), introduced(assumption)).
% 1.64/1.82 tff(4061,plain,
% 1.64/1.82 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4057, 268, 238, 258])).
% 1.64/1.82 tff(4062,plain,
% 1.64/1.82 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[356])).
% 1.64/1.82 tff(4063,plain,
% 1.64/1.82 ((~r(s(s(s(s(s(z))))), elem!1)) <=> (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4062])).
% 1.64/1.82 tff(4064,plain,
% 1.64/1.82 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[636, 4063])).
% 1.64/1.82 tff(4065,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[256, 4064])).
% 1.64/1.82 tff(4066,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | r(s(s(s(s(s(z))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4067,plain,
% 1.64/1.82 (~(s(s(s(z))) = elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4066, 256, 4061])).
% 1.64/1.82 tff(4068,plain,
% 1.64/1.82 (b(s(s(s(z))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[74, 4067, 2])).
% 1.64/1.82 tff(4069,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(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4070,plain,
% 1.64/1.82 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4071,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4070])).
% 1.64/1.82 tff(4072,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4071, 4069])).
% 1.64/1.82 tff(4073,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4074,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4073, 4072])).
% 1.64/1.82 tff(4075,plain,
% 1.64/1.82 (~b(s(s(s(z))), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4074, 453, 1291, 923, 922])).
% 1.64/1.82 tff(4076,plain,
% 1.64/1.82 (r(s(s(s(z))), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2534, 69, 160, 4075])).
% 1.64/1.82 tff(4077,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[929, 453, 923, 922, 646, 2494])).
% 1.64/1.82 tff(4078,plain,((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4079,plain,
% 1.64/1.82 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4078, 922, 646, 923])).
% 1.64/1.82 tff(4080,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[768, 69, 52, 2482, 2490])).
% 1.64/1.82 tff(4081,plain,(b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4082,plain,
% 1.64/1.82 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4081, 4079])).
% 1.64/1.82 tff(4083,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2586, 268, 256, 4082, 4076])).
% 1.64/1.82 tff(4084,plain,((~b(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4085,plain,
% 1.64/1.82 (~b(s(s(z)), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4084, 256, 4068, 923, 646])).
% 1.64/1.82 tff(4086,plain,
% 1.64/1.82 (r(s(s(z)), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[782, 4085, 4060])).
% 1.64/1.82 tff(4087,plain,
% 1.64/1.82 (~r(s(z), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[276, 256, 258])).
% 1.64/1.82 tff(4088,plain,
% 1.64/1.82 (b(s(z), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[227, 4087])).
% 1.64/1.82 tff(4089,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), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4090,plain,
% 1.64/1.82 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4091,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4090])).
% 1.64/1.82 tff(4092,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4091, 4089])).
% 1.64/1.82 tff(4093,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4094,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4093, 4092])).
% 1.64/1.82 tff(4095,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4094, 453, 499, 1291, 923, 2090])).
% 1.64/1.82 tff(4096,plain,((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4097,plain,
% 1.64/1.82 (~b(s(z), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4096, 4068, 923, 4088])).
% 1.64/1.82 tff(4098,plain,
% 1.64/1.82 (r(s(z), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[506, 4097, 492])).
% 1.64/1.82 tff(4099,plain,
% 1.64/1.82 (~r(s(s(z)), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[707, 268, 4098, 4086])).
% 1.64/1.82 tff(4100,plain,
% 1.64/1.82 (b(s(s(z)), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[720, 69, 717, 4099])).
% 1.64/1.82 tff(4101,plain,
% 1.64/1.82 (~r(s(z), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[741, 4086, 4098])).
% 1.64/1.82 tff(4102,plain,
% 1.64/1.82 (b(s(z), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[757, 4101])).
% 1.64/1.82 tff(4103,plain,
% 1.64/1.82 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3465, 258, 238])).
% 1.64/1.82 tff(4104,plain,
% 1.64/1.82 (~r(s(s(s(s(z)))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1167, 1132, 701])).
% 1.64/1.82 tff(4105,plain,
% 1.64/1.82 (s(s(s(s(z)))) = elem!1),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[254, 4104, 249])).
% 1.64/1.82 tff(4106,assumption,(~(s(s(s(s(s(z))))) = s(elem!1))), introduced(assumption)).
% 1.64/1.82 tff(4107,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4106, 1171])).
% 1.64/1.82 tff(4108,plain,((~(s(s(s(s(z)))) = elem!1)) | (s(s(s(s(s(z))))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4109,plain,
% 1.64/1.82 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4108, 4105])).
% 1.64/1.82 tff(4110,plain,
% 1.64/1.82 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[4109])).
% 1.64/1.82 tff(4111,assumption,(~r(elem!1, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.64/1.82 tff(4112,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4113,plain,
% 1.64/1.82 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4114,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4113])).
% 1.64/1.83 tff(4115,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[4114, 4112])).
% 1.64/1.83 tff(4116,plain,
% 1.64/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4117,plain,
% 1.64/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4116, 4115])).
% 1.64/1.83 tff(4118,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4117, 268, 11, 233, 1132])).
% 1.64/1.83 tff(4119,plain,((~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)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(4120,plain,
% 1.64/1.83 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4119, 1132, 233])).
% 1.64/1.83 tff(4121,plain,
% 1.64/1.83 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[518, 4120])).
% 1.64/1.83 tff(4122,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[249, 524])).
% 1.64/1.83 tff(4123,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(s(s(z)))), elem!1) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(4124,plain,
% 1.64/1.83 (~(s(s(s(z))) = elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4123, 4121, 249])).
% 1.64/1.83 tff(4125,plain,
% 1.64/1.83 (b(s(s(s(z))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[74, 4124, 2])).
% 1.64/1.83 tff(4126,plain,
% 1.64/1.83 (~b(s(z), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4096, 4125, 923, 2090])).
% 1.64/1.83 tff(4127,plain,
% 1.64/1.83 (r(s(z), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[506, 4126, 492])).
% 1.64/1.83 tff(4128,plain,
% 1.64/1.83 (~r(s(s(s(s(z)))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1167, 4127, 1132])).
% 1.64/1.83 tff(4129,plain,
% 1.64/1.83 (s(s(s(s(z)))) = elem!1),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[254, 4128, 249])).
% 1.64/1.83 tff(4130,plain,
% 1.64/1.83 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4108, 4129])).
% 1.64/1.83 tff(4131,plain,
% 1.64/1.83 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.64/1.83 inference(symmetry,[status(thm)],[4130])).
% 1.64/1.83 tff(4132,plain,
% 1.64/1.83 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4131])).
% 1.64/1.83 tff(4133,plain,
% 1.64/1.83 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.64/1.83 inference(commutativity,[status(thm)],[])).
% 1.64/1.83 tff(4134,plain,
% 1.64/1.83 ((s(s(z)) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4131])).
% 1.64/1.83 tff(4135,plain,
% 1.64/1.83 ((s(s(z)) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.64/1.83 inference(transitivity,[status(thm)],[4134, 4133])).
% 1.64/1.83 tff(4136,plain,
% 1.64/1.83 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = s(elem!1))),
% 1.64/1.83 inference(symmetry,[status(thm)],[4135])).
% 1.64/1.83 tff(4137,plain,
% 1.64/1.83 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = s(elem!1)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4136])).
% 1.64/1.83 tff(4138,plain,
% 1.64/1.83 (~(s(s(z)) = s(elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[52, 4137])).
% 1.64/1.83 tff(4139,plain,
% 1.64/1.83 (b(s(s(s(s(z)))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4129])).
% 1.64/1.83 tff(4140,assumption,(s(s(s(s(z)))) = s(elem!1)), introduced(assumption)).
% 1.64/1.83 tff(4141,plain,
% 1.64/1.83 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4140])).
% 1.64/1.83 tff(4142,plain,
% 1.64/1.83 (s(s(s(z))) = elem!1),
% 1.64/1.83 inference(transitivity,[status(thm)],[38, 4141, 85])).
% 1.64/1.83 tff(4143,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[59, 4142])).
% 1.64/1.83 tff(4144,plain,((~(s(s(s(s(z)))) = s(elem!1))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(4145,plain,
% 1.64/1.83 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4144, 4124])).
% 1.64/1.83 tff(4146,assumption,(s(s(s(s(s(z))))) = s(elem!1)), introduced(assumption)).
% 1.64/1.83 tff(4147,plain,
% 1.64/1.83 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4146])).
% 1.64/1.83 tff(4148,plain,
% 1.64/1.83 (s(s(s(s(z)))) = elem!1),
% 1.64/1.83 inference(transitivity,[status(thm)],[284, 4147, 85])).
% 1.64/1.83 tff(4149,plain,
% 1.64/1.83 (r(s(s(s(s(z)))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4148])).
% 1.64/1.83 tff(4150,plain,
% 1.64/1.83 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.83 inference(symmetry,[status(thm)],[4149])).
% 1.64/1.83 tff(4151,plain,
% 1.64/1.83 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4150])).
% 1.64/1.83 tff(4152,plain,
% 1.64/1.83 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4146])).
% 1.64/1.83 tff(4153,plain,
% 1.64/1.83 ((~r(elem!1, s(s(s(s(s(z))))))) <=> (~r(elem!1, s(elem!1)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4152])).
% 1.64/1.83 tff(4154,plain,
% 1.64/1.83 (~r(elem!1, s(elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4111, 4153])).
% 1.64/1.83 tff(4155,plain,
% 1.64/1.83 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4154, 4151])).
% 1.64/1.83 tff(4156,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2389, 4155])).
% 1.64/1.83 tff(4157,plain,((~(s(s(s(s(s(z))))) = s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | r(elem!1, s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(4158,plain,
% 1.64/1.83 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4157, 4130, 4111])).
% 1.64/1.83 tff(4159,plain,
% 1.64/1.83 (b(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2398, 4158, 4145])).
% 1.64/1.83 tff(4160,plain,
% 1.64/1.83 (b(elem!1, s(elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4159, 4139])).
% 1.64/1.83 tff(4161,plain,
% 1.64/1.83 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.64/1.83 inference(commutativity,[status(thm)],[])).
% 1.64/1.83 tff(4162,plain,
% 1.64/1.83 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.64/1.83 inference(symmetry,[status(thm)],[4161])).
% 1.64/1.83 tff(4163,plain,
% 1.64/1.83 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4162])).
% 1.64/1.83 tff(4164,plain,
% 1.64/1.83 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[555, 4163])).
% 1.64/1.83 tff(4165,plain,
% 1.64/1.83 (b(s(s(s(z))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[74, 59, 2])).
% 1.64/1.83 tff(4166,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(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4167,plain,
% 1.64/1.83 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4168,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4167])).
% 1.64/1.83 tff(4169,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.83 inference(transitivity,[status(thm)],[4168, 4166])).
% 1.64/1.83 tff(4170,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4171,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(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4170, 4169])).
% 1.64/1.83 tff(4172,plain,
% 1.64/1.83 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4171, 453, 1071, 909, 4165])).
% 1.64/1.83 tff(4173,plain,
% 1.64/1.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4174,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4175,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4174, 4173])).
% 1.64/1.83 tff(4176,plain,
% 1.64/1.83 ((s(s(elem!1)) = s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4175, 69, 4172])).
% 1.64/1.83 tff(4177,plain,
% 1.64/1.83 (r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4176, 4164])).
% 1.64/1.83 tff(4178,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(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4179,plain,
% 1.64/1.83 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4180,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4179])).
% 1.64/1.83 tff(4181,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.64/1.83 inference(transitivity,[status(thm)],[4180, 4178])).
% 1.64/1.83 tff(4182,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4183,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(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4182, 4181])).
% 1.64/1.83 tff(4184,plain,
% 1.64/1.83 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4183, 453, 1071, 4165, 646])).
% 1.64/1.83 tff(4185,plain,
% 1.64/1.83 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[685, 69, 111, 4184])).
% 1.64/1.83 tff(4186,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4187,plain,
% 1.64/1.83 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4188,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4187])).
% 1.64/1.83 tff(4189,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[4188, 4186])).
% 1.64/1.83 tff(4190,plain,
% 1.64/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4191,plain,
% 1.64/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4190, 4189])).
% 1.64/1.83 tff(4192,plain,
% 1.64/1.83 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4191, 268, 4185, 4177])).
% 1.64/1.83 tff(4193,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(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4194,plain,
% 1.64/1.83 (((~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(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4195,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4194])).
% 1.64/1.83 tff(4196,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.64/1.83 inference(transitivity,[status(thm)],[4195, 4193])).
% 1.64/1.83 tff(4197,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4198,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(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4197, 4196])).
% 1.64/1.83 tff(4199,plain,
% 1.64/1.83 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4198, 453, 1071, 909, 646])).
% 1.64/1.83 tff(4200,plain,
% 1.64/1.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4201,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4202,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4201, 4200])).
% 1.64/1.83 tff(4203,plain,
% 1.64/1.83 ((s(s(s(s(s(z))))) = s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4202, 69, 4199])).
% 1.64/1.83 tff(4204,plain,
% 1.64/1.83 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4203, 4192])).
% 1.64/1.83 tff(4205,plain,
% 1.64/1.83 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4204])).
% 1.64/1.83 tff(4206,plain,
% 1.64/1.83 (s(s(s(s(z)))) = s(elem!1)),
% 1.64/1.83 inference(transitivity,[status(thm)],[284, 4205, 194])).
% 1.64/1.83 tff(4207,plain,
% 1.64/1.83 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4206])).
% 1.64/1.83 tff(4208,plain,
% 1.64/1.83 (s(s(s(z))) = elem!1),
% 1.64/1.83 inference(transitivity,[status(thm)],[38, 4207, 85])).
% 1.64/1.83 tff(4209,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[59, 4208])).
% 1.64/1.83 tff(4210,plain,((s(s(s(z))) = elem!1) | (s(s(s(z))) = s(s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(4211,plain,
% 1.64/1.83 (~b(s(s(elem!1)), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4210, 4160, 2, 548, 4124, 646])).
% 1.64/1.83 tff(4212,plain,
% 1.64/1.83 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4130])).
% 1.64/1.83 tff(4213,plain,
% 1.64/1.83 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.64/1.83 inference(symmetry,[status(thm)],[4212])).
% 1.64/1.83 tff(4214,plain,
% 1.64/1.83 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4213])).
% 1.64/1.83 tff(4215,plain,
% 1.64/1.83 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4214])).
% 1.64/1.83 tff(4216,plain,
% 1.64/1.83 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[4215, 1307])).
% 1.64/1.83 tff(4217,plain,
% 1.64/1.83 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.64/1.83 inference(symmetry,[status(thm)],[4216])).
% 1.64/1.83 tff(4218,plain,
% 1.64/1.83 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4217])).
% 1.64/1.83 tff(4219,plain,
% 1.64/1.83 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1273, 4129])).
% 1.64/1.83 tff(4220,plain,
% 1.64/1.83 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1436, 4219])).
% 1.64/1.83 tff(4221,plain,
% 1.64/1.83 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4220, 4218])).
% 1.64/1.83 tff(4222,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1810, 3336])).
% 1.64/1.83 tff(4223,plain,((~(elem!1 = s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(4224,plain,
% 1.64/1.83 (~(elem!1 = s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4223, 4221])).
% 1.64/1.83 tff(4225,plain,
% 1.64/1.83 (~(s(s(elem!1)) = elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3359, 4224])).
% 1.64/1.83 tff(4226,plain,
% 1.64/1.83 (r(s(s(elem!1)), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2240, 4225, 4211])).
% 1.64/1.83 tff(4227,assumption,(~(s(s(z)) = s(s(elem!1)))), introduced(assumption)).
% 1.64/1.83 tff(4228,plain,
% 1.64/1.83 (~r(s(s(elem!1)), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1970, 4226, 238])).
% 1.64/1.83 tff(4229,plain,
% 1.64/1.83 (b(s(s(elem!1)), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1047, 4228])).
% 1.64/1.83 tff(4230,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4231,plain,
% 1.64/1.83 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4232,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4231])).
% 1.64/1.83 tff(4233,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[4232, 4230])).
% 1.64/1.83 tff(4234,plain,
% 1.64/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4235,plain,
% 1.64/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4234, 4233])).
% 1.64/1.83 tff(4236,plain,
% 1.64/1.83 (~r(s(s(z)), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4235, 268, 869, 700])).
% 1.64/1.83 tff(4237,plain,
% 1.64/1.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4238,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(4239,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4238, 4237])).
% 1.64/1.84 tff(4240,plain,
% 1.64/1.84 (b(s(s(z)), s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4239, 69, 4227, 4236])).
% 1.64/1.84 tff(4241,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4242,plain,
% 1.64/1.84 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4243,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(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4242])).
% 1.64/1.84 tff(4244,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(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[4243, 4241])).
% 1.64/1.84 tff(4245,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(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(4246,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4245, 4244])).
% 1.64/1.84 tff(4247,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4246, 453, 1050, 758, 721, 4240])).
% 1.64/1.84 tff(4248,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4249,plain,
% 1.64/1.84 (~r(s(s(z)), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4248, 4229, 4127, 4227, 4226])).
% 1.64/1.84 tff(4250,plain,
% 1.64/1.84 (b(s(s(z)), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[782, 4249, 4060])).
% 1.64/1.84 tff(4251,plain,
% 1.64/1.84 (b(s(elem!1), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1336, 4129, 646])).
% 1.64/1.84 tff(4252,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(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4253,plain,
% 1.64/1.84 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4254,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(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4253])).
% 1.64/1.84 tff(4255,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(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[4254, 4252])).
% 1.64/1.84 tff(4256,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(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(4257,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(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4256, 4255])).
% 1.64/1.84 tff(4258,plain,
% 1.64/1.84 (~b(s(s(z)), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4257, 453, 4251, 4160, 4250])).
% 1.64/1.84 tff(4259,plain,
% 1.64/1.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4260,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(4261,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4260, 4259])).
% 1.64/1.84 tff(4262,plain,
% 1.64/1.84 ((s(s(z)) = s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4261, 69, 4258])).
% 1.64/1.84 tff(4263,plain,
% 1.64/1.84 (r(s(s(z)), s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4262, 4138])).
% 1.64/1.84 tff(4264,plain,
% 1.64/1.84 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4263, 4132])).
% 1.64/1.84 tff(4265,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(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4266,plain,
% 1.64/1.84 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4267,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(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4266])).
% 1.64/1.84 tff(4268,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(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[4267, 4265])).
% 1.64/1.84 tff(4269,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(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(4270,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4269, 4268])).
% 1.64/1.84 tff(4271,plain,
% 1.64/1.84 (~b(s(s(z)), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4270, 453, 4160, 4125, 4250])).
% 1.64/1.84 tff(4272,plain,
% 1.64/1.84 ((s(s(z)) = s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1350, 69, 4271])).
% 1.64/1.84 tff(4273,plain,
% 1.64/1.84 (r(s(s(z)), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4272, 1243])).
% 1.64/1.84 tff(4274,plain,
% 1.64/1.84 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2795, 4273, 256])).
% 1.64/1.84 tff(4275,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4274, 4264])).
% 1.64/1.84 tff(4276,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (s(s(z)) = elem!1) | (s(s(z)) = s(s(elem!1))) | (~r(elem!1, s(z))) | r(s(s(s(z))), elem!1) | (~b(s(s(s(s(s(z))))), elem!1)) | r(elem!1, s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), elem!1) | (s(z) = elem!1) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4277,plain,
% 1.64/1.84 (s(s(z)) = s(s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4276, 1132, 4060, 256, 238, 2, 646, 4111, 249, 492, 923, 2090, 233])).
% 1.64/1.84 tff(4278,plain,
% 1.64/1.84 (s(elem!1) = s(z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1188, 4277])).
% 1.64/1.84 tff(4279,plain,
% 1.64/1.84 (s(z) = s(elem!1)),
% 1.64/1.84 inference(symmetry,[status(thm)],[4278])).
% 1.64/1.84 tff(4280,plain,
% 1.64/1.84 (s(z) = s(s(s(s(s(z)))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[4279, 4110])).
% 1.64/1.84 tff(4281,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[289, 4280])).
% 1.64/1.84 tff(4282,plain,((~r(s(s(s(s(z)))), s(z))) | b(s(s(s(s(z)))), elem!1) | (~r(s(z), elem!1)) | (s(s(z)) = elem!1) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(z))) | r(s(s(s(z))), elem!1) | (~b(s(s(s(s(s(z))))), elem!1)) | r(elem!1, s(s(s(s(s(z)))))) | (s(z) = elem!1) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4283,plain,
% 1.64/1.84 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4282, 4098, 249, 4060, 256, 238, 2, 646, 4103, 492, 923, 4088, 233])).
% 1.64/1.84 tff(4284,plain,
% 1.64/1.84 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1098, 4283])).
% 1.64/1.84 tff(4285,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(s(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4286,plain,
% 1.64/1.84 (((~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(s(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))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4287,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(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(s(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)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4286])).
% 1.64/1.84 tff(4288,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(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(s(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))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[4287, 4285])).
% 1.64/1.84 tff(4289,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(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)))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(4290,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4289, 4288])).
% 1.64/1.84 tff(4291,plain,
% 1.64/1.84 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4290, 453, 4284, 4102, 4100])).
% 1.64/1.84 tff(4292,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[795, 69, 153, 2403, 2391])).
% 1.64/1.84 tff(4293,plain,(r(s(s(s(s(z)))), s(s(z))) | b(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4294,plain,
% 1.64/1.84 (r(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4293, 4291])).
% 1.64/1.84 tff(4295,assumption,(r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.64/1.84 tff(4296,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2058, 268, 700, 1159, 4295])).
% 1.64/1.84 tff(4297,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4298,plain,
% 1.64/1.84 (~r(s(s(s(s(z)))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4297, 4294, 4086])).
% 1.64/1.84 tff(4299,plain,
% 1.64/1.84 (s(s(s(s(z)))) = elem!1),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[254, 4298, 249])).
% 1.64/1.84 tff(4300,plain,
% 1.64/1.84 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4108, 4299])).
% 1.64/1.84 tff(4301,plain,
% 1.64/1.84 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4300, 624])).
% 1.64/1.84 tff(4302,assumption,(s(elem!1) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.64/1.84 tff(4303,plain,
% 1.64/1.84 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(z))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4302])).
% 1.64/1.84 tff(4304,plain,
% 1.64/1.84 (elem!1 = s(s(s(s(z))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[86, 4303, 23])).
% 1.64/1.84 tff(4305,plain,
% 1.64/1.84 (b(elem!1, s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4304])).
% 1.64/1.84 tff(4306,plain,
% 1.64/1.84 (b(s(s(s(s(z)))), s(z)) <=> b(elem!1, s(z))),
% 1.64/1.84 inference(symmetry,[status(thm)],[4305])).
% 1.64/1.84 tff(4307,plain,
% 1.64/1.84 (b(elem!1, s(z))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[1764, 4306])).
% 1.64/1.84 tff(4308,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[10, 4307])).
% 1.64/1.84 tff(4309,plain,((~(s(elem!1) = s(s(s(s(s(z))))))) | b(elem!1, s(z)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4310,plain,
% 1.64/1.84 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4309, 4284, 10])).
% 1.64/1.84 tff(4311,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4310, 4301])).
% 1.64/1.84 tff(4312,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | b(s(s(s(s(z)))), elem!1) | b(elem!1, s(z)) | (s(s(z)) = elem!1) | (~r(elem!1, s(z))) | r(s(s(s(z))), elem!1) | (~b(s(s(s(s(s(z))))), elem!1)) | (s(z) = elem!1) | (~b(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4313,plain,
% 1.64/1.84 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4312, 4059, 10, 4051, 3449, 2, 249, 3447, 3467, 233, 258])).
% 1.64/1.84 tff(4314,plain,
% 1.64/1.84 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[687, 4313])).
% 1.64/1.84 tff(4315,plain,
% 1.64/1.84 (b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[643, 4061, 637])).
% 1.64/1.84 tff(4316,plain,
% 1.64/1.84 (b(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[466, 4111, 2925])).
% 1.64/1.84 tff(4317,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(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4318,plain,
% 1.64/1.84 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4319,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(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4318])).
% 1.64/1.84 tff(4320,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(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[4319, 4317])).
% 1.64/1.84 tff(4321,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(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(4322,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4321, 4320])).
% 1.64/1.84 tff(4323,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4322, 453, 1291, 4316, 4315, 1779])).
% 1.64/1.84 tff(4324,plain,(r(elem!1, s(s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (s(s(s(s(s(z))))) = elem!1) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4325,plain,
% 1.64/1.84 (~b(s(s(s(z))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4324, 4314, 3466, 637, 3449, 258])).
% 1.64/1.84 tff(4326,plain,
% 1.64/1.84 (s(s(s(z))) = elem!1),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[74, 4325, 2])).
% 1.64/1.84 tff(4327,plain,
% 1.64/1.84 (s(elem!1) = s(s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[81, 4326])).
% 1.64/1.84 tff(4328,plain,
% 1.64/1.84 (s(s(s(s(z)))) = s(elem!1)),
% 1.64/1.84 inference(symmetry,[status(thm)],[4327])).
% 1.64/1.84 tff(4329,plain,
% 1.64/1.84 (~(s(z) = s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[171, 4327])).
% 1.64/1.84 tff(4330,plain,
% 1.64/1.84 (~(s(elem!1) = s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[179, 4329])).
% 1.64/1.84 tff(4331,plain,
% 1.64/1.84 (~(s(s(s(elem!1))) = elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[199, 4330, 4326])).
% 1.64/1.84 tff(4332,plain,
% 1.64/1.84 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4123, 4326, 249])).
% 1.64/1.84 tff(4333,plain,
% 1.64/1.84 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[518, 4332])).
% 1.64/1.84 tff(4334,plain,
% 1.64/1.84 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4119, 4333, 233])).
% 1.64/1.84 tff(4335,plain,
% 1.64/1.84 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1098, 4334])).
% 1.64/1.84 tff(4336,plain,
% 1.64/1.84 (b(s(elem!1), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1795, 4335, 4327])).
% 1.64/1.84 tff(4337,plain,
% 1.64/1.84 (b(s(elem!1), s(z)) <=> b(elem!1, s(z))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[3345])).
% 1.64/1.84 tff(4338,plain,
% 1.64/1.84 (b(elem!1, s(z)) <=> b(s(elem!1), s(z))),
% 1.64/1.84 inference(symmetry,[status(thm)],[4337])).
% 1.64/1.84 tff(4339,plain,
% 1.64/1.84 ((~b(elem!1, s(z))) <=> (~b(s(elem!1), s(z)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4338])).
% 1.64/1.84 tff(4340,plain,
% 1.64/1.84 (~b(s(elem!1), s(z))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[10, 4339])).
% 1.64/1.84 tff(4341,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1059, 4340])).
% 1.64/1.84 tff(4342,plain,((~(s(elem!1) = elem!1)) | (~b(s(elem!1), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4343,plain,
% 1.64/1.84 (~(s(elem!1) = elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4342, 4336, 10])).
% 1.64/1.84 tff(4344,plain,
% 1.64/1.84 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[607, 4343])).
% 1.64/1.85 tff(4345,plain,
% 1.64/1.85 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4326])).
% 1.64/1.85 tff(4346,plain,
% 1.64/1.85 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4345])).
% 1.64/1.85 tff(4347,plain,
% 1.64/1.85 (~(s(s(s(s(z)))) = elem!1)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[142, 4346])).
% 1.64/1.85 tff(4348,plain,
% 1.64/1.85 (b(s(z), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2070, 4347, 4326, 10, 233])).
% 1.64/1.85 tff(4349,plain,
% 1.64/1.85 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4326])).
% 1.64/1.85 tff(4350,plain,
% 1.64/1.85 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.85 inference(symmetry,[status(thm)],[4349])).
% 1.64/1.85 tff(4351,plain,
% 1.64/1.85 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3467, 4350])).
% 1.64/1.85 tff(4352,plain,
% 1.64/1.85 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[612])).
% 1.64/1.85 tff(4353,plain,
% 1.64/1.85 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.64/1.85 inference(symmetry,[status(thm)],[4352])).
% 1.64/1.85 tff(4354,plain,
% 1.64/1.85 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[610])).
% 1.64/1.85 tff(4355,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4356,plain,
% 1.64/1.85 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4357,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(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(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(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4356])).
% 1.64/1.85 tff(4358,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(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(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(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[4357, 4355])).
% 1.64/1.85 tff(4359,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(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(4360,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4359, 4358])).
% 1.64/1.85 tff(4361,plain,
% 1.64/1.85 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4360, 453, 1779, 2611, 609])).
% 1.64/1.85 tff(4362,plain,
% 1.64/1.85 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4361, 962])).
% 1.64/1.85 tff(4363,plain,
% 1.64/1.85 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[675, 4362, 617])).
% 1.64/1.85 tff(4364,plain,
% 1.64/1.85 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4363, 4354])).
% 1.64/1.85 tff(4365,plain,
% 1.64/1.85 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4364, 4353])).
% 1.64/1.85 tff(4366,plain,
% 1.64/1.85 ((s(z) = s(s(s(s(s(s(z))))))) <=> (s(z) = s(s(s(elem!1))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[612])).
% 1.64/1.85 tff(4367,plain,
% 1.64/1.85 ((s(z) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = s(z))),
% 1.64/1.85 inference(transitivity,[status(thm)],[4366, 1470])).
% 1.64/1.85 tff(4368,plain,
% 1.64/1.85 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(s(s(s(z)))))))),
% 1.64/1.85 inference(symmetry,[status(thm)],[4367])).
% 1.64/1.85 tff(4369,plain,
% 1.64/1.85 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = s(s(s(s(s(s(z))))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4368])).
% 1.64/1.85 tff(4370,plain,
% 1.64/1.85 (~(s(z) = s(s(s(s(s(s(z)))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[851, 4369])).
% 1.64/1.85 tff(4371,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(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4372,plain,
% 1.64/1.85 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4373,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(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4372])).
% 1.64/1.85 tff(4374,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(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(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[4373, 4371])).
% 1.64/1.85 tff(4375,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(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(4376,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4375, 4374])).
% 1.64/1.85 tff(4377,plain,
% 1.64/1.85 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4376, 453, 2611, 2090, 609])).
% 1.64/1.85 tff(4378,plain,
% 1.64/1.85 ((s(z) = s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z)))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1944, 69, 4377])).
% 1.64/1.85 tff(4379,plain,
% 1.64/1.85 (r(s(z), s(s(s(s(s(s(z)))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4378, 4370])).
% 1.64/1.85 tff(4380,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(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4381,plain,
% 1.64/1.85 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4382,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(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4381])).
% 1.64/1.85 tff(4383,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(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[4382, 4380])).
% 1.64/1.85 tff(4384,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(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(4385,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(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4384, 4383])).
% 1.64/1.85 tff(4386,plain,
% 1.64/1.85 (~b(s(s(s(s(s(z))))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4385, 453, 1779, 2611, 2090])).
% 1.64/1.85 tff(4387,plain,
% 1.64/1.85 (r(s(s(s(s(s(z))))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[297, 4386])).
% 1.64/1.85 tff(4388,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(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4389,plain,
% 1.64/1.85 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4390,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(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4389])).
% 1.64/1.85 tff(4391,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(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[4390, 4388])).
% 1.64/1.85 tff(4392,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(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(4393,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(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4392, 4391])).
% 1.64/1.85 tff(4394,plain,
% 1.64/1.85 (~b(s(z), s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4393, 453, 1779, 2611, 2090])).
% 1.64/1.85 tff(4395,plain,
% 1.64/1.85 (r(s(z), s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[372, 4394])).
% 1.64/1.85 tff(4396,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4397,plain,
% 1.64/1.85 (((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4398,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4397])).
% 1.64/1.85 tff(4399,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[4398, 4396])).
% 1.64/1.85 tff(4400,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(4401,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4400, 4399])).
% 1.64/1.85 tff(4402,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4401, 268, 4395, 4387, 4379, 4365])).
% 1.64/1.85 tff(4403,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(4404,plain,
% 1.64/1.85 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4403, 4351, 4348, 4327, 4344, 4314])).
% 1.64/1.85 tff(4405,plain,
% 1.64/1.85 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[611, 494])).
% 1.64/1.85 tff(4406,plain,
% 1.64/1.85 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[572, 4405])).
% 1.64/1.85 tff(4407,assumption,(~b(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 1.64/1.85 tff(4408,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4407, 4406])).
% 1.64/1.85 tff(4409,plain,((~b(s(s(s(elem!1))), elem!1)) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | (~(s(elem!1) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(4410,plain,
% 1.64/1.85 (~b(s(s(s(elem!1))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4409, 4404, 4327])).
% 1.64/1.85 tff(4411,plain,
% 1.64/1.85 (r(s(s(s(elem!1))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[567, 4410, 4331])).
% 1.64/1.85 tff(4412,plain,
% 1.64/1.85 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[992, 4411, 4327])).
% 1.64/1.86 tff(4413,plain,
% 1.64/1.86 (r(s(s(s(s(z)))), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[512, 4333, 4327])).
% 1.64/1.86 tff(4414,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4415,plain,
% 1.64/1.86 (((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4416,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4415])).
% 1.64/1.86 tff(4417,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[4416, 4414])).
% 1.64/1.86 tff(4418,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(4419,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4418, 4417])).
% 1.64/1.86 tff(4420,plain,
% 1.64/1.86 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4419, 268, 4413, 4412])).
% 1.64/1.86 tff(4421,plain,
% 1.64/1.86 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4327])).
% 1.64/1.86 tff(4422,plain,
% 1.64/1.86 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4421])).
% 1.64/1.86 tff(4423,plain,
% 1.64/1.86 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4422])).
% 1.64/1.86 tff(4424,plain,
% 1.64/1.86 (~r(s(s(s(elem!1))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[842, 4411, 3449])).
% 1.64/1.86 tff(4425,plain,
% 1.64/1.86 (b(s(s(s(elem!1))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[856, 4424])).
% 1.64/1.86 tff(4426,plain,
% 1.64/1.86 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4425, 4423])).
% 1.64/1.86 tff(4427,plain,
% 1.64/1.86 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.64/1.86 inference(symmetry,[status(thm)],[4422])).
% 1.64/1.86 tff(4428,plain,
% 1.64/1.86 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4427, 4327])).
% 1.64/1.86 tff(4429,plain,
% 1.64/1.86 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.64/1.86 inference(symmetry,[status(thm)],[4428])).
% 1.64/1.86 tff(4430,plain,
% 1.64/1.86 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(s(z)))))) = s(elem!1)))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4429])).
% 1.64/1.86 tff(4431,plain,
% 1.64/1.86 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[547, 3447])).
% 1.64/1.86 tff(4432,plain,
% 1.64/1.86 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[557, 4431])).
% 1.64/1.86 tff(4433,plain,
% 1.64/1.86 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4432, 4430])).
% 1.64/1.86 tff(4434,plain,
% 1.64/1.86 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4327])).
% 1.64/1.86 tff(4435,plain,
% 1.64/1.86 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.64/1.86 inference(symmetry,[status(thm)],[4434])).
% 1.64/1.86 tff(4436,plain,
% 1.64/1.86 (r(s(elem!1), elem!1)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4413, 4435])).
% 1.64/1.86 tff(4437,plain,
% 1.64/1.86 (~r(s(z), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1947, 4412, 4326, 4436, 4433])).
% 1.64/1.86 tff(4438,plain,
% 1.64/1.86 (b(s(z), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[506, 4437, 3447])).
% 1.64/1.86 tff(4439,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(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), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4440,plain,
% 1.64/1.86 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4441,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(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(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4440])).
% 1.64/1.86 tff(4442,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(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(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[4441, 4439])).
% 1.64/1.86 tff(4443,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(4444,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4443, 4442])).
% 1.64/1.86 tff(4445,plain,
% 1.64/1.86 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4444, 453, 4438, 4335, 4426])).
% 1.64/1.86 tff(4446,plain,
% 1.64/1.86 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[591, 69, 4445, 4420])).
% 1.64/1.86 tff(4447,plain,
% 1.64/1.86 (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 1.64/1.86 inference(symmetry,[status(thm)],[4446])).
% 1.64/1.86 tff(4448,plain,
% 1.64/1.86 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 1.64/1.86 inference(transitivity,[status(thm)],[4447, 4328])).
% 1.64/1.86 tff(4449,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4433, 4448])).
% 1.64/1.86 tff(4450,plain,((~r(s(s(s(s(s(z))))), s(z))) | b(elem!1, s(z)) | (~r(s(s(s(z))), s(z))) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(z))), elem!1) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4451,plain,
% 1.64/1.86 (~r(s(s(s(s(s(z))))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4450, 3448, 10, 249, 2, 637])).
% 1.64/1.86 tff(4452,plain,
% 1.64/1.86 (b(s(s(s(s(s(z))))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[297, 4451])).
% 1.64/1.86 tff(4453,plain,
% 1.64/1.86 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4123, 76, 249])).
% 1.64/1.86 tff(4454,plain,
% 1.64/1.86 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[518, 4453])).
% 1.64/1.86 tff(4455,plain,
% 1.64/1.86 (b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1779, 901])).
% 1.64/1.86 tff(4456,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[638, 4455])).
% 1.64/1.86 tff(4457,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | b(s(s(s(s(s(z))))), elem!1) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4458,plain,
% 1.64/1.86 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4457, 76, 638])).
% 1.64/1.86 tff(4459,plain,
% 1.64/1.86 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[687, 4458])).
% 1.64/1.86 tff(4460,plain,
% 1.64/1.86 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1982, 4459, 4454])).
% 1.64/1.86 tff(4461,plain,
% 1.64/1.86 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[328, 4460])).
% 1.64/1.86 tff(4462,plain,
% 1.64/1.86 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4119, 4454, 3448])).
% 1.64/1.86 tff(4463,plain,
% 1.64/1.86 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1098, 4462])).
% 1.64/1.86 tff(4464,plain,
% 1.64/1.86 (s(s(s(s(z)))) = elem!1),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2070, 2081, 221, 76, 3448])).
% 1.64/1.86 tff(4465,plain,
% 1.64/1.86 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1170])).
% 1.64/1.86 tff(4466,plain,
% 1.64/1.86 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.86 inference(symmetry,[status(thm)],[4465])).
% 1.64/1.86 tff(4467,plain,
% 1.64/1.86 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[722, 4466])).
% 1.64/1.86 tff(4468,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[322, 4467])).
% 1.64/1.86 tff(4469,plain,((~(s(s(s(s(z)))) = elem!1)) | r(s(s(s(s(s(z))))), s(s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4470,plain,
% 1.64/1.86 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4469, 4464, 722])).
% 1.64/1.86 tff(4471,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1982, 4470, 4454, 4459])).
% 1.64/1.86 tff(4472,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | b(s(z), s(s(s(z)))) | b(s(s(s(s(s(z))))), elem!1) | b(s(s(s(s(z)))), elem!1) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4473,plain,
% 1.64/1.86 (b(s(z), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4472, 76, 249, 638, 722, 128])).
% 1.64/1.86 tff(4474,plain,
% 1.64/1.86 (b(s(z), elem!1)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4473, 115])).
% 1.64/1.86 tff(4475,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), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(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), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4476,plain,
% 1.64/1.86 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~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), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4477,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), elem!1)) | (~b(s(z), elem!1)) | (~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), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4476])).
% 1.64/1.86 tff(4478,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), elem!1)) | (~b(s(z), elem!1)) | (~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), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[4477, 4475])).
% 1.64/1.86 tff(4479,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), elem!1)) | (~b(s(z), elem!1)) | (~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)))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(4480,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4479, 4478])).
% 1.64/1.86 tff(4481,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4480, 453, 4474, 4463, 4461, 374])).
% 1.64/1.86 tff(4482,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | b(s(s(s(s(z)))), elem!1) | b(s(s(s(s(s(z))))), elem!1) | (~r(s(s(s(s(s(z))))), elem!1)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4483,plain,
% 1.64/1.86 (~(s(s(s(z))) = elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4482, 638, 249, 4452, 3457, 128])).
% 1.64/1.86 tff(4484,assumption,(elem!1 = s(s(s(z)))), introduced(assumption)).
% 1.64/1.86 tff(4485,plain,
% 1.64/1.86 (s(s(s(z))) = elem!1),
% 1.64/1.86 inference(symmetry,[status(thm)],[4484])).
% 1.64/1.86 tff(4486,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[59, 4485])).
% 1.64/1.86 tff(4487,plain,((~(elem!1 = s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4488,plain,
% 1.64/1.86 (~(elem!1 = s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4487, 4483])).
% 1.64/1.86 tff(4489,assumption,(~(elem!1 = s(s(s(z))))), introduced(assumption)).
% 1.64/1.86 tff(4490,assumption,(~b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.64/1.86 tff(4491,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1203, 69, 1200, 4490, 4489])).
% 1.64/1.86 tff(4492,plain,(r(elem!1, s(s(s(z)))) | b(elem!1, s(s(s(z)))) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4493,plain,
% 1.64/1.86 (b(elem!1, s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4492, 4488, 3456])).
% 1.64/1.86 tff(4494,plain,
% 1.64/1.86 (b(s(s(s(z))), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[74, 4483, 2])).
% 1.64/1.86 tff(4495,plain,
% 1.64/1.86 (~(s(z) = elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1125, 1123])).
% 1.64/1.86 tff(4496,plain,
% 1.64/1.86 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4309, 1764, 10])).
% 1.64/1.86 tff(4497,plain,
% 1.64/1.86 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4146, 624])).
% 1.64/1.86 tff(4498,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3700, 4497])).
% 1.64/1.86 tff(4499,plain,((~(s(s(s(s(s(z))))) = s(elem!1))) | (s(elem!1) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4500,plain,
% 1.64/1.86 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4499, 4496])).
% 1.64/1.86 tff(4501,plain,
% 1.64/1.86 (~(s(s(s(s(z)))) = elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4108, 4500])).
% 1.64/1.86 tff(4502,plain,
% 1.64/1.86 (r(s(s(s(s(z)))), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[254, 4501, 249])).
% 1.64/1.86 tff(4503,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4504,plain,
% 1.64/1.86 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4505,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4504])).
% 1.64/1.86 tff(4506,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[4505, 4503])).
% 1.64/1.86 tff(4507,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(4508,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4507, 4506])).
% 1.64/1.86 tff(4509,plain,
% 1.64/1.86 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4508, 268, 722, 4502])).
% 1.64/1.86 tff(4510,plain,
% 1.64/1.86 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[328, 4509])).
% 1.64/1.86 tff(4511,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4512,plain,
% 1.64/1.86 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4513,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4512])).
% 1.64/1.86 tff(4514,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[4513, 4511])).
% 1.64/1.86 tff(4515,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(4516,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4515, 4514])).
% 1.64/1.86 tff(4517,plain,
% 1.64/1.86 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4516, 268, 722, 4502])).
% 1.64/1.86 tff(4518,plain,
% 1.64/1.86 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2463, 69, 4517, 2453])).
% 1.64/1.86 tff(4519,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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4520,plain,
% 1.64/1.86 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4521,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4520])).
% 1.64/1.86 tff(4522,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[4521, 4519])).
% 1.64/1.86 tff(4523,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(4524,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4523, 4522])).
% 1.64/1.86 tff(4525,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4524, 453, 443, 1764, 1779, 2497])).
% 1.64/1.86 tff(4526,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4527,plain,
% 1.64/1.86 (~b(s(z), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4526, 4518, 1764, 1779])).
% 1.64/1.86 tff(4528,plain,
% 1.64/1.86 (r(s(z), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[372, 4527])).
% 1.64/1.86 tff(4529,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[364, 268, 701, 722, 2246])).
% 1.64/1.86 tff(4530,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4531,plain,
% 1.64/1.86 (~r(s(z), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4530, 4528, 722])).
% 1.64/1.86 tff(4532,plain,
% 1.64/1.86 (b(s(z), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[506, 4531, 492])).
% 1.64/1.86 tff(4533,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4480, 453, 4532, 1764, 4510, 374])).
% 1.64/1.86 tff(4534,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (s(z) = elem!1) | (~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | b(s(s(s(s(z)))), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4535,plain,
% 1.64/1.86 (~b(s(s(s(s(z)))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4534, 1779, 4495, 722, 374, 249, 10])).
% 1.64/1.86 tff(4536,plain,
% 1.64/1.86 (r(s(s(s(s(z)))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1098, 4535])).
% 1.64/1.86 tff(4537,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1663, 268, 233, 1132, 300])).
% 1.64/1.86 tff(4538,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4539,plain,
% 1.64/1.86 (~r(s(s(s(z))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4538, 1099, 300])).
% 1.64/1.86 tff(4540,plain,
% 1.64/1.86 (b(s(s(s(z))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[134, 4539])).
% 1.64/1.87 tff(4541,assumption,(~r(s(z), elem!1)), introduced(assumption)).
% 1.64/1.87 tff(4542,plain,
% 1.64/1.87 (b(s(z), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[506, 4541, 4495])).
% 1.64/1.87 tff(4543,plain,
% 1.64/1.87 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[501, 221, 499])).
% 1.64/1.87 tff(4544,plain,
% 1.64/1.87 (~(s(s(s(z))) = elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[81, 4543])).
% 1.64/1.87 tff(4545,plain,
% 1.64/1.87 (~(elem!1 = s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4487, 4544])).
% 1.64/1.87 tff(4546,plain,
% 1.64/1.87 (r(s(s(s(s(z)))), s(z)) <=> r(elem!1, s(z))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[1170])).
% 1.64/1.87 tff(4547,plain,
% 1.64/1.87 (r(elem!1, s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.64/1.87 inference(symmetry,[status(thm)],[4546])).
% 1.64/1.87 tff(4548,plain,
% 1.64/1.87 ((~r(elem!1, s(z))) <=> (~r(s(s(s(s(z)))), s(z)))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4547])).
% 1.64/1.87 tff(4549,plain,
% 1.64/1.87 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[2076, 4548])).
% 1.64/1.87 tff(4550,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1132, 4549])).
% 1.64/1.87 tff(4551,plain,((~(s(s(s(s(z)))) = elem!1)) | (~r(s(s(s(s(z)))), s(z))) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(4552,plain,
% 1.64/1.87 (~(s(s(s(s(z)))) = elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4551, 2076, 1132])).
% 1.64/1.87 tff(4553,plain,
% 1.64/1.87 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[201])).
% 1.64/1.87 tff(4554,plain,
% 1.64/1.87 (r(s(z), elem!1) <=> r(s(z), s(s(s(z))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[414])).
% 1.64/1.87 tff(4555,plain,
% 1.64/1.87 (r(s(z), s(s(s(z)))) <=> r(s(z), elem!1)),
% 1.64/1.87 inference(symmetry,[status(thm)],[4554])).
% 1.64/1.87 tff(4556,plain,
% 1.64/1.87 (r(s(z), elem!1)),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[228, 4555])).
% 1.64/1.87 tff(4557,plain,
% 1.64/1.87 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.64/1.87 inference(symmetry,[status(thm)],[401])).
% 1.64/1.87 tff(4558,plain,
% 1.64/1.87 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.64/1.87 inference(symmetry,[status(thm)],[400])).
% 1.64/1.87 tff(4559,plain,
% 1.64/1.87 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.64/1.87 inference(transitivity,[status(thm)],[4558, 4557])).
% 1.64/1.87 tff(4560,plain,
% 1.64/1.87 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4559])).
% 1.64/1.87 tff(4561,plain,
% 1.64/1.87 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[240])).
% 1.64/1.87 tff(4562,plain,
% 1.64/1.87 (r(s(s(s(s(s(s(z)))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.64/1.87 inference(symmetry,[status(thm)],[4561])).
% 1.64/1.87 tff(4563,plain,
% 1.64/1.87 ((~r(s(s(s(s(s(s(z)))))), s(z))) <=> (~r(s(s(s(elem!1))), s(z)))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4562])).
% 1.64/1.87 tff(4564,plain,
% 1.64/1.87 (r(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.64/1.87 inference(monotonicity,[status(thm)],[483])).
% 1.64/1.87 tff(4565,plain,
% 1.64/1.87 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.64/1.87 inference(symmetry,[status(thm)],[4564])).
% 1.64/1.87 tff(4566,plain,
% 1.64/1.87 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.64/1.87 inference(monotonicity,[status(thm)],[240])).
% 1.64/1.87 tff(4567,plain,
% 1.64/1.87 ((s(z) = elem!1) <=> (s(z) = s(s(s(z))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[414])).
% 1.64/1.87 tff(4568,plain,
% 1.64/1.87 ((s(z) = s(s(s(z)))) <=> (s(z) = elem!1)),
% 1.64/1.87 inference(symmetry,[status(thm)],[4567])).
% 1.64/1.87 tff(4569,plain,
% 1.64/1.87 ((~(s(z) = s(s(s(z))))) <=> (~(s(z) = elem!1))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4568])).
% 1.64/1.87 tff(4570,plain,
% 1.64/1.87 (~(s(z) = elem!1)),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[109, 4569])).
% 1.64/1.87 tff(4571,plain,
% 1.64/1.87 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[416])).
% 1.64/1.87 tff(4572,plain,
% 1.64/1.87 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[414])).
% 1.64/1.87 tff(4573,plain,
% 1.64/1.87 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.87 inference(symmetry,[status(thm)],[4572])).
% 1.64/1.87 tff(4574,plain,
% 1.64/1.87 (~r(s(z), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3158, 268, 256, 228])).
% 1.64/1.87 tff(4575,plain,
% 1.64/1.87 (b(s(z), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[372, 4574])).
% 1.64/1.87 tff(4576,plain,
% 1.64/1.87 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3141, 453, 4575, 860, 120])).
% 1.64/1.87 tff(4577,plain,
% 1.64/1.87 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2570, 4576])).
% 1.64/1.87 tff(4578,plain,
% 1.64/1.87 (r(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4577, 4573])).
% 1.64/1.87 tff(4579,plain,
% 1.64/1.87 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[461, 4575, 860, 76, 4578, 228])).
% 1.64/1.87 tff(4580,plain,
% 1.64/1.87 (~r(elem!1, s(s(s(s(z)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4579, 4571])).
% 1.64/1.87 tff(4581,plain,
% 1.64/1.87 (b(elem!1, s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1087, 4580, 9])).
% 1.64/1.87 tff(4582,plain,
% 1.64/1.87 (r(s(s(s(elem!1))), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[831, 4581, 3, 76, 4570, 221, 239])).
% 1.64/1.87 tff(4583,plain,
% 1.64/1.87 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4582, 4566])).
% 1.64/1.87 tff(4584,plain,
% 1.64/1.87 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4583, 4565])).
% 1.64/1.87 tff(4585,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4586,plain,
% 1.64/1.87 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4587,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4586])).
% 1.64/1.87 tff(4588,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[4587, 4585])).
% 1.64/1.87 tff(4589,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(4590,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4589, 4588])).
% 1.64/1.87 tff(4591,plain,
% 1.64/1.87 ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4590, 268, 228])).
% 1.64/1.87 tff(4592,plain,
% 1.64/1.87 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4591, 4584])).
% 1.64/1.87 tff(4593,plain,
% 1.64/1.87 (~r(s(s(s(elem!1))), s(z))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4592, 4563])).
% 1.64/1.87 tff(4594,plain,
% 1.64/1.87 (b(s(s(s(elem!1))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[856, 4593])).
% 1.64/1.87 tff(4595,plain,
% 1.64/1.87 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4594, 243])).
% 1.64/1.87 tff(4596,plain,
% 1.64/1.87 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[201, 414])).
% 1.64/1.87 tff(4597,plain,
% 1.64/1.87 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(elem!1)), elem!1)),
% 1.64/1.87 inference(symmetry,[status(thm)],[4596])).
% 1.64/1.87 tff(4598,plain,
% 1.64/1.87 (r(s(s(elem!1)), elem!1)),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[256, 4597])).
% 1.64/1.87 tff(4599,plain,
% 1.64/1.87 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[877, 4582, 4598])).
% 1.64/1.87 tff(4600,plain,
% 1.64/1.87 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[675, 4599, 608])).
% 1.64/1.87 tff(4601,plain,
% 1.64/1.87 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4600, 864])).
% 1.64/1.87 tff(4602,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[888, 453, 4575, 4601, 860, 4595])).
% 1.64/1.87 tff(4603,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (~(s(s(s(z))) = elem!1)) | b(s(z), s(s(s(z)))) | r(s(s(s(s(z)))), elem!1) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(4604,plain,
% 1.64/1.87 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4603, 239, 76, 221, 3, 120])).
% 1.64/1.87 tff(4605,plain,
% 1.64/1.87 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[687, 4604])).
% 1.64/1.87 tff(4606,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4607,plain,
% 1.64/1.87 (((~b(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(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4608,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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4607])).
% 1.64/1.87 tff(4609,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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[4608, 4606])).
% 1.64/1.87 tff(4610,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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(4611,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4610, 4609])).
% 1.64/1.87 tff(4612,plain,
% 1.64/1.87 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4611, 453, 895, 4605, 120])).
% 1.64/1.87 tff(4613,plain,
% 1.64/1.87 (~b(s(elem!1), s(s(elem!1)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4612, 4560])).
% 1.64/1.87 tff(4614,plain,
% 1.64/1.87 (r(s(elem!1), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[440, 4613, 411])).
% 1.64/1.87 tff(4615,plain,
% 1.64/1.87 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[435, 4614, 76])).
% 1.64/1.87 tff(4616,plain,
% 1.64/1.87 ((s(z) = s(s(s(s(s(s(z))))))) <=> (s(z) = s(s(s(elem!1))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[241])).
% 1.64/1.87 tff(4617,plain,
% 1.64/1.87 ((s(z) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = s(z))),
% 1.64/1.87 inference(transitivity,[status(thm)],[4616, 1470])).
% 1.64/1.87 tff(4618,plain,
% 1.64/1.87 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(s(s(s(z)))))))),
% 1.64/1.87 inference(symmetry,[status(thm)],[4617])).
% 1.64/1.87 tff(4619,plain,
% 1.64/1.87 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = s(s(s(s(s(s(z))))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4618])).
% 1.64/1.87 tff(4620,plain,
% 1.64/1.87 (~(s(z) = s(s(s(s(s(s(z)))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[851, 4619])).
% 1.64/1.87 tff(4621,assumption,(r(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.64/1.87 tff(4622,plain,
% 1.64/1.87 (r(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4621, 4573])).
% 1.64/1.87 tff(4623,plain,
% 1.64/1.87 (~r(elem!1, s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[427, 4622, 4615])).
% 1.64/1.87 tff(4624,plain,
% 1.64/1.87 (b(elem!1, s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1087, 4623, 9])).
% 1.64/1.87 tff(4625,plain,
% 1.64/1.87 (r(s(s(s(elem!1))), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[831, 4624, 3, 76, 4570, 221, 239])).
% 1.64/1.87 tff(4626,plain,
% 1.64/1.87 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4625, 4566])).
% 1.64/1.87 tff(4627,plain,
% 1.64/1.87 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4626, 4565])).
% 1.64/1.87 tff(4628,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4629,plain,
% 1.64/1.87 (((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4630,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4629])).
% 1.64/1.87 tff(4631,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[4630, 4628])).
% 1.64/1.87 tff(4632,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(4633,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4632, 4631])).
% 1.64/1.87 tff(4634,plain,
% 1.64/1.87 ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4633, 268, 228])).
% 1.64/1.87 tff(4635,plain,
% 1.64/1.87 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4634, 4627])).
% 1.64/1.87 tff(4636,plain,
% 1.64/1.87 ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z)))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1944, 69, 4635])).
% 1.64/1.87 tff(4637,plain,
% 1.64/1.87 (b(s(z), s(s(s(s(s(s(z)))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4636, 4620])).
% 1.64/1.87 tff(4638,plain,
% 1.64/1.87 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[201])).
% 1.64/1.87 tff(4639,plain,
% 1.64/1.87 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[162])).
% 1.64/1.87 tff(4640,plain,
% 1.64/1.87 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.64/1.87 inference(symmetry,[status(thm)],[4639])).
% 1.64/1.87 tff(4641,plain,
% 1.64/1.87 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[201])).
% 1.64/1.87 tff(4642,plain,
% 1.64/1.87 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.64/1.87 inference(symmetry,[status(thm)],[4641])).
% 1.64/1.87 tff(4643,plain,
% 1.64/1.87 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.64/1.87 inference(transitivity,[status(thm)],[4642, 4640])).
% 1.64/1.87 tff(4644,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4645,plain,
% 1.64/1.87 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4646,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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4645])).
% 1.64/1.87 tff(4647,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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[4646, 4644])).
% 1.64/1.87 tff(4648,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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(4649,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4648, 4647])).
% 1.64/1.87 tff(4650,plain,
% 1.64/1.87 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4649, 453, 895, 4605, 120])).
% 1.64/1.87 tff(4651,plain,
% 1.64/1.87 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[328, 4650])).
% 1.64/1.87 tff(4652,plain,
% 1.64/1.87 (r(s(s(elem!1)), s(elem!1))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4651, 4643])).
% 1.64/1.87 tff(4653,plain,
% 1.64/1.87 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(elem!1))),
% 1.64/1.87 inference(symmetry,[status(thm)],[375])).
% 1.64/1.87 tff(4654,plain,
% 1.64/1.87 ((~b(s(z), s(s(s(s(z)))))) <=> (~b(s(z), s(elem!1)))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4653])).
% 1.64/1.87 tff(4655,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4656,plain,
% 1.64/1.87 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4657,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4656])).
% 1.64/1.87 tff(4658,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[4657, 4655])).
% 1.64/1.87 tff(4659,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(4660,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4659, 4658])).
% 1.64/1.87 tff(4661,plain,
% 1.64/1.87 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4660, 268, 4621, 4615])).
% 1.64/1.87 tff(4662,plain,
% 1.64/1.87 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1656, 4661])).
% 1.64/1.87 tff(4663,plain,
% 1.64/1.87 (~b(s(z), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2894, 4662, 895, 120])).
% 1.64/1.87 tff(4664,plain,
% 1.64/1.87 (~b(s(z), s(elem!1))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4663, 4654])).
% 1.64/1.87 tff(4665,plain,
% 1.64/1.87 (r(s(z), s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[397, 4664, 172])).
% 1.64/1.87 tff(4666,plain,
% 1.64/1.87 (~r(s(s(elem!1)), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3414, 4665, 4652])).
% 1.64/1.87 tff(4667,plain,
% 1.64/1.87 (b(s(s(elem!1)), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1047, 4666])).
% 1.64/1.87 tff(4668,plain,
% 1.64/1.87 (b(s(s(s(s(s(z))))), s(z))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4667, 4638])).
% 1.64/1.87 tff(4669,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(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(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(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4670,plain,
% 1.64/1.88 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(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(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4671,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(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(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(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4670])).
% 1.64/1.88 tff(4672,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(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(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(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4671, 4669])).
% 1.64/1.88 tff(4673,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(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4674,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4673, 4672])).
% 1.64/1.88 tff(4675,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4674, 453, 4605, 4668, 120, 4637])).
% 1.64/1.88 tff(4676,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = elem!1) | (~(s(s(s(z))) = elem!1)) | b(s(z), s(s(s(z)))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(4677,plain,
% 1.64/1.88 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4676, 239, 3, 76, 221, 120])).
% 1.64/1.88 tff(4678,plain,
% 1.64/1.88 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2570, 4677])).
% 1.64/1.88 tff(4679,plain,
% 1.64/1.88 (~b(s(z), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2619, 4605, 4678, 120])).
% 1.64/1.88 tff(4680,plain,
% 1.64/1.88 (r(s(z), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[372, 4679])).
% 1.64/1.88 tff(4681,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4682,plain,
% 1.64/1.88 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4683,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4682])).
% 1.64/1.88 tff(4684,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4683, 4681])).
% 1.64/1.88 tff(4685,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4686,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4685, 4684])).
% 1.64/1.88 tff(4687,plain,
% 1.64/1.88 (~r(s(z), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4686, 268, 4680, 4615])).
% 1.64/1.88 tff(4688,plain,
% 1.64/1.88 (~r(s(z), s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[392, 4687, 76])).
% 1.64/1.88 tff(4689,plain,
% 1.64/1.88 (b(s(z), s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[397, 4688, 172])).
% 1.64/1.88 tff(4690,plain,
% 1.64/1.88 (b(s(z), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1758, 4689, 162])).
% 1.64/1.88 tff(4691,plain,
% 1.64/1.88 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[569])).
% 1.64/1.88 tff(4692,plain,
% 1.64/1.88 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(z), s(s(elem!1)))),
% 1.64/1.88 inference(symmetry,[status(thm)],[4691])).
% 1.64/1.88 tff(4693,plain,
% 1.64/1.88 (r(s(z), s(s(elem!1)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[2246, 4692])).
% 1.64/1.88 tff(4694,assumption,(~r(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.64/1.88 tff(4695,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4694, 4693])).
% 1.64/1.88 tff(4696,plain,(r(s(z), s(s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(4697,plain,
% 1.64/1.88 (r(s(z), s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4696, 4680, 76])).
% 1.64/1.88 tff(4698,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.64/1.88 tff(4699,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4700,plain,
% 1.64/1.88 (((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4701,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4700])).
% 1.64/1.88 tff(4702,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4701, 4699])).
% 1.64/1.88 tff(4703,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4704,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4703, 4702])).
% 1.64/1.88 tff(4705,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4704, 268, 340, 431, 4698])).
% 1.64/1.88 tff(4706,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(4707,plain,
% 1.64/1.88 (~r(s(elem!1), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4706, 4697, 4614])).
% 1.64/1.88 tff(4708,plain,
% 1.64/1.88 (b(s(elem!1), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[353, 4707, 180])).
% 1.64/1.88 tff(4709,plain,
% 1.64/1.88 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4708, 330])).
% 1.64/1.88 tff(4710,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(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4711,plain,
% 1.64/1.88 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4712,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(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4711])).
% 1.64/1.88 tff(4713,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(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4712, 4710])).
% 1.64/1.88 tff(4714,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(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4715,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4714, 4713])).
% 1.64/1.88 tff(4716,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4715, 453, 895, 4709, 4690, 120])).
% 1.64/1.88 tff(4717,plain,(r(s(s(s(s(z)))), elem!1) | (~b(s(s(s(z))), s(z))) | (~(s(s(s(z))) = elem!1)) | (s(s(s(s(z)))) = elem!1) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(4718,plain,
% 1.64/1.88 (r(s(s(s(s(z)))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4717, 76, 120, 3, 221])).
% 1.64/1.88 tff(4719,plain,
% 1.64/1.88 (r(s(elem!1), elem!1)),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4718, 231])).
% 1.64/1.88 tff(4720,plain,
% 1.64/1.88 (~r(s(z), s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1912, 4719, 4556])).
% 1.64/1.88 tff(4721,plain,
% 1.64/1.88 (b(s(z), s(elem!1))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[397, 4720, 172])).
% 1.64/1.88 tff(4722,plain,
% 1.64/1.88 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[414])).
% 1.64/1.88 tff(4723,plain,
% 1.64/1.88 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 1.64/1.88 inference(symmetry,[status(thm)],[4722])).
% 1.64/1.88 tff(4724,plain,
% 1.64/1.88 (b(elem!1, s(z))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[120, 4723])).
% 1.64/1.88 tff(4725,plain,
% 1.64/1.88 ((elem!1 = s(s(elem!1))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[414])).
% 1.64/1.88 tff(4726,plain,
% 1.64/1.88 ((s(s(s(z))) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 1.64/1.88 inference(symmetry,[status(thm)],[4725])).
% 1.64/1.88 tff(4727,plain,
% 1.64/1.88 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[201])).
% 1.64/1.88 tff(4728,plain,
% 1.64/1.88 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4727, 57])).
% 1.64/1.88 tff(4729,plain,
% 1.64/1.88 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.64/1.88 inference(symmetry,[status(thm)],[4728])).
% 1.64/1.88 tff(4730,plain,
% 1.64/1.88 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (elem!1 = s(s(elem!1)))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4729, 4726])).
% 1.64/1.88 tff(4731,plain,
% 1.64/1.88 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4730])).
% 1.64/1.88 tff(4732,plain,
% 1.64/1.88 (~(elem!1 = s(s(elem!1)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[111, 4731])).
% 1.64/1.88 tff(4733,plain,
% 1.64/1.88 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[162, 201])).
% 1.64/1.88 tff(4734,plain,
% 1.64/1.88 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.64/1.88 inference(symmetry,[status(thm)],[4733])).
% 1.64/1.88 tff(4735,plain,
% 1.64/1.88 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[162])).
% 1.64/1.88 tff(4736,plain,
% 1.64/1.88 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4735, 4734])).
% 1.64/1.88 tff(4737,plain,
% 1.64/1.88 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[531])).
% 1.64/1.88 tff(4738,plain,
% 1.64/1.88 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4737, 624])).
% 1.64/1.88 tff(4739,plain,
% 1.64/1.88 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(s(s(s(z)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4738])).
% 1.64/1.88 tff(4740,plain,
% 1.64/1.88 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[319, 4739])).
% 1.64/1.88 tff(4741,plain,
% 1.64/1.88 (b(s(z), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1758, 4721, 162])).
% 1.64/1.88 tff(4742,plain,
% 1.64/1.88 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1167, 4718, 4556])).
% 1.64/1.88 tff(4743,plain,
% 1.64/1.88 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1098, 4742])).
% 1.64/1.88 tff(4744,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4745,plain,
% 1.64/1.88 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4746,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(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(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(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4745])).
% 1.64/1.88 tff(4747,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(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(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(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4746, 4744])).
% 1.64/1.88 tff(4748,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(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4749,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4748, 4747])).
% 1.64/1.88 tff(4750,plain,
% 1.64/1.88 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4749, 453, 4743, 4741, 120])).
% 1.64/1.88 tff(4751,plain,
% 1.64/1.88 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1656, 4750])).
% 1.64/1.88 tff(4752,plain,
% 1.64/1.88 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[201])).
% 1.64/1.88 tff(4753,plain,
% 1.64/1.88 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[414])).
% 1.64/1.88 tff(4754,plain,
% 1.64/1.88 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4753, 4752, 4573])).
% 1.64/1.88 tff(4755,plain,
% 1.64/1.88 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.64/1.88 inference(symmetry,[status(thm)],[4553])).
% 1.64/1.88 tff(4756,plain,
% 1.64/1.88 ((~r(s(s(s(s(s(z))))), s(z))) <=> (~r(s(s(elem!1)), s(z)))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4755])).
% 1.64/1.88 tff(4757,plain,
% 1.64/1.88 (~r(s(s(elem!1)), s(z))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[277, 4756])).
% 1.64/1.88 tff(4758,plain,
% 1.64/1.88 (b(s(s(elem!1)), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1047, 4757])).
% 1.64/1.88 tff(4759,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(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4760,plain,
% 1.64/1.88 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4761,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(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4760])).
% 1.64/1.88 tff(4762,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(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4761, 4759])).
% 1.64/1.88 tff(4763,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(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4764,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4763, 4762])).
% 1.64/1.88 tff(4765,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4764, 453, 1549, 2077, 1050, 907])).
% 1.64/1.88 tff(4766,plain,((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(4767,plain,
% 1.64/1.88 (~b(elem!1, s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4766, 4758, 2077, 1549])).
% 1.64/1.88 tff(4768,plain,
% 1.64/1.88 (r(elem!1, s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1024, 4767, 4732])).
% 1.64/1.88 tff(4769,plain,
% 1.64/1.88 (r(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4768, 4754])).
% 1.64/1.88 tff(4770,plain,
% 1.64/1.88 (~r(s(z), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[3158, 268, 256, 257])).
% 1.64/1.88 tff(4771,plain,
% 1.64/1.88 (b(s(z), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[372, 4770])).
% 1.64/1.88 tff(4772,plain,
% 1.64/1.88 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[461, 4771, 300, 76, 298, 257])).
% 1.64/1.88 tff(4773,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4772, 4769])).
% 1.64/1.89 tff(4774,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~(s(s(s(z))) = elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4775,plain,
% 1.64/1.89 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4774, 4751, 76, 228, 4724, 4721])).
% 1.64/1.89 tff(4776,plain,
% 1.64/1.89 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[687, 4775])).
% 1.64/1.89 tff(4777,plain,
% 1.64/1.89 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[218, 4732, 76])).
% 1.64/1.89 tff(4778,plain,
% 1.64/1.89 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1947, 4719, 76, 4556, 4777])).
% 1.64/1.89 tff(4779,plain,
% 1.64/1.89 (~r(s(s(s(elem!1))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[992, 4778, 162])).
% 1.64/1.89 tff(4780,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[567, 4779, 200])).
% 1.64/1.89 tff(4781,plain,
% 1.64/1.89 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4409, 4780, 162])).
% 1.64/1.89 tff(4782,plain,
% 1.64/1.89 (b(s(s(s(s(s(s(z)))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[612])).
% 1.64/1.89 tff(4783,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.89 inference(symmetry,[status(thm)],[4782])).
% 1.64/1.89 tff(4784,plain,
% 1.64/1.89 (r(s(s(s(s(s(s(z)))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.64/1.89 inference(symmetry,[status(thm)],[2180])).
% 1.64/1.89 tff(4785,plain,
% 1.64/1.89 ((~r(s(s(s(s(s(s(z)))))), s(z))) <=> (~r(s(s(s(elem!1))), s(z)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4784])).
% 1.64/1.89 tff(4786,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4787,plain,
% 1.64/1.89 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4788,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4787])).
% 1.64/1.89 tff(4789,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[4788, 4786])).
% 1.64/1.89 tff(4790,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4791,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4790, 4789])).
% 1.64/1.89 tff(4792,plain,
% 1.64/1.89 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4791, 453, 1779, 120, 609])).
% 1.64/1.89 tff(4793,plain,
% 1.64/1.89 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4792, 962])).
% 1.64/1.89 tff(4794,plain,
% 1.64/1.89 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[675, 4793, 617])).
% 1.64/1.89 tff(4795,plain,
% 1.64/1.89 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4794, 4354])).
% 1.64/1.89 tff(4796,plain,
% 1.64/1.89 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4795, 4353])).
% 1.64/1.89 tff(4797,assumption,(r(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 1.64/1.89 tff(4798,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4799,plain,
% 1.64/1.89 (((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4800,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4799])).
% 1.64/1.89 tff(4801,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[4800, 4798])).
% 1.64/1.89 tff(4802,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4803,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4802, 4801])).
% 1.64/1.89 tff(4804,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4803, 268, 258, 4797, 2040])).
% 1.64/1.89 tff(4805,plain,((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4806,plain,
% 1.64/1.89 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4805, 4796, 258])).
% 1.64/1.89 tff(4807,plain,
% 1.64/1.89 (~r(s(s(s(elem!1))), s(z))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4806, 4785])).
% 1.64/1.89 tff(4808,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[856, 4807])).
% 1.64/1.89 tff(4809,plain,
% 1.64/1.89 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4808, 4783])).
% 1.64/1.89 tff(4810,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4811,plain,
% 1.64/1.89 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4812,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(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4811])).
% 1.64/1.89 tff(4813,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(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[4812, 4810])).
% 1.64/1.89 tff(4814,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(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4815,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4814, 4813])).
% 1.64/1.89 tff(4816,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4815, 453, 1974, 120, 609, 4809])).
% 1.64/1.89 tff(4817,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4818,plain,
% 1.64/1.89 (~r(s(s(s(s(s(z))))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4817, 4781, 120, 162, 4741, 608, 4776])).
% 1.64/1.89 tff(4819,plain,
% 1.64/1.89 (b(s(s(s(s(s(z))))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[297, 4818])).
% 1.64/1.89 tff(4820,plain,
% 1.64/1.89 (b(s(elem!1), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1795, 4743, 162])).
% 1.64/1.89 tff(4821,plain,
% 1.64/1.89 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(s(z)), elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[484])).
% 1.64/1.89 tff(4822,plain,
% 1.64/1.89 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4791, 453, 4776, 120, 4781])).
% 1.64/1.89 tff(4823,plain,
% 1.64/1.89 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4822, 2027])).
% 1.64/1.89 tff(4824,plain,
% 1.64/1.89 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[675, 4823, 608])).
% 1.64/1.89 tff(4825,plain,
% 1.64/1.89 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4824, 2024])).
% 1.64/1.89 tff(4826,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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(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(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4827,plain,
% 1.64/1.89 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4828,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4827])).
% 1.64/1.89 tff(4829,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[4828, 4826])).
% 1.64/1.89 tff(4830,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4831,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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4830, 4829])).
% 1.64/1.89 tff(4832,plain,
% 1.64/1.89 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4831, 453, 1779, 120])).
% 1.64/1.89 tff(4833,plain,
% 1.64/1.89 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4832, 2957])).
% 1.64/1.89 tff(4834,plain,
% 1.64/1.89 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[768, 69, 52, 4833])).
% 1.64/1.89 tff(4835,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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4836,plain,
% 1.64/1.89 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4837,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4836])).
% 1.64/1.89 tff(4838,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[4837, 4835])).
% 1.64/1.89 tff(4839,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4840,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4839, 4838])).
% 1.64/1.89 tff(4841,plain,
% 1.64/1.89 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4840, 453, 120, 609])).
% 1.64/1.89 tff(4842,plain,
% 1.64/1.89 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4841, 2957])).
% 1.64/1.89 tff(4843,plain,
% 1.64/1.89 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[822, 69, 1005, 4842])).
% 1.64/1.89 tff(4844,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2046, 268, 2040, 4843, 4834])).
% 1.64/1.89 tff(4845,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (s(s(z)) = s(s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.90 tff(4846,plain,
% 1.64/1.90 (~b(s(s(z)), s(s(s(z))))),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[4845, 4825, 819, 4776, 120, 4781])).
% 1.64/1.90 tff(4847,plain,
% 1.64/1.90 (~b(s(s(z)), elem!1)),
% 1.64/1.90 inference(modus_ponens,[status(thm)],[4846, 4821])).
% 1.64/1.90 tff(4848,plain,
% 1.64/1.90 (r(s(s(z)), elem!1)),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[782, 4847, 491])).
% 1.64/1.90 tff(4849,plain,
% 1.64/1.90 (~r(s(z), s(s(z)))),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[741, 4848, 4556])).
% 1.64/1.90 tff(4850,plain,
% 1.64/1.90 (b(s(z), s(s(z)))),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[757, 4849])).
% 1.64/1.90 tff(4851,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(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(z), 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(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.90 inference(rewrite,[status(thm)],[])).
% 1.64/1.90 tff(4852,plain,
% 1.64/1.90 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.90 inference(rewrite,[status(thm)],[])).
% 1.64/1.90 tff(4853,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(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.64/1.90 inference(monotonicity,[status(thm)],[4852])).
% 1.64/1.90 tff(4854,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(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.90 inference(transitivity,[status(thm)],[4853, 4851])).
% 1.64/1.90 tff(4855,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(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.64/1.90 inference(quant_inst,[status(thm)],[])).
% 1.64/1.90 tff(4856,plain,
% 1.64/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.64/1.90 inference(modus_ponens,[status(thm)],[4855, 4854])).
% 1.64/1.90 tff(4857,plain,
% 1.64/1.90 ($false),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[4856, 453, 1059, 645, 374, 1008])).
% 1.64/1.90 tff(4858,plain,((~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.90 tff(4859,plain,
% 1.64/1.90 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[4858, 4850, 4820, 4819])).
% 1.64/1.90 tff(4860,plain,
% 1.64/1.90 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[659, 4859, 4740])).
% 1.64/1.90 tff(4861,plain,
% 1.64/1.90 (r(s(elem!1), s(s(elem!1)))),
% 1.64/1.90 inference(modus_ponens,[status(thm)],[4860, 4736])).
% 1.74/1.90 tff(4862,plain,
% 1.74/1.90 (~r(elem!1, s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2005, 4861, 4719])).
% 1.74/1.90 tff(4863,plain,
% 1.74/1.90 (b(elem!1, s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1024, 4862, 4732])).
% 1.74/1.90 tff(4864,plain,
% 1.74/1.90 (~b(s(s(elem!1)), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4766, 4863, 4724, 4721])).
% 1.74/1.90 tff(4865,plain,
% 1.74/1.90 (r(s(s(elem!1)), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1047, 4864])).
% 1.74/1.90 tff(4866,plain,
% 1.74/1.90 (r(s(s(s(s(s(z))))), s(z))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4865, 4553])).
% 1.74/1.90 tff(4867,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4818, 4866])).
% 1.74/1.90 tff(4868,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = elem!1) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(4869,plain,
% 1.74/1.90 (~(s(s(s(z))) = elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4868, 120, 3, 221])).
% 1.74/1.90 tff(4870,plain,
% 1.74/1.90 (r(s(s(s(z))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[74, 4869, 58])).
% 1.74/1.90 tff(4871,plain,
% 1.74/1.90 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(z))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1100])).
% 1.74/1.90 tff(4872,plain,
% 1.74/1.90 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 1.74/1.90 inference(symmetry,[status(thm)],[4871])).
% 1.74/1.90 tff(4873,plain,
% 1.74/1.90 (b(s(s(s(z))), elem!1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[120, 4872])).
% 1.74/1.90 tff(4874,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[58, 4873])).
% 1.74/1.90 tff(4875,plain,((~(elem!1 = s(z))) | b(s(s(s(z))), elem!1) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(4876,plain,
% 1.74/1.90 (~(elem!1 = s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4875, 120, 58])).
% 1.74/1.90 tff(4877,plain,
% 1.74/1.90 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[547, 4495])).
% 1.74/1.90 tff(4878,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4879,plain,
% 1.74/1.90 (((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4880,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4879])).
% 1.74/1.90 tff(4881,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4880, 4878])).
% 1.74/1.90 tff(4882,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4883,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4882, 4881])).
% 1.74/1.90 tff(4884,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4883, 268, 701, 1545, 257])).
% 1.74/1.90 tff(4885,plain,((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(4886,plain,
% 1.74/1.90 (~r(s(z), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4885, 1545, 228])).
% 1.74/1.90 tff(4887,plain,
% 1.74/1.90 (b(s(z), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[506, 4886, 4495])).
% 1.74/1.90 tff(4888,plain,
% 1.74/1.90 (r(elem!1, s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1130, 10, 1123])).
% 1.74/1.90 tff(4889,plain,
% 1.74/1.90 (r(s(s(s(elem!1))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1711, 10, 221, 1057])).
% 1.74/1.90 tff(4890,plain,
% 1.74/1.90 (~r(s(s(s(elem!1))), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[842, 4889, 4888])).
% 1.74/1.90 tff(4891,plain,
% 1.74/1.90 (b(s(s(s(elem!1))), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[856, 4890])).
% 1.74/1.90 tff(4892,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(z), 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), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4893,plain,
% 1.74/1.90 (((~b(s(z), elem!1)) | (~b(s(z), 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), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4894,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), elem!1)) | (~b(s(z), 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), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4893])).
% 1.74/1.90 tff(4895,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), elem!1)) | (~b(s(z), 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), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4894, 4892])).
% 1.74/1.90 tff(4896,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), elem!1)) | (~b(s(z), 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))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4897,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(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4896, 4895])).
% 1.74/1.90 tff(4898,plain,
% 1.74/1.90 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4897, 453, 4887, 4891, 120])).
% 1.74/1.90 tff(4899,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4900,plain,
% 1.74/1.90 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4901,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4900])).
% 1.74/1.90 tff(4902,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4901, 4899])).
% 1.74/1.90 tff(4903,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4904,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4903, 4902])).
% 1.74/1.90 tff(4905,plain,
% 1.74/1.90 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4904, 268, 4889, 1545])).
% 1.74/1.90 tff(4906,plain,
% 1.74/1.90 (((~![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)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4907,plain,
% 1.74/1.90 ((~![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)))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4908,plain,
% 1.74/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4907, 4906])).
% 1.74/1.90 tff(4909,plain,
% 1.74/1.90 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4908, 69, 4905, 4898])).
% 1.74/1.90 tff(4910,assumption,(s(s(s(z))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.74/1.90 tff(4911,plain,
% 1.74/1.90 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.74/1.90 inference(symmetry,[status(thm)],[4910])).
% 1.74/1.90 tff(4912,plain,
% 1.74/1.90 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4911])).
% 1.74/1.90 tff(4913,plain,
% 1.74/1.90 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[4912])).
% 1.74/1.90 tff(4914,plain,
% 1.74/1.90 (s(s(z)) = s(s(elem!1))),
% 1.74/1.90 inference(transitivity,[status(thm)],[98, 4913, 550])).
% 1.74/1.90 tff(4915,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4227, 4914])).
% 1.74/1.90 tff(4916,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(4917,plain,
% 1.74/1.90 (s(s(z)) = s(s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4916, 4909])).
% 1.74/1.90 tff(4918,plain,
% 1.74/1.90 (s(elem!1) = s(z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1188, 4917])).
% 1.74/1.90 tff(4919,plain,
% 1.74/1.90 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4918])).
% 1.74/1.90 tff(4920,plain,
% 1.74/1.90 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.74/1.90 inference(symmetry,[status(thm)],[4919])).
% 1.74/1.90 tff(4921,plain,
% 1.74/1.90 (z = inj_0(s(z))),
% 1.74/1.90 inference(symmetry,[status(thm)],[32])).
% 1.74/1.90 tff(4922,plain,
% 1.74/1.90 (z = elem!1),
% 1.74/1.90 inference(transitivity,[status(thm)],[4921, 4920, 85])).
% 1.74/1.90 tff(4923,plain,
% 1.74/1.90 (b(z, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4922])).
% 1.74/1.90 tff(4924,plain,
% 1.74/1.90 (b(elem!1, s(s(s(s(s(z)))))) <=> b(z, s(s(s(s(s(z))))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[4923])).
% 1.74/1.90 tff(4925,plain,
% 1.74/1.90 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4922])).
% 1.74/1.90 tff(4926,plain,
% 1.74/1.90 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4925, 55])).
% 1.74/1.90 tff(4927,plain,
% 1.74/1.90 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4926])).
% 1.74/1.90 tff(4928,plain,
% 1.74/1.90 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[2549, 4927])).
% 1.74/1.90 tff(4929,plain,
% 1.74/1.90 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4918])).
% 1.74/1.90 tff(4930,plain,
% 1.74/1.90 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.74/1.90 inference(symmetry,[status(thm)],[4929])).
% 1.74/1.90 tff(4931,plain,
% 1.74/1.90 (r(elem!1, s(elem!1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4888, 4930])).
% 1.74/1.90 tff(4932,plain,
% 1.74/1.90 (~(elem!1 = s(s(s(z))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4869, 1599])).
% 1.74/1.90 tff(4933,plain,
% 1.74/1.90 (~r(elem!1, s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1157, 4888, 228])).
% 1.74/1.90 tff(4934,plain,
% 1.74/1.90 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1203, 69, 4933])).
% 1.74/1.90 tff(4935,plain,
% 1.74/1.90 (b(elem!1, s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4934, 4932])).
% 1.74/1.90 tff(4936,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(z))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4918])).
% 1.74/1.90 tff(4937,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.90 inference(symmetry,[status(thm)],[4936])).
% 1.74/1.90 tff(4938,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1099, 4937])).
% 1.74/1.90 tff(4939,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4940,plain,
% 1.74/1.90 (((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4941,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4940])).
% 1.74/1.90 tff(4942,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4941, 4939])).
% 1.74/1.90 tff(4943,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4944,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4943, 4942])).
% 1.74/1.90 tff(4945,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4944, 268, 339, 419, 2389])).
% 1.74/1.90 tff(4946,plain,((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(4947,plain,
% 1.74/1.90 (~r(elem!1, s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4946, 4938, 4931])).
% 1.74/1.90 tff(4948,plain,
% 1.74/1.90 (b(elem!1, s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1087, 4947, 9])).
% 1.74/1.90 tff(4949,plain,
% 1.74/1.90 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1621, 4948, 120, 4935])).
% 1.74/1.90 tff(4950,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[518, 4949])).
% 1.74/1.90 tff(4951,plain,
% 1.74/1.90 (~r(s(z), s(s(s(s(s(z))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2629, 4950, 228, 1099])).
% 1.74/1.90 tff(4952,plain,
% 1.74/1.90 (b(s(z), s(s(s(s(s(z))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[372, 4951])).
% 1.74/1.90 tff(4953,plain,
% 1.74/1.90 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[501, 4887, 221])).
% 1.74/1.90 tff(4954,plain,
% 1.74/1.90 (s(z) = s(elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[179, 4918])).
% 1.74/1.90 tff(4955,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4956,plain,
% 1.74/1.90 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4957,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4956])).
% 1.74/1.90 tff(4958,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4957, 4955])).
% 1.74/1.90 tff(4959,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4960,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4959, 4958])).
% 1.74/1.90 tff(4961,plain,
% 1.74/1.90 ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4960, 268])).
% 1.74/1.90 tff(4962,plain,
% 1.74/1.90 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4961, 4950, 1545])).
% 1.74/1.90 tff(4963,plain,
% 1.74/1.90 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[254, 4962, 3])).
% 1.74/1.90 tff(4964,plain,
% 1.74/1.90 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[163])).
% 1.74/1.90 tff(4965,plain,
% 1.74/1.90 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 1.74/1.90 inference(symmetry,[status(thm)],[4964])).
% 1.74/1.90 tff(4966,plain,
% 1.74/1.90 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[2373])).
% 1.74/1.90 tff(4967,plain,
% 1.74/1.90 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[79, 4966])).
% 1.74/1.90 tff(4968,plain,
% 1.74/1.90 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[163])).
% 1.74/1.90 tff(4969,plain,
% 1.74/1.90 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.74/1.90 inference(symmetry,[status(thm)],[4968])).
% 1.74/1.90 tff(4970,plain,
% 1.74/1.90 (b(elem!1, s(z))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1071, 4969])).
% 1.74/1.90 tff(4971,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[10, 4970])).
% 1.74/1.90 tff(4972,plain,((~(s(z) = s(elem!1))) | b(elem!1, s(z)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(4973,plain,
% 1.74/1.91 (~b(elem!1, s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4972, 163, 10])).
% 1.74/1.91 tff(4974,plain,
% 1.74/1.91 (z = elem!1),
% 1.74/1.91 inference(transitivity,[status(thm)],[4921, 164, 85])).
% 1.74/1.91 tff(4975,plain,
% 1.74/1.91 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4974])).
% 1.74/1.91 tff(4976,plain,
% 1.74/1.91 ((s(elem!1) = z) <=> (elem!1 = s(elem!1))),
% 1.74/1.91 inference(transitivity,[status(thm)],[4975, 1028])).
% 1.74/1.91 tff(4977,plain,
% 1.74/1.91 ((~(s(elem!1) = z)) <=> (~(elem!1 = s(elem!1)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4976])).
% 1.74/1.91 tff(4978,plain,
% 1.74/1.91 (~(elem!1 = s(elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[814, 4977])).
% 1.74/1.91 tff(4979,plain,
% 1.74/1.91 (r(elem!1, s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1069, 4978, 4973])).
% 1.74/1.91 tff(4980,plain,
% 1.74/1.91 (s(s(z)) = s(s(elem!1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[163])).
% 1.74/1.91 tff(4981,plain,
% 1.74/1.91 (s(s(elem!1)) = s(s(z))),
% 1.74/1.91 inference(symmetry,[status(thm)],[4980])).
% 1.74/1.91 tff(4982,plain,
% 1.74/1.91 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4981])).
% 1.74/1.91 tff(4983,plain,
% 1.74/1.91 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4982])).
% 1.74/1.91 tff(4984,plain,
% 1.74/1.91 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4974])).
% 1.74/1.91 tff(4985,plain,
% 1.74/1.91 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[4984, 1391])).
% 1.74/1.91 tff(4986,plain,
% 1.74/1.91 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4985])).
% 1.74/1.91 tff(4987,plain,
% 1.74/1.91 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(4988,plain,
% 1.74/1.91 (~(s(s(s(elem!1))) = z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4987, 46])).
% 1.74/1.91 tff(4989,plain,
% 1.74/1.91 (~(elem!1 = s(s(s(elem!1))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4988, 4986])).
% 1.74/1.91 tff(4990,plain,
% 1.74/1.91 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4982])).
% 1.74/1.91 tff(4991,plain,
% 1.74/1.91 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.74/1.91 inference(symmetry,[status(thm)],[4990])).
% 1.74/1.91 tff(4992,plain,
% 1.74/1.91 ((~r(elem!1, s(s(s(z))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4991])).
% 1.74/1.91 tff(4993,plain,
% 1.74/1.91 ((s(z) = elem!1) <=> (s(elem!1) = elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[163])).
% 1.74/1.91 tff(4994,plain,
% 1.74/1.91 ((s(elem!1) = elem!1) <=> (s(z) = elem!1)),
% 1.74/1.91 inference(symmetry,[status(thm)],[4993])).
% 1.74/1.91 tff(4995,plain,
% 1.74/1.91 ((s(elem!1) = z) <=> (elem!1 = s(z))),
% 1.74/1.91 inference(transitivity,[status(thm)],[4975, 4994, 1120])).
% 1.74/1.91 tff(4996,plain,
% 1.74/1.91 ((~(s(elem!1) = z)) <=> (~(elem!1 = s(z)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4995])).
% 1.74/1.91 tff(4997,plain,
% 1.74/1.91 (~(elem!1 = s(z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[814, 4996])).
% 1.74/1.91 tff(4998,plain,
% 1.74/1.91 (r(elem!1, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1130, 4997, 10])).
% 1.74/1.91 tff(4999,plain,
% 1.74/1.91 (~r(elem!1, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1157, 4998, 257])).
% 1.74/1.91 tff(5000,plain,
% 1.74/1.91 (~r(elem!1, s(s(s(elem!1))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4999, 4992])).
% 1.74/1.91 tff(5001,plain,
% 1.74/1.91 (b(elem!1, s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1428, 5000, 4989])).
% 1.74/1.91 tff(5002,plain,
% 1.74/1.91 (b(elem!1, s(s(s(z))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5001, 4983])).
% 1.74/1.91 tff(5003,plain,
% 1.74/1.91 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1566, 256, 1545])).
% 1.74/1.91 tff(5004,plain,
% 1.74/1.91 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4974])).
% 1.74/1.91 tff(5005,plain,
% 1.74/1.91 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[5004, 55])).
% 1.74/1.91 tff(5006,plain,
% 1.74/1.91 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.91 inference(transitivity,[status(thm)],[5005, 56])).
% 1.74/1.91 tff(5007,plain,
% 1.74/1.91 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5006])).
% 1.74/1.91 tff(5008,plain,
% 1.74/1.91 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[2549, 5007])).
% 1.74/1.91 tff(5009,plain,
% 1.74/1.91 (b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[643, 5008, 5003])).
% 1.74/1.91 tff(5010,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(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5011,plain,
% 1.74/1.91 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5012,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~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(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5011])).
% 1.74/1.91 tff(5013,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~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(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[5012, 5010])).
% 1.74/1.91 tff(5014,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(5015,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(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5014, 5013])).
% 1.74/1.91 tff(5016,plain,
% 1.74/1.91 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5015, 453, 5009, 299, 5002])).
% 1.74/1.91 tff(5017,plain,
% 1.74/1.91 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[328, 5016])).
% 1.74/1.91 tff(5018,plain,
% 1.74/1.91 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1982, 5017, 256])).
% 1.74/1.91 tff(5019,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[518, 5018])).
% 1.74/1.91 tff(5020,plain,
% 1.74/1.91 (~b(elem!1, s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1621, 5019, 120, 5002])).
% 1.74/1.91 tff(5021,plain,
% 1.74/1.91 (r(elem!1, s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1087, 5020, 1055])).
% 1.74/1.91 tff(5022,plain,
% 1.74/1.91 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4946, 5021, 4979])).
% 1.74/1.91 tff(5023,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2398, 5022, 4967])).
% 1.74/1.91 tff(5024,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5023, 4965])).
% 1.74/1.91 tff(5025,plain,
% 1.74/1.91 ((~(s(elem!1) = z)) <=> (~(s(elem!1) = elem!1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[4975])).
% 1.74/1.91 tff(5026,plain,
% 1.74/1.91 (~(s(elem!1) = elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[814, 5025])).
% 1.74/1.91 tff(5027,plain,
% 1.74/1.91 (s(elem!1) = s(z)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[163, 173])).
% 1.74/1.91 tff(5028,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[197, 5027])).
% 1.74/1.91 tff(5029,plain,((~(s(z) = s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(5030,plain,
% 1.74/1.91 (s(elem!1) = s(z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5029, 163])).
% 1.74/1.91 tff(5031,plain,
% 1.74/1.91 (s(s(elem!1)) = s(s(z))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[175])).
% 1.74/1.91 tff(5032,plain,
% 1.74/1.91 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5031])).
% 1.74/1.91 tff(5033,plain,
% 1.74/1.91 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5032])).
% 1.74/1.91 tff(5034,plain,
% 1.74/1.91 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[175])).
% 1.74/1.91 tff(5035,plain,
% 1.74/1.91 (elem!1 = z),
% 1.74/1.91 inference(transitivity,[status(thm)],[86, 5034, 32])).
% 1.74/1.91 tff(5036,plain,
% 1.74/1.91 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), z)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5032, 5035])).
% 1.74/1.91 tff(5037,plain,
% 1.74/1.91 (r(s(s(s(z))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 1.74/1.91 inference(symmetry,[status(thm)],[5036])).
% 1.74/1.91 tff(5038,plain,
% 1.74/1.91 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.74/1.91 inference(symmetry,[status(thm)],[5034])).
% 1.74/1.91 tff(5039,plain,
% 1.74/1.91 (z = elem!1),
% 1.74/1.91 inference(transitivity,[status(thm)],[4921, 5038, 85])).
% 1.74/1.91 tff(5040,plain,
% 1.74/1.91 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5039])).
% 1.74/1.91 tff(5041,plain,
% 1.74/1.91 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 1.74/1.91 inference(symmetry,[status(thm)],[5040])).
% 1.74/1.91 tff(5042,plain,
% 1.74/1.91 (r(s(s(s(z))), z)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1545, 5041])).
% 1.74/1.91 tff(5043,assumption,(~r(s(s(s(z))), z)), introduced(assumption)).
% 1.74/1.91 tff(5044,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5043, 5042])).
% 1.74/1.91 tff(5045,plain,(r(s(s(s(z))), z) | (~r(s(s(s(z))), elem!1)) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(5046,plain,
% 1.74/1.91 (r(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5045, 175, 1545])).
% 1.74/1.91 tff(5047,plain,
% 1.74/1.91 (r(s(s(s(elem!1))), elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5046, 5037])).
% 1.74/1.91 tff(5048,plain,
% 1.74/1.91 ((s(elem!1) = elem!1) <=> (s(z) = elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[175])).
% 1.74/1.91 tff(5049,plain,
% 1.74/1.91 ((s(elem!1) = elem!1) <=> (elem!1 = s(z))),
% 1.74/1.91 inference(transitivity,[status(thm)],[5048, 1120])).
% 1.74/1.91 tff(5050,plain,
% 1.74/1.91 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(z)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5049])).
% 1.74/1.91 tff(5051,plain,
% 1.74/1.91 (~(elem!1 = s(z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[605, 5050])).
% 1.74/1.91 tff(5052,plain,
% 1.74/1.91 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1566, 1545, 256])).
% 1.74/1.91 tff(5053,plain,
% 1.74/1.91 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5039])).
% 1.74/1.91 tff(5054,plain,
% 1.74/1.91 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[5053, 55])).
% 1.74/1.91 tff(5055,plain,
% 1.74/1.91 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.91 inference(transitivity,[status(thm)],[5054, 56])).
% 1.74/1.91 tff(5056,plain,
% 1.74/1.91 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5055])).
% 1.74/1.91 tff(5057,plain,
% 1.74/1.91 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[2549, 5056])).
% 1.74/1.91 tff(5058,plain,
% 1.74/1.91 (b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[643, 5057, 5052])).
% 1.74/1.91 tff(5059,plain,
% 1.74/1.91 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5039])).
% 1.74/1.91 tff(5060,plain,
% 1.74/1.91 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.74/1.91 inference(symmetry,[status(thm)],[5059])).
% 1.74/1.91 tff(5061,plain,
% 1.74/1.91 ((~(s(elem!1) = elem!1)) <=> (~(s(z) = elem!1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5048])).
% 1.74/1.91 tff(5062,plain,
% 1.74/1.91 (~(s(z) = elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[605, 5061])).
% 1.74/1.91 tff(5063,plain,
% 1.74/1.91 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5039])).
% 1.74/1.91 tff(5064,plain,
% 1.74/1.91 ((~r(s(z), z)) <=> (~r(s(z), elem!1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5063])).
% 1.74/1.91 tff(5065,assumption,(r(s(z), z)), introduced(assumption)).
% 1.74/1.91 tff(5066,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 1.74/1.91 tff(5067,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5068,plain,
% 1.74/1.91 (((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5069,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5068])).
% 1.74/1.91 tff(5070,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[5069, 5067])).
% 1.74/1.91 tff(5071,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(5072,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5071, 5070])).
% 1.74/1.91 tff(5073,plain,
% 1.74/1.91 ((~r(s(z), s(s(s(z))))) | (~r(s(z), z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5072, 268, 5066])).
% 1.74/1.91 tff(5074,plain,
% 1.74/1.91 (~r(s(z), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5073, 5065])).
% 1.74/1.91 tff(5075,plain,
% 1.74/1.91 (b(s(z), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[225, 69, 5074, 109])).
% 1.74/1.91 tff(5076,plain,
% 1.74/1.91 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(z))), s(z))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5032])).
% 1.74/1.91 tff(5077,plain,
% 1.74/1.91 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.74/1.91 inference(symmetry,[status(thm)],[5076])).
% 1.74/1.91 tff(5078,plain,
% 1.74/1.91 ((~r(s(s(s(z))), s(z))) <=> (~r(s(s(s(elem!1))), s(z)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5077])).
% 1.74/1.91 tff(5079,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5080,plain,
% 1.74/1.91 (((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5081,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5080])).
% 1.74/1.91 tff(5082,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[5081, 5079])).
% 1.74/1.91 tff(5083,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(5084,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5083, 5082])).
% 1.74/1.91 tff(5085,plain,
% 1.74/1.91 ((~r(s(s(s(z))), s(z))) | (~r(s(z), z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5084, 268, 5066])).
% 1.74/1.91 tff(5086,plain,
% 1.74/1.91 (~r(s(s(s(z))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5085, 5065])).
% 1.74/1.91 tff(5087,plain,
% 1.74/1.91 (~r(s(s(s(elem!1))), s(z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5086, 5078])).
% 1.74/1.91 tff(5088,plain,
% 1.74/1.91 (b(s(s(s(elem!1))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[856, 5087])).
% 1.74/1.91 tff(5089,plain,
% 1.74/1.91 (b(s(s(s(z))), s(z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5088, 5033])).
% 1.74/1.91 tff(5090,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3780, 453, 523, 1764, 5089, 5075])).
% 1.74/1.91 tff(5091,plain,((~r(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~(s(elem!1) = s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(5092,plain,
% 1.74/1.91 (~r(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5091, 175, 1764, 523, 5046])).
% 1.74/1.91 tff(5093,plain,
% 1.74/1.91 (~r(s(z), elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5092, 5064])).
% 1.74/1.91 tff(5094,plain,
% 1.74/1.91 (b(s(z), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[506, 5093, 5062])).
% 1.74/1.91 tff(5095,plain,
% 1.74/1.91 (b(s(z), z)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5094, 5060])).
% 1.74/1.91 tff(5096,plain,
% 1.74/1.91 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5039])).
% 1.74/1.91 tff(5097,plain,
% 1.74/1.91 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), z)),
% 1.74/1.91 inference(symmetry,[status(thm)],[5096])).
% 1.74/1.91 tff(5098,plain,
% 1.74/1.91 (b(s(s(s(s(s(z))))), z)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[646, 5097])).
% 1.74/1.91 tff(5099,plain,
% 1.74/1.91 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5039])).
% 1.74/1.91 tff(5100,plain,
% 1.74/1.91 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.74/1.91 inference(symmetry,[status(thm)],[5099])).
% 1.74/1.91 tff(5101,plain,
% 1.74/1.91 (~r(elem!1, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[842, 834, 833])).
% 1.74/1.91 tff(5102,plain,
% 1.74/1.91 (b(elem!1, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1130, 5101, 1123])).
% 1.74/1.91 tff(5103,plain,
% 1.74/1.91 (b(z, s(z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5102, 5100])).
% 1.74/1.91 tff(5104,assumption,(b(s(z), z)), introduced(assumption)).
% 1.74/1.91 tff(5105,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(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5106,plain,
% 1.74/1.91 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5107,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(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5106])).
% 1.74/1.91 tff(5108,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(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[5107, 5105])).
% 1.74/1.91 tff(5109,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(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(5110,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(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5109, 5108])).
% 1.74/1.91 tff(5111,plain,
% 1.74/1.91 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5110, 453, 5104])).
% 1.74/1.91 tff(5112,plain,
% 1.74/1.91 (~b(s(s(s(s(s(z))))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5111, 5103, 5098])).
% 1.74/1.91 tff(5113,plain,
% 1.74/1.91 (r(s(s(s(s(s(z))))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[295, 69, 291, 5112])).
% 1.74/1.91 tff(5114,plain,
% 1.74/1.91 (r(s(s(s(z))), s(z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[834, 5076])).
% 1.74/1.91 tff(5115,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5116,plain,
% 1.74/1.91 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(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(z))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5117,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5116])).
% 1.74/1.91 tff(5118,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[5117, 5115])).
% 1.74/1.91 tff(5119,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(5120,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5119, 5118])).
% 1.74/1.91 tff(5121,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5120, 268, 256, 5114, 5113])).
% 1.74/1.91 tff(5122,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~(s(elem!1) = s(z))) | (elem!1 = s(z)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(5123,plain,
% 1.74/1.91 (~r(s(s(s(elem!1))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5122, 5095, 256, 5058, 175, 5051, 5047])).
% 1.74/1.91 tff(5124,plain,
% 1.74/1.91 (b(s(s(s(elem!1))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[856, 5123])).
% 1.74/1.91 tff(5125,plain,
% 1.74/1.91 (b(s(s(s(z))), s(z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5124, 5033])).
% 1.74/1.91 tff(5126,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(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5127,plain,
% 1.74/1.91 (((~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(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5128,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(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5127])).
% 1.74/1.91 tff(5129,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(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)))),
% 1.74/1.92 inference(transitivity,[status(thm)],[5128, 5126])).
% 1.74/1.92 tff(5130,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(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(5131,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[5130, 5129])).
% 1.74/1.92 tff(5132,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5131, 453, 523, 1764, 5104, 120])).
% 1.74/1.92 tff(5133,plain,((~b(s(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)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(5134,plain,
% 1.74/1.92 (~b(s(s(s(z))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5133, 5095, 1764, 523])).
% 1.74/1.92 tff(5135,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5134, 5125])).
% 1.74/1.92 tff(5136,plain,((~(s(elem!1) = s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (s(elem!1) = elem!1) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(5137,plain,
% 1.74/1.92 (~b(s(s(s(s(z)))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5136, 5019, 1545, 5030, 5026, 256])).
% 1.74/1.92 tff(5138,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5137, 5024])).
% 1.74/1.92 tff(5139,plain,((~(s(z) = s(elem!1))) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(5140,plain,
% 1.74/1.92 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5139, 4963, 120, 1545, 4954, 10, 4953, 228, 9])).
% 1.74/1.92 tff(5141,plain,
% 1.74/1.92 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[687, 5140])).
% 1.74/1.92 tff(5142,plain,
% 1.74/1.92 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2619, 5141, 4952, 120])).
% 1.74/1.92 tff(5143,plain,
% 1.74/1.92 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2570, 5142])).
% 1.74/1.92 tff(5144,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5145,plain,
% 1.74/1.92 (((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5146,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5145])).
% 1.74/1.92 tff(5147,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[5146, 5144])).
% 1.74/1.92 tff(5148,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(5149,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[5148, 5147])).
% 1.74/1.92 tff(5150,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5149, 268, 339, 412, 1545, 4621])).
% 1.74/1.92 tff(5151,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(5152,plain,
% 1.74/1.92 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5151, 5143, 1545, 4931])).
% 1.74/1.92 tff(5153,plain,
% 1.74/1.92 (b(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[466, 5152, 4928])).
% 1.74/1.92 tff(5154,plain,
% 1.74/1.92 (b(z, s(s(s(s(s(z))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[5153, 4924])).
% 1.74/1.92 tff(5155,plain,
% 1.74/1.92 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[4922])).
% 1.74/1.92 tff(5156,plain,
% 1.74/1.92 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.74/1.92 inference(symmetry,[status(thm)],[5155])).
% 1.74/1.92 tff(5157,plain,
% 1.74/1.92 (b(s(z), z)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[4887, 5156])).
% 1.74/1.92 tff(5158,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(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5159,plain,
% 1.74/1.92 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5160,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5159])).
% 1.74/1.92 tff(5161,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[5160, 5158])).
% 1.74/1.92 tff(5162,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(5163,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z)))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[5162, 5161])).
% 1.74/1.92 tff(5164,plain,
% 1.74/1.92 (~b(z, s(s(s(s(s(z))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5163, 453, 4952, 5141, 5157])).
% 1.74/1.92 tff(5165,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5164, 5154])).
% 1.74/1.92 tff(5166,plain,(b(elem!1, s(z)) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = elem!1) | b(s(z), s(s(s(z)))) | b(s(s(s(s(z)))), s(z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(5167,plain,
% 1.74/1.92 (b(elem!1, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5166, 1057, 120, 3, 221, 1545, 1123])).
% 1.74/1.92 tff(5168,assumption,(s(s(s(s(s(z))))) = elem!1), introduced(assumption)).
% 1.74/1.92 tff(5169,plain,
% 1.74/1.92 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5168])).
% 1.74/1.92 tff(5170,plain,
% 1.74/1.92 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5169])).
% 1.74/1.92 tff(5171,plain,
% 1.74/1.92 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 1.74/1.92 inference(symmetry,[status(thm)],[5170])).
% 1.74/1.92 tff(5172,plain,
% 1.74/1.92 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5171])).
% 1.74/1.92 tff(5173,plain,
% 1.74/1.92 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(s(elem!1)))),
% 1.74/1.92 inference(symmetry,[status(thm)],[5172])).
% 1.74/1.92 tff(5174,plain,
% 1.74/1.92 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = elem!1)),
% 1.74/1.92 inference(transitivity,[status(thm)],[5173, 2170])).
% 1.74/1.92 tff(5175,plain,
% 1.74/1.92 ((~(elem!1 = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5174])).
% 1.74/1.92 tff(5176,plain,
% 1.74/1.92 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5168])).
% 1.74/1.92 tff(5177,plain,
% 1.74/1.92 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[5176, 3858])).
% 1.74/1.92 tff(5178,plain,
% 1.74/1.92 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5177])).
% 1.74/1.92 tff(5179,plain,
% 1.74/1.92 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[2729, 5178])).
% 1.74/1.92 tff(5180,plain,
% 1.74/1.92 (~(s(s(elem!1)) = elem!1)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[5179, 5175])).
% 1.74/1.92 tff(5181,assumption,(~(s(s(elem!1)) = elem!1)), introduced(assumption)).
% 1.74/1.92 tff(5182,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5183,plain,
% 1.74/1.92 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5184,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), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5183])).
% 1.74/1.92 tff(5185,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), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.74/1.92 inference(transitivity,[status(thm)],[5184, 5182])).
% 1.74/1.92 tff(5186,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), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(5187,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[5186, 5185])).
% 1.74/1.92 tff(5188,plain,
% 1.74/1.92 (~b(s(s(elem!1)), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5187, 453, 499, 2077, 1050])).
% 1.74/1.92 tff(5189,plain,
% 1.74/1.92 (r(s(s(elem!1)), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2240, 5188, 5181])).
% 1.74/1.92 tff(5190,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5191,plain,
% 1.74/1.92 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5192,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5191])).
% 1.74/1.92 tff(5193,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[5192, 5190])).
% 1.74/1.92 tff(5194,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(5195,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[5194, 5193])).
% 1.74/1.92 tff(5196,plain,
% 1.74/1.92 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5195, 453, 499, 1050, 120])).
% 1.74/1.92 tff(5197,assumption,(~r(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.74/1.92 tff(5198,assumption,(~b(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.74/1.92 tff(5199,plain,
% 1.74/1.92 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5200,plain,
% 1.74/1.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(5201,plain,
% 1.74/1.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[5200, 5199])).
% 1.74/1.92 tff(5202,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5201, 69, 555, 5198, 5197])).
% 1.74/1.92 tff(5203,plain,(r(s(s(s(z))), s(s(elem!1))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(5204,plain,
% 1.74/1.92 (r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5203, 5196, 555])).
% 1.74/1.92 tff(5205,assumption,(r(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.74/1.92 tff(5206,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5207,plain,
% 1.74/1.92 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5208,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5207])).
% 1.74/1.92 tff(5209,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[5208, 5206])).
% 1.74/1.92 tff(5210,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(5211,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[5210, 5209])).
% 1.74/1.92 tff(5212,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5211, 268, 869, 1545, 5205])).
% 1.74/1.92 tff(5213,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(5214,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5213, 5204, 5189, 1545])).
% 1.74/1.92 tff(5215,plain,((~b(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (s(s(elem!1)) = elem!1) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(5216,plain,
% 1.74/1.93 (~b(s(s(elem!1)), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5215, 5180, 555, 1545, 499, 120, 2077])).
% 1.74/1.93 tff(5217,plain,
% 1.74/1.93 (r(s(s(elem!1)), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1047, 5216])).
% 1.74/1.93 tff(5218,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5219,plain,
% 1.74/1.93 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5220,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5219])).
% 1.74/1.93 tff(5221,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[5220, 5218])).
% 1.74/1.93 tff(5222,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(5223,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5222, 5221])).
% 1.74/1.93 tff(5224,plain,
% 1.74/1.93 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5223, 268, 5217, 1132])).
% 1.74/1.93 tff(5225,plain,
% 1.74/1.93 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5171])).
% 1.74/1.93 tff(5226,plain,
% 1.74/1.93 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[5225, 2674])).
% 1.74/1.93 tff(5227,plain,
% 1.74/1.93 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5226])).
% 1.74/1.93 tff(5228,plain,
% 1.74/1.93 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5227])).
% 1.74/1.93 tff(5229,plain,
% 1.74/1.93 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[2690, 5228])).
% 1.74/1.93 tff(5230,plain,
% 1.74/1.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5231,plain,
% 1.74/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(5232,plain,
% 1.74/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5231, 5230])).
% 1.74/1.93 tff(5233,plain,
% 1.74/1.93 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5232, 69, 5229, 5224])).
% 1.74/1.93 tff(5234,plain,
% 1.74/1.93 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5223, 268, 1033, 1132])).
% 1.74/1.93 tff(5235,plain,
% 1.74/1.93 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5232, 69, 5229, 5234])).
% 1.74/1.93 tff(5236,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5170])).
% 1.74/1.93 tff(5237,plain,
% 1.74/1.93 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5171])).
% 1.74/1.93 tff(5238,plain,
% 1.74/1.93 ((~r(s(s(s(s(z)))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5237])).
% 1.74/1.93 tff(5239,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5240,plain,
% 1.74/1.93 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5241,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5240])).
% 1.74/1.93 tff(5242,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[5241, 5239])).
% 1.74/1.93 tff(5243,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(5244,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5243, 5242])).
% 1.74/1.93 tff(5245,plain,
% 1.74/1.93 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5244, 268, 1033, 1132])).
% 1.74/1.93 tff(5246,plain,
% 1.74/1.93 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5245, 5238])).
% 1.74/1.93 tff(5247,plain,
% 1.74/1.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5248,plain,
% 1.74/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(5249,plain,
% 1.74/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5248, 5247])).
% 1.74/1.93 tff(5250,plain,
% 1.74/1.93 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5249, 69])).
% 1.74/1.93 tff(5251,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5250, 5246, 2690])).
% 1.74/1.93 tff(5252,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5251, 5236])).
% 1.74/1.93 tff(5253,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5254,plain,
% 1.74/1.93 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5255,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5254])).
% 1.74/1.93 tff(5256,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[5255, 5253])).
% 1.74/1.93 tff(5257,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(5258,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5257, 5256])).
% 1.74/1.93 tff(5259,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5258, 453, 499, 2077, 299, 1974])).
% 1.74/1.93 tff(5260,plain,((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(5261,plain,
% 1.74/1.93 (~b(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5260, 299, 499, 2077])).
% 1.74/1.93 tff(5262,plain,
% 1.74/1.93 (r(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1677, 69, 50, 5261])).
% 1.74/1.93 tff(5263,plain,
% 1.74/1.93 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[384, 5262, 257])).
% 1.74/1.93 tff(5264,plain,
% 1.74/1.93 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1656, 5263])).
% 1.74/1.93 tff(5265,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))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5266,plain,
% 1.74/1.93 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5267,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5266])).
% 1.74/1.93 tff(5268,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[5267, 5265])).
% 1.74/1.93 tff(5269,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(5270,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))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5269, 5268])).
% 1.74/1.93 tff(5271,plain,
% 1.74/1.93 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5270, 453, 5264, 5252, 5235])).
% 1.74/1.93 tff(5272,plain,
% 1.74/1.93 (r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5203, 5271, 555])).
% 1.74/1.93 tff(5273,plain,
% 1.74/1.93 (~r(s(s(elem!1)), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5213, 5272, 1545])).
% 1.74/1.93 tff(5274,plain,
% 1.74/1.93 (b(s(s(elem!1)), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2240, 5273, 5180])).
% 1.74/1.93 tff(5275,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5276,plain,
% 1.74/1.93 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5277,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5276])).
% 1.74/1.93 tff(5278,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[5277, 5275])).
% 1.74/1.93 tff(5279,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(5280,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5279, 5278])).
% 1.74/1.93 tff(5281,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5280, 453, 2077, 5274, 299, 5235])).
% 1.74/1.93 tff(5282,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~(s(s(s(s(s(z))))) = elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(5283,plain,
% 1.74/1.93 (~b(s(s(s(s(z)))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5282, 5168, 1545, 555, 2077, 5217, 1132, 257, 499])).
% 1.74/1.93 tff(5284,plain,
% 1.74/1.93 (r(s(s(s(s(z)))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[254, 5283, 3])).
% 1.74/1.93 tff(5285,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5286,plain,
% 1.74/1.93 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5287,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5286])).
% 1.74/1.93 tff(5288,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.74/1.93 inference(transitivity,[status(thm)],[5287, 5285])).
% 1.74/1.93 tff(5289,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(5290,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5289, 5288])).
% 1.74/1.93 tff(5291,plain,
% 1.74/1.93 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5290, 268, 1545, 5284])).
% 1.74/1.93 tff(5292,plain,
% 1.74/1.93 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1656, 5291])).
% 1.74/1.93 tff(5293,plain,
% 1.74/1.93 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4961, 5284, 1545])).
% 1.74/1.93 tff(5294,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[518, 5293])).
% 1.74/1.93 tff(5295,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5296,plain,
% 1.74/1.93 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5297,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5296])).
% 1.74/1.94 tff(5298,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[5297, 5295])).
% 1.74/1.94 tff(5299,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(5300,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5299, 5298])).
% 1.74/1.94 tff(5301,plain,
% 1.74/1.94 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5300, 453, 5294, 5292, 5233])).
% 1.74/1.94 tff(5302,plain,
% 1.74/1.94 (r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5203, 5301, 555])).
% 1.74/1.94 tff(5303,plain,
% 1.74/1.94 (~r(s(s(elem!1)), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5213, 5302, 1545])).
% 1.74/1.94 tff(5304,plain,
% 1.74/1.94 (b(s(s(elem!1)), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2240, 5303, 5180])).
% 1.74/1.94 tff(5305,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), 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(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5306,plain,
% 1.74/1.94 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5307,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5306])).
% 1.74/1.94 tff(5308,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[5307, 5305])).
% 1.74/1.94 tff(5309,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(5310,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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5309, 5308])).
% 1.74/1.94 tff(5311,plain,
% 1.74/1.94 (~b(s(z), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5310, 453, 499, 2077, 5304])).
% 1.74/1.94 tff(5312,plain,
% 1.74/1.94 ((s(z) = s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3670, 69, 5311])).
% 1.74/1.94 tff(5313,plain,
% 1.74/1.94 (r(s(z), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5312, 3550])).
% 1.74/1.94 tff(5314,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5315,plain,
% 1.74/1.94 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5316,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5315])).
% 1.74/1.94 tff(5317,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[5316, 5314])).
% 1.74/1.94 tff(5318,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(5319,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5318, 5317])).
% 1.74/1.94 tff(5320,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5319, 268, 1545, 257, 5302, 5313])).
% 1.74/1.94 tff(5321,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(5322,plain,
% 1.74/1.94 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5321, 5167, 228, 4887, 1545, 4877, 1099, 3, 120])).
% 1.74/1.94 tff(5323,plain,
% 1.74/1.94 (b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[643, 5003, 637])).
% 1.74/1.94 tff(5324,plain,
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% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5325,plain,
% 1.74/1.94 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5326,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5325])).
% 1.74/1.94 tff(5327,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[5326, 5324])).
% 1.74/1.94 tff(5328,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(5329,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5328, 5327])).
% 1.74/1.94 tff(5330,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5329, 453, 499, 2077, 646, 374])).
% 1.74/1.94 tff(5331,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(5332,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5331, 5323, 298, 2077, 499])).
% 1.74/1.94 tff(5333,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(5334,plain,
% 1.74/1.94 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5333, 5167, 4887, 5322, 1545, 228])).
% 1.74/1.94 tff(5335,plain,
% 1.74/1.94 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[687, 5334])).
% 1.74/1.94 tff(5336,plain,
% 1.74/1.94 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.74/1.94 inference(symmetry,[status(thm)],[3539])).
% 1.74/1.94 tff(5337,plain,
% 1.74/1.94 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(z)))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5336])).
% 1.74/1.94 tff(5338,plain,
% 1.74/1.94 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[319, 5337])).
% 1.74/1.94 tff(5339,plain,
% 1.74/1.94 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4961, 1159, 1545])).
% 1.74/1.94 tff(5340,plain,
% 1.74/1.94 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[518, 5339])).
% 1.74/1.94 tff(5341,plain,
% 1.74/1.94 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4611, 453, 5340, 1779, 120])).
% 1.74/1.94 tff(5342,plain,
% 1.74/1.94 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2463, 69, 5341])).
% 1.74/1.94 tff(5343,plain,
% 1.74/1.94 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5342, 5338])).
% 1.74/1.94 tff(5344,plain,
% 1.74/1.94 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4649, 453, 5340, 1779, 120])).
% 1.74/1.94 tff(5345,plain,
% 1.74/1.94 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[328, 5344])).
% 1.74/1.94 tff(5346,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5347,plain,
% 1.74/1.94 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5348,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5347])).
% 1.74/1.94 tff(5349,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[5348, 5346])).
% 1.74/1.94 tff(5350,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(5351,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5350, 5349])).
% 1.74/1.94 tff(5352,plain,
% 1.74/1.94 ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5351, 268])).
% 1.74/1.94 tff(5353,plain,
% 1.74/1.94 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5352, 5345, 1159, 1132])).
% 1.74/1.94 tff(5354,plain,
% 1.74/1.94 (b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[643, 5353, 637])).
% 1.74/1.94 tff(5355,plain,
% 1.74/1.94 (~b(s(s(s(s(s(z))))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5331, 5354, 2077, 499])).
% 1.74/1.94 tff(5356,plain,
% 1.74/1.94 (r(s(s(s(s(s(z))))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[297, 5355])).
% 1.74/1.94 tff(5357,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2459, 268, 1132, 5356, 5343])).
% 1.74/1.94 tff(5358,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(5359,plain,
% 1.74/1.94 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5358, 1099, 5167, 4887, 5322, 5335, 120, 1545])).
% 1.74/1.94 tff(5360,plain,
% 1.74/1.94 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[254, 5359, 3])).
% 1.74/1.94 tff(5361,plain,
% 1.74/1.94 (~b(s(z), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5260, 5360, 4887, 5167])).
% 1.74/1.94 tff(5362,plain,
% 1.74/1.94 (r(s(z), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1677, 69, 50, 5361])).
% 1.74/1.94 tff(5363,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5364,plain,
% 1.74/1.94 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5365,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5364])).
% 1.74/1.94 tff(5366,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[5365, 5363])).
% 1.74/1.94 tff(5367,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(5368,plain,
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% 1.74/1.94 inference(modus_ponens,[status(thm)],[5367, 5366])).
% 1.74/1.94 tff(5369,plain,
% 1.74/1.94 (~r(s(s(s(s(s(z))))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5368, 268, 301, 376])).
% 1.74/1.94 tff(5370,plain,
% 1.74/1.94 (b(s(s(s(s(s(z))))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[297, 5369])).
% 1.74/1.94 tff(5371,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5372,plain,
% 1.74/1.94 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5373,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5372])).
% 1.74/1.94 tff(5374,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[5373, 5371])).
% 1.74/1.94 tff(5375,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(5376,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5375, 5374])).
% 1.74/1.94 tff(5377,plain,
% 1.74/1.94 (~r(s(z), s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5376, 268, 301, 376])).
% 1.74/1.94 tff(5378,plain,
% 1.74/1.94 (b(s(z), s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[372, 5377])).
% 1.74/1.94 tff(5379,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2943, 453, 5378, 1779, 5370, 120])).
% 1.74/1.94 tff(5380,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(5381,plain,
% 1.74/1.94 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5380, 5335, 120, 5362])).
% 1.74/1.94 tff(5382,plain,
% 1.74/1.94 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[328, 5381])).
% 1.74/1.94 tff(5383,plain,
% 1.74/1.94 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[384, 5362, 228])).
% 1.74/1.94 tff(5384,plain,
% 1.74/1.94 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1656, 5383])).
% 1.74/1.94 tff(5385,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), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5386,plain,
% 1.74/1.95 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5387,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(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(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5386])).
% 1.74/1.95 tff(5388,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(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(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[5387, 5385])).
% 1.74/1.95 tff(5389,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(5390,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[5389, 5388])).
% 1.74/1.95 tff(5391,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5390, 453, 4887, 5384, 5382, 5335, 5360, 120])).
% 1.74/1.95 tff(5392,plain,(b(s(s(s(s(z)))), s(z)) | (~b(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(z))), elem!1)) | b(s(z), s(s(s(z)))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(5393,plain,
% 1.74/1.95 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5392, 120, 3, 4870, 221, 4876])).
% 1.74/1.95 tff(5394,plain,
% 1.74/1.95 (~(s(z) = elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1125, 4876])).
% 1.74/1.95 tff(5395,plain,
% 1.74/1.95 (~r(s(z), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4885, 4870, 228])).
% 1.74/1.95 tff(5396,plain,
% 1.74/1.95 (b(s(z), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[506, 5395, 5394])).
% 1.74/1.95 tff(5397,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), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5398,plain,
% 1.74/1.95 (((~b(s(z), elem!1)) | (~b(s(z), 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), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5399,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), elem!1)) | (~b(s(z), 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), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5398])).
% 1.74/1.95 tff(5400,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), elem!1)) | (~b(s(z), 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), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[5399, 5397])).
% 1.74/1.95 tff(5401,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), elem!1)) | (~b(s(z), 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)))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(5402,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), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[5401, 5400])).
% 1.74/1.95 tff(5403,plain,
% 1.74/1.95 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5402, 453, 5396, 5393, 120])).
% 1.74/1.95 tff(5404,plain,
% 1.74/1.95 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1656, 5403])).
% 1.74/1.95 tff(5405,plain,
% 1.74/1.95 (~(elem!1 = s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4487, 4869])).
% 1.74/1.95 tff(5406,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5407,plain,
% 1.74/1.95 (((~b(s(z), elem!1)) | (~b(s(z), 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5408,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), elem!1)) | (~b(s(z), 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5407])).
% 1.74/1.95 tff(5409,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[5408, 5406])).
% 1.74/1.95 tff(5410,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(5411,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[5410, 5409])).
% 1.74/1.95 tff(5412,plain,
% 1.74/1.95 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5411, 453, 5396, 5393, 120])).
% 1.74/1.95 tff(5413,plain,
% 1.74/1.95 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[518, 5412])).
% 1.74/1.95 tff(5414,plain,
% 1.74/1.95 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4961, 5413, 4870])).
% 1.74/1.95 tff(5415,plain,
% 1.74/1.95 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[254, 5414, 3])).
% 1.74/1.95 tff(5416,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), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5417,plain,
% 1.74/1.95 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5418,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5417])).
% 1.74/1.95 tff(5419,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[5418, 5416])).
% 1.74/1.95 tff(5420,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(5421,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[5420, 5419])).
% 1.74/1.95 tff(5422,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5421, 453, 499, 1764, 299, 1275])).
% 1.74/1.95 tff(5423,plain,((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(5424,plain,
% 1.74/1.95 (~b(elem!1, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5423, 5415, 5396, 5393])).
% 1.74/1.95 tff(5425,plain,
% 1.74/1.95 (r(elem!1, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4492, 5424, 5405])).
% 1.74/1.95 tff(5426,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5427,plain,
% 1.74/1.95 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5428,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5427])).
% 1.74/1.95 tff(5429,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[5428, 5426])).
% 1.74/1.95 tff(5430,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(5431,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[5430, 5429])).
% 1.74/1.95 tff(5432,plain,
% 1.74/1.95 ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5431, 268])).
% 1.74/1.95 tff(5433,plain,
% 1.74/1.95 (~r(elem!1, s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5432, 5425, 5404, 4870])).
% 1.74/1.95 tff(5434,plain,
% 1.74/1.95 (b(elem!1, s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1087, 5433, 9])).
% 1.74/1.95 tff(5435,plain,
% 1.74/1.95 (~r(elem!1, s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1157, 5425, 228])).
% 1.74/1.95 tff(5436,plain,
% 1.74/1.95 (b(elem!1, s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1130, 5435, 4876])).
% 1.74/1.95 tff(5437,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, 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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5438,plain,
% 1.74/1.95 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5439,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5438])).
% 1.74/1.95 tff(5440,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[5439, 5437])).
% 1.74/1.95 tff(5441,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(5442,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[5441, 5440])).
% 1.74/1.95 tff(5443,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5442, 453, 5396, 5436, 5393, 5434])).
% 1.74/1.95 tff(5444,plain,((~b(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = elem!1) | b(s(z), s(s(s(z)))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(5445,plain,
% 1.74/1.95 (b(s(s(s(z))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5444, 4552, 120, 221])).
% 1.74/1.95 tff(5446,plain,
% 1.74/1.95 (b(elem!1, s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1130, 2076, 1123])).
% 1.74/1.95 tff(5447,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5448,plain,
% 1.74/1.95 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5449,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), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5448])).
% 1.74/1.96 tff(5450,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), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.96 inference(transitivity,[status(thm)],[5449, 5447])).
% 1.74/1.96 tff(5451,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), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(5452,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5451, 5450])).
% 1.74/1.96 tff(5453,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5452, 453, 499, 5446, 5445, 120])).
% 1.74/1.96 tff(5454,plain,(r(elem!1, s(z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | b(s(z), s(s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(5455,plain,
% 1.74/1.96 (r(elem!1, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5454, 221, 120, 499, 1099, 1123])).
% 1.74/1.96 tff(5456,plain,
% 1.74/1.96 (~r(elem!1, s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1157, 5455, 228])).
% 1.74/1.96 tff(5457,plain,
% 1.74/1.96 (b(elem!1, s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4492, 5456, 4545])).
% 1.74/1.96 tff(5458,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), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5459,plain,
% 1.74/1.96 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5460,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5459])).
% 1.74/1.96 tff(5461,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[5460, 5458])).
% 1.74/1.96 tff(5462,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(5463,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5462, 5461])).
% 1.74/1.96 tff(5464,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5463, 453, 499, 1291, 120, 1275])).
% 1.74/1.96 tff(5465,plain,((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(5466,plain,
% 1.74/1.96 (~b(s(s(s(z))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5465, 5457, 120, 499])).
% 1.74/1.96 tff(5467,plain,
% 1.74/1.96 (s(s(s(s(z)))) = elem!1),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5444, 5466, 120, 221])).
% 1.74/1.96 tff(5468,plain,
% 1.74/1.96 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5467])).
% 1.74/1.96 tff(5469,plain,
% 1.74/1.96 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5468])).
% 1.74/1.96 tff(5470,plain,
% 1.74/1.96 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.74/1.96 inference(symmetry,[status(thm)],[5469])).
% 1.74/1.96 tff(5471,plain,
% 1.74/1.96 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5470])).
% 1.74/1.96 tff(5472,plain,
% 1.74/1.96 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 1.74/1.96 inference(symmetry,[status(thm)],[5471])).
% 1.74/1.96 tff(5473,plain,
% 1.74/1.96 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5472])).
% 1.74/1.96 tff(5474,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.74/1.96 inference(symmetry,[status(thm)],[5473])).
% 1.74/1.96 tff(5475,plain,
% 1.74/1.96 (b(s(s(s(s(z)))), s(z)) <=> b(elem!1, s(z))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5467])).
% 1.74/1.96 tff(5476,plain,
% 1.74/1.96 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(elem!1, s(z)))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5475])).
% 1.74/1.96 tff(5477,plain,
% 1.74/1.96 (~b(elem!1, s(z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[1057, 5476])).
% 1.74/1.96 tff(5478,plain,
% 1.74/1.96 (r(s(s(s(elem!1))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1711, 5477, 1057, 221])).
% 1.74/1.96 tff(5479,plain,
% 1.74/1.96 (~r(s(s(s(elem!1))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[842, 5478, 5455])).
% 1.74/1.96 tff(5480,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[856, 5479])).
% 1.74/1.96 tff(5481,plain,
% 1.74/1.96 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5480, 5474])).
% 1.74/1.96 tff(5482,plain,
% 1.74/1.96 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5471])).
% 1.74/1.96 tff(5483,plain,
% 1.74/1.96 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5478, 5482])).
% 1.74/1.96 tff(5484,plain,
% 1.74/1.96 (r(s(s(s(z))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[74, 5466, 4544])).
% 1.74/1.96 tff(5485,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5486,plain,
% 1.74/1.96 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5487,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5486])).
% 1.74/1.96 tff(5488,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[5487, 5485])).
% 1.74/1.96 tff(5489,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(5490,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5489, 5488])).
% 1.74/1.96 tff(5491,plain,
% 1.74/1.96 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5490, 268, 5484, 5483])).
% 1.74/1.96 tff(5492,plain,
% 1.74/1.96 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1191, 5467])).
% 1.74/1.96 tff(5493,plain,
% 1.74/1.96 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1238, 69, 5492, 5491])).
% 1.74/1.96 tff(5494,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(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(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5495,plain,
% 1.74/1.96 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5496,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5495])).
% 1.74/1.96 tff(5497,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[5496, 5494])).
% 1.74/1.96 tff(5498,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(5499,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5498, 5497])).
% 1.74/1.96 tff(5500,plain,
% 1.74/1.96 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5499, 453, 499, 120])).
% 1.74/1.96 tff(5501,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5500, 5493, 5481])).
% 1.74/1.96 tff(5502,plain,(b(s(z), s(s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | b(s(s(s(s(z)))), s(z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(5503,plain,
% 1.74/1.96 (b(s(z), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5502, 4542, 4540, 1057, 1123])).
% 1.74/1.96 tff(5504,plain,
% 1.74/1.96 (~(s(s(s(s(z)))) = elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4551, 2076, 1099])).
% 1.74/1.96 tff(5505,plain,
% 1.74/1.96 (b(s(z), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[506, 4541, 492])).
% 1.74/1.96 tff(5506,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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5507,plain,
% 1.74/1.96 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5508,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5507])).
% 1.74/1.96 tff(5509,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[5508, 5506])).
% 1.74/1.96 tff(5510,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(5511,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5510, 5509])).
% 1.74/1.96 tff(5512,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5511, 453, 499, 2077, 1291, 2090])).
% 1.74/1.96 tff(5513,plain,((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(5514,plain,
% 1.74/1.96 (~b(s(s(s(z))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5513, 2077, 5505, 2090])).
% 1.74/1.96 tff(5515,plain,
% 1.74/1.96 (r(s(s(s(z))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[74, 59, 5514])).
% 1.74/1.96 tff(5516,plain,
% 1.74/1.96 (~r(s(s(s(z))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4538, 1132, 300])).
% 1.74/1.96 tff(5517,plain,
% 1.74/1.96 (b(s(s(s(z))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[134, 5516])).
% 1.74/1.96 tff(5518,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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5519,plain,
% 1.74/1.96 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5520,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5519])).
% 1.74/1.96 tff(5521,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[5520, 5518])).
% 1.74/1.96 tff(5522,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(5523,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5522, 5521])).
% 1.74/1.96 tff(5524,plain,
% 1.74/1.96 (~b(elem!1, s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5523, 453, 5505, 2077, 5517])).
% 1.74/1.96 tff(5525,plain,
% 1.74/1.96 (~(elem!1 = s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4487, 59])).
% 1.74/1.96 tff(5526,plain,
% 1.74/1.96 (r(elem!1, s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4492, 5525, 5524])).
% 1.74/1.96 tff(5527,plain,
% 1.74/1.96 (~r(elem!1, s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5432, 5526, 300, 5515])).
% 1.74/1.96 tff(5528,plain,
% 1.74/1.96 (b(elem!1, s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1087, 5527, 9])).
% 1.74/1.96 tff(5529,assumption,(elem!1 = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.74/1.96 tff(5530,plain,
% 1.74/1.96 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5529])).
% 1.74/1.96 tff(5531,plain,
% 1.74/1.96 ((~r(elem!1, s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5530])).
% 1.74/1.96 tff(5532,plain,
% 1.74/1.96 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[1085, 5531])).
% 1.74/1.96 tff(5533,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[301, 5532])).
% 1.74/1.96 tff(5534,plain,(r(elem!1, s(s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(5535,plain,
% 1.74/1.96 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5534, 301, 1085])).
% 1.74/1.96 tff(5536,plain,
% 1.74/1.96 (elem!1 = s(s(s(s(s(z)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5168, 55])).
% 1.74/1.96 tff(5537,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2073, 5536])).
% 1.74/1.96 tff(5538,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (elem!1 = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(5539,plain,
% 1.74/1.96 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5538, 5535])).
% 1.74/1.96 tff(5540,plain,
% 1.74/1.96 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[309, 301, 300])).
% 1.74/1.96 tff(5541,plain,
% 1.74/1.96 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[687, 5540])).
% 1.74/1.96 tff(5542,plain,
% 1.74/1.96 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5358, 5541, 1132, 2077, 499, 5539, 5517, 1545])).
% 1.74/1.96 tff(5543,plain,
% 1.74/1.96 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[254, 5542, 3])).
% 1.74/1.96 tff(5544,plain,
% 1.74/1.96 (~b(s(z), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5260, 5543, 499, 2077])).
% 1.74/1.96 tff(5545,plain,
% 1.74/1.96 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5380, 5541, 5517, 301])).
% 1.74/1.96 tff(5546,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1677, 69, 5545, 50, 5544])).
% 1.74/1.96 tff(5547,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), elem!1)) | r(elem!1, s(s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(5548,plain,
% 1.74/1.96 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5547, 5515, 2077, 3, 1132, 5505, 5527, 300])).
% 1.74/1.96 tff(5549,plain,
% 1.74/1.96 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[328, 322])).
% 1.74/1.96 tff(5550,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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5551,plain,
% 1.74/1.96 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5552,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5551])).
% 1.74/1.97 tff(5553,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5552, 5550])).
% 1.74/1.97 tff(5554,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5555,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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5554, 5553])).
% 1.74/1.97 tff(5556,plain,
% 1.74/1.97 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5555, 453, 5549, 530, 299])).
% 1.74/1.97 tff(5557,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(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5558,plain,
% 1.74/1.97 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5559,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), 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(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5558])).
% 1.74/1.97 tff(5560,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), 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(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5559, 5557])).
% 1.74/1.97 tff(5561,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5562,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5561, 5560])).
% 1.74/1.97 tff(5563,plain,
% 1.74/1.97 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5562, 453, 2077, 922, 299])).
% 1.74/1.97 tff(5564,plain,
% 1.74/1.97 (r(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[795, 69, 153, 5563])).
% 1.74/1.97 tff(5565,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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5566,plain,
% 1.74/1.97 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5567,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), 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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5566])).
% 1.74/1.97 tff(5568,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), 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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5567, 5565])).
% 1.74/1.97 tff(5569,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5570,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5569, 5568])).
% 1.74/1.97 tff(5571,plain,
% 1.74/1.97 (~b(s(s(z)), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5570, 453, 499, 2077, 922])).
% 1.74/1.97 tff(5572,plain,
% 1.74/1.97 (r(s(s(z)), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[720, 69, 717, 5571])).
% 1.74/1.97 tff(5573,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2385, 268, 1132, 5572, 5564])).
% 1.74/1.97 tff(5574,plain,((~b(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(5575,plain,
% 1.74/1.97 (~b(s(s(z)), elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5574, 299, 2077, 1132, 5505])).
% 1.74/1.97 tff(5576,plain,
% 1.74/1.97 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 1.74/1.97 inference(symmetry,[status(thm)],[4133])).
% 1.74/1.97 tff(5577,plain,
% 1.74/1.97 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5576])).
% 1.74/1.97 tff(5578,plain,
% 1.74/1.97 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[52, 5577])).
% 1.74/1.97 tff(5579,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(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(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5580,plain,
% 1.74/1.97 (((~b(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(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5581,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5580])).
% 1.74/1.97 tff(5582,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5581, 5579])).
% 1.74/1.97 tff(5583,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5584,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5583, 5582])).
% 1.74/1.97 tff(5585,plain,
% 1.74/1.97 (~b(s(z), s(s(s(s(s(z))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5584, 453, 1779, 120, 2090])).
% 1.74/1.97 tff(5586,plain,
% 1.74/1.97 (r(s(z), s(s(s(s(s(z))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[372, 5585])).
% 1.74/1.97 tff(5587,plain,
% 1.74/1.97 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(z), elem!1)),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5168])).
% 1.74/1.97 tff(5588,plain,
% 1.74/1.97 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(s(z))))))),
% 1.74/1.97 inference(symmetry,[status(thm)],[5587])).
% 1.74/1.97 tff(5589,plain,
% 1.74/1.97 ((~r(s(z), elem!1)) <=> (~r(s(z), s(s(s(s(s(z)))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5588])).
% 1.74/1.97 tff(5590,plain,
% 1.74/1.97 (~r(s(z), s(s(s(s(s(z))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[4541, 5589])).
% 1.74/1.97 tff(5591,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2246, 5590])).
% 1.74/1.97 tff(5592,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(5593,plain,
% 1.74/1.97 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5592, 5586, 4541])).
% 1.74/1.97 tff(5594,plain,
% 1.74/1.97 (r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[643, 5593, 638])).
% 1.74/1.97 tff(5595,assumption,(s(s(s(s(s(s(s(s(z)))))))) = elem!1), introduced(assumption)).
% 1.74/1.97 tff(5596,plain,
% 1.74/1.97 (s(s(s(s(s(s(s(s(z)))))))) = s(s(z))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5595, 3804])).
% 1.74/1.97 tff(5597,plain,
% 1.74/1.97 (inj_0(s(s(s(s(s(s(s(s(z))))))))) = inj_0(s(s(z)))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5596])).
% 1.74/1.97 tff(5598,plain,
% 1.74/1.97 (s(s(s(s(s(s(s(z))))))) = s(z)),
% 1.74/1.97 inference(transitivity,[status(thm)],[2336, 5597, 28])).
% 1.74/1.97 tff(5599,plain,
% 1.74/1.97 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(z))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5598])).
% 1.74/1.97 tff(5600,plain,
% 1.74/1.97 (s(s(s(s(s(s(z)))))) = z),
% 1.74/1.97 inference(transitivity,[status(thm)],[1375, 5599, 32])).
% 1.74/1.97 tff(5601,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2341, 5600])).
% 1.74/1.97 tff(5602,plain,((~(s(s(s(s(s(s(s(s(z)))))))) = elem!1)) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(5603,plain,
% 1.74/1.97 (~(s(s(s(s(s(s(s(s(z)))))))) = elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5602, 3468])).
% 1.74/1.97 tff(5604,plain,
% 1.74/1.97 (b(s(z), s(elem!1))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[2090, 3638])).
% 1.74/1.97 tff(5605,plain,
% 1.74/1.97 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[3469])).
% 1.74/1.97 tff(5606,plain,
% 1.74/1.97 (b(s(elem!1), s(z))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[120, 5605])).
% 1.74/1.97 tff(5607,plain,
% 1.74/1.97 (b(s(s(elem!1)), elem!1)),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[299, 3504])).
% 1.74/1.97 tff(5608,assumption,(s(s(elem!1)) = s(s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.74/1.97 tff(5609,plain,
% 1.74/1.97 (s(s(s(s(s(s(s(s(z)))))))) = s(s(elem!1))),
% 1.74/1.97 inference(symmetry,[status(thm)],[5608])).
% 1.74/1.97 tff(5610,plain,
% 1.74/1.97 (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(z))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5609, 3478])).
% 1.74/1.97 tff(5611,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2727, 5610])).
% 1.74/1.97 tff(5612,plain,((~(s(s(elem!1)) = s(s(s(s(s(s(s(s(z)))))))))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(5613,plain,
% 1.74/1.97 (~(s(s(elem!1)) = s(s(s(s(s(s(s(s(z)))))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5612, 3468])).
% 1.74/1.97 tff(5614,plain,
% 1.74/1.97 (~b(s(s(elem!1)), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5215, 3502, 555, 120, 499, 2077, 1545])).
% 1.74/1.97 tff(5615,plain,
% 1.74/1.97 (r(s(s(elem!1)), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1047, 5614])).
% 1.74/1.97 tff(5616,assumption,(b(s(s(s(s(s(s(s(s(z)))))))), elem!1)), introduced(assumption)).
% 1.74/1.97 tff(5617,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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5618,plain,
% 1.74/1.97 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5619,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5618])).
% 1.74/1.97 tff(5620,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5619, 5617])).
% 1.74/1.97 tff(5621,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5622,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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5621, 5620])).
% 1.74/1.97 tff(5623,plain,
% 1.74/1.97 (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5622, 453, 2077, 909, 5616])).
% 1.74/1.97 tff(5624,assumption,(~(s(s(elem!1)) = s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 1.74/1.97 tff(5625,plain,
% 1.74/1.97 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5626,plain,
% 1.74/1.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5627,plain,
% 1.74/1.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5626, 5625])).
% 1.74/1.97 tff(5628,plain,
% 1.74/1.97 (r(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5627, 69, 5624, 5623])).
% 1.74/1.97 tff(5629,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(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5630,plain,
% 1.74/1.97 (((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5631,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(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(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(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5630])).
% 1.74/1.97 tff(5632,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(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(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(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5631, 5629])).
% 1.74/1.97 tff(5633,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(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5634,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(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5633, 5632])).
% 1.74/1.97 tff(5635,plain,
% 1.74/1.97 (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5634, 453, 1059, 1549, 499, 2077, 5616])).
% 1.74/1.97 tff(5636,plain,
% 1.74/1.97 (r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2906, 69, 2886, 5635])).
% 1.74/1.97 tff(5637,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5638,plain,
% 1.74/1.97 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5639,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5638])).
% 1.74/1.98 tff(5640,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5639, 5637])).
% 1.74/1.98 tff(5641,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5642,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5641, 5640])).
% 1.74/1.98 tff(5643,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5642, 268, 1033, 5636, 5628])).
% 1.74/1.98 tff(5644,plain,((~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(5645,plain,
% 1.74/1.98 (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5644, 5615, 5613, 2077, 5607, 5606, 5604, 499])).
% 1.74/1.98 tff(5646,plain,
% 1.74/1.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = elem!1) | b(s(s(s(s(s(s(s(s(z)))))))), elem!1) | r(s(s(s(s(s(s(s(s(z)))))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = elem!1) | b(s(s(s(s(s(s(s(s(z)))))))), elem!1) | r(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5647,plain,
% 1.74/1.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = elem!1) | b(s(s(s(s(s(s(s(s(z)))))))), elem!1) | r(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5648,plain,
% 1.74/1.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = elem!1) | b(s(s(s(s(s(s(s(s(z)))))))), elem!1) | r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5647, 5646])).
% 1.74/1.98 tff(5649,plain,
% 1.74/1.98 ((s(s(s(s(s(s(s(s(z)))))))) = elem!1) | b(s(s(s(s(s(s(s(s(z)))))))), elem!1) | r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5648, 69])).
% 1.74/1.98 tff(5650,plain,
% 1.74/1.98 (r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5649, 5645, 5603])).
% 1.74/1.98 tff(5651,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5652,plain,
% 1.74/1.98 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5653,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5652])).
% 1.74/1.98 tff(5654,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5653, 5651])).
% 1.74/1.98 tff(5655,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5656,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5655, 5654])).
% 1.74/1.98 tff(5657,plain,
% 1.74/1.98 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5656, 268, 722, 5650])).
% 1.74/1.98 tff(5658,plain,
% 1.74/1.98 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2833, 69, 2688, 5657])).
% 1.74/1.98 tff(5659,plain,
% 1.74/1.98 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[3469])).
% 1.74/1.98 tff(5660,plain,
% 1.74/1.98 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 1.74/1.98 inference(commutativity,[status(thm)],[])).
% 1.74/1.98 tff(5661,plain,
% 1.74/1.98 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[5660])).
% 1.74/1.98 tff(5662,plain,
% 1.74/1.98 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[3469])).
% 1.74/1.98 tff(5663,plain,
% 1.74/1.98 ((s(elem!1) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[5662])).
% 1.74/1.98 tff(5664,plain,
% 1.74/1.98 ((s(elem!1) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5663, 5661])).
% 1.74/1.98 tff(5665,plain,
% 1.74/1.98 ((~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))) <=> (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5664])).
% 1.74/1.98 tff(5666,plain,
% 1.74/1.98 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[3815, 5665])).
% 1.74/1.98 tff(5667,plain,
% 1.74/1.98 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[3469])).
% 1.74/1.98 tff(5668,plain,
% 1.74/1.98 (r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[5667])).
% 1.74/1.98 tff(5669,plain,
% 1.74/1.98 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) <=> (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5668])).
% 1.74/1.98 tff(5670,plain,
% 1.74/1.98 (r(s(elem!1), elem!1)),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[1545, 3523])).
% 1.74/1.98 tff(5671,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5672,plain,
% 1.74/1.98 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5673,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5672])).
% 1.74/1.98 tff(5674,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5673, 5671])).
% 1.74/1.98 tff(5675,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5676,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5675, 5674])).
% 1.74/1.98 tff(5677,plain,
% 1.74/1.98 (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5676, 268, 5670, 5650])).
% 1.74/1.98 tff(5678,plain,
% 1.74/1.98 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5677, 5669])).
% 1.74/1.98 tff(5679,plain,
% 1.74/1.98 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2846, 5678, 5666])).
% 1.74/1.98 tff(5680,plain,
% 1.74/1.98 (b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5679, 5659])).
% 1.74/1.98 tff(5681,plain,
% 1.74/1.98 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[1779, 3553])).
% 1.74/1.98 tff(5682,plain,
% 1.74/1.98 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[3469])).
% 1.74/1.98 tff(5683,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5684,plain,
% 1.74/1.98 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5685,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5684])).
% 1.74/1.98 tff(5686,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5685, 5683])).
% 1.74/1.98 tff(5687,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5688,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5687, 5686])).
% 1.74/1.98 tff(5689,plain,
% 1.74/1.98 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5688, 268, 722, 1545])).
% 1.74/1.98 tff(5690,plain,
% 1.74/1.98 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2570, 5689])).
% 1.74/1.98 tff(5691,plain,
% 1.74/1.98 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5690, 5682])).
% 1.74/1.98 tff(5692,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(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5693,plain,
% 1.74/1.98 (((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5694,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(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5693])).
% 1.74/1.98 tff(5695,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(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5694, 5692])).
% 1.74/1.98 tff(5696,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(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5697,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5696, 5695])).
% 1.74/1.98 tff(5698,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5697, 453, 5606, 5604, 5691, 5681, 5680, 5658])).
% 1.74/1.98 tff(5699,plain,((~(s(s(z)) = elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(5700,plain,
% 1.74/1.98 (~(s(s(z)) = elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5699, 5594, 2077, 499, 299, 2090, 120, 1779, 1545, 555])).
% 1.74/1.98 tff(5701,plain,
% 1.74/1.98 (r(s(s(z)), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[782, 5700, 4])).
% 1.74/1.98 tff(5702,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5703,plain,
% 1.74/1.98 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5704,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5703])).
% 1.74/1.98 tff(5705,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5704, 5702])).
% 1.74/1.98 tff(5706,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5707,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5706, 5705])).
% 1.74/1.98 tff(5708,plain,
% 1.74/1.98 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5707, 268, 5701, 5594])).
% 1.74/1.98 tff(5709,plain,
% 1.74/1.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5710,plain,
% 1.74/1.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5711,plain,
% 1.74/1.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5710, 5709])).
% 1.74/1.98 tff(5712,plain,
% 1.74/1.98 ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5711, 69, 5708])).
% 1.74/1.98 tff(5713,plain,
% 1.74/1.98 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5712, 5578])).
% 1.74/1.98 tff(5714,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5715,plain,
% 1.74/1.98 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5716,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5715])).
% 1.74/1.98 tff(5717,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5716, 5714])).
% 1.74/1.98 tff(5718,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5719,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5718, 5717])).
% 1.74/1.98 tff(5720,plain,
% 1.74/1.98 (~r(s(s(z)), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5719, 268, 5701, 1545])).
% 1.74/1.98 tff(5721,plain,
% 1.74/1.98 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1350, 69, 5720])).
% 1.74/1.98 tff(5722,plain,
% 1.74/1.98 (b(s(s(z)), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5721, 1243])).
% 1.74/1.99 tff(5723,plain,
% 1.74/1.99 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5688, 268, 5594, 1545])).
% 1.74/1.99 tff(5724,plain,
% 1.74/1.99 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2570, 5723])).
% 1.74/1.99 tff(5725,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(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5726,plain,
% 1.74/1.99 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5727,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5726])).
% 1.74/1.99 tff(5728,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5727, 5725])).
% 1.74/1.99 tff(5729,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(5730,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5729, 5728])).
% 1.74/1.99 tff(5731,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5730, 453, 1780, 5724, 5722, 5713])).
% 1.74/1.99 tff(5732,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | b(s(s(z)), elem!1) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5733,plain,
% 1.74/1.99 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5732, 5575, 5515, 5549, 2077, 5505, 299, 2090, 120, 548, 5556, 4541])).
% 1.74/1.99 tff(5734,plain,
% 1.74/1.99 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[687, 5733])).
% 1.74/1.99 tff(5735,plain,
% 1.74/1.99 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1566, 5734, 5515])).
% 1.74/1.99 tff(5736,plain,
% 1.74/1.99 (s(s(s(s(s(z))))) = elem!1),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[643, 5735, 5556])).
% 1.74/1.99 tff(5737,plain,
% 1.74/1.99 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5736])).
% 1.74/1.99 tff(5738,plain,
% 1.74/1.99 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5737])).
% 1.74/1.99 tff(5739,plain,
% 1.74/1.99 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 1.74/1.99 inference(symmetry,[status(thm)],[5738])).
% 1.74/1.99 tff(5740,plain,
% 1.74/1.99 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5739])).
% 1.74/1.99 tff(5741,plain,
% 1.74/1.99 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(s(elem!1)))),
% 1.74/1.99 inference(symmetry,[status(thm)],[5740])).
% 1.74/1.99 tff(5742,plain,
% 1.74/1.99 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = elem!1)),
% 1.74/1.99 inference(transitivity,[status(thm)],[5741, 2170])).
% 1.74/1.99 tff(5743,plain,
% 1.74/1.99 ((~(elem!1 = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5742])).
% 1.74/1.99 tff(5744,plain,
% 1.74/1.99 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5736])).
% 1.74/1.99 tff(5745,plain,
% 1.74/1.99 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5744, 3858])).
% 1.74/1.99 tff(5746,plain,
% 1.74/1.99 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5745])).
% 1.74/1.99 tff(5747,plain,
% 1.74/1.99 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2729, 5746])).
% 1.74/1.99 tff(5748,plain,
% 1.74/1.99 (~(s(s(elem!1)) = elem!1)),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5747, 5743])).
% 1.74/1.99 tff(5749,plain,
% 1.74/1.99 (~b(s(s(elem!1)), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5215, 5748, 548, 120, 5505, 2077, 5515])).
% 1.74/1.99 tff(5750,plain,
% 1.74/1.99 (r(s(s(elem!1)), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1047, 5749])).
% 1.74/1.99 tff(5751,plain,
% 1.74/1.99 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5223, 268, 5750, 1132])).
% 1.74/1.99 tff(5752,plain,
% 1.74/1.99 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5739])).
% 1.74/1.99 tff(5753,plain,
% 1.74/1.99 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5752, 2674])).
% 1.74/1.99 tff(5754,plain,
% 1.74/1.99 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.74/1.99 inference(symmetry,[status(thm)],[5753])).
% 1.74/1.99 tff(5755,plain,
% 1.74/1.99 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5754])).
% 1.74/1.99 tff(5756,plain,
% 1.74/1.99 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2690, 5755])).
% 1.74/1.99 tff(5757,plain,
% 1.74/1.99 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5232, 69, 5756, 5751])).
% 1.74/1.99 tff(5758,plain,
% 1.74/1.99 ((s(s(s(s(s(z))))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5736])).
% 1.74/1.99 tff(5759,plain,
% 1.74/1.99 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.74/1.99 inference(transitivity,[status(thm)],[5758, 144])).
% 1.74/1.99 tff(5760,plain,
% 1.74/1.99 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5759])).
% 1.74/1.99 tff(5761,plain,
% 1.74/1.99 (~(s(s(z)) = elem!1)),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[52, 5760])).
% 1.74/1.99 tff(5762,plain,
% 1.74/1.99 (r(s(s(z)), elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[782, 5761, 5575])).
% 1.74/1.99 tff(5763,plain,
% 1.74/1.99 (elem!1 = s(s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5538, 5736])).
% 1.74/1.99 tff(5764,plain,
% 1.74/1.99 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5592, 4541, 2246])).
% 1.74/1.99 tff(5765,plain,
% 1.74/1.99 (~(s(s(s(s(z)))) = elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4469, 722, 322])).
% 1.74/1.99 tff(5766,plain,
% 1.74/1.99 (~(elem!1 = s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[8, 5765])).
% 1.74/1.99 tff(5767,plain,
% 1.74/1.99 (b(elem!1, s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1087, 5766, 1085])).
% 1.74/1.99 tff(5768,plain,
% 1.74/1.99 (~r(s(s(s(z))), elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1566, 722, 256])).
% 1.74/1.99 tff(5769,plain,
% 1.74/1.99 (b(s(s(s(z))), elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[74, 5768, 59])).
% 1.74/1.99 tff(5770,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), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, 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), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5771,plain,
% 1.74/1.99 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5772,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5771])).
% 1.74/1.99 tff(5773,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5772, 5770])).
% 1.74/1.99 tff(5774,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(5775,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5774, 5773])).
% 1.74/1.99 tff(5776,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5775, 453, 499, 5769, 5767, 2090])).
% 1.74/1.99 tff(5777,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | r(elem!1, s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5778,plain,
% 1.74/1.99 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5777, 5505, 2090, 1085, 322, 59, 256])).
% 1.74/1.99 tff(5779,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[643, 5778, 5764, 638])).
% 1.74/1.99 tff(5780,plain,(r(s(z), elem!1) | b(s(s(s(s(s(z))))), elem!1) | (~b(s(z), s(s(s(z))))) | r(elem!1, s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5781,plain,
% 1.74/1.99 (~r(s(z), s(s(s(s(s(z))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5780, 5734, 4541, 2090, 322, 59, 5556, 1085, 492])).
% 1.74/1.99 tff(5782,plain,
% 1.74/1.99 (b(s(z), s(s(s(s(s(z))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[372, 5781])).
% 1.74/1.99 tff(5783,plain,
% 1.74/1.99 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5736])).
% 1.74/1.99 tff(5784,plain,
% 1.74/1.99 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/1.99 inference(symmetry,[status(thm)],[5783])).
% 1.74/1.99 tff(5785,plain,
% 1.74/1.99 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[299, 5784])).
% 1.74/1.99 tff(5786,plain,
% 1.74/1.99 (s(elem!1) = s(s(s(s(s(s(z))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5529])).
% 1.74/1.99 tff(5787,plain,
% 1.74/1.99 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5786])).
% 1.74/1.99 tff(5788,plain,
% 1.74/1.99 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 1.74/1.99 inference(symmetry,[status(thm)],[5787])).
% 1.74/1.99 tff(5789,plain,
% 1.74/1.99 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5788])).
% 1.74/1.99 tff(5790,plain,
% 1.74/1.99 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.74/1.99 inference(symmetry,[status(thm)],[5789])).
% 1.74/1.99 tff(5791,plain,
% 1.74/1.99 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5787])).
% 1.74/1.99 tff(5792,plain,
% 1.74/1.99 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5791, 2674])).
% 1.74/1.99 tff(5793,plain,
% 1.74/1.99 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.74/1.99 inference(symmetry,[status(thm)],[5792])).
% 1.74/1.99 tff(5794,plain,
% 1.74/1.99 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5793])).
% 1.74/1.99 tff(5795,plain,
% 1.74/1.99 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2690, 5794])).
% 1.74/1.99 tff(5796,plain,
% 1.74/1.99 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5529])).
% 1.74/1.99 tff(5797,plain,
% 1.74/1.99 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[909, 5796])).
% 1.74/1.99 tff(5798,assumption,(b(s(s(elem!1)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.74/1.99 tff(5799,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5800,plain,
% 1.74/1.99 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5801,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(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(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5800])).
% 1.74/1.99 tff(5802,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(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(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5801, 5799])).
% 1.74/1.99 tff(5803,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(5804,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5803, 5802])).
% 1.74/1.99 tff(5805,plain,
% 1.74/1.99 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5804, 453, 1780, 2497, 5798])).
% 1.74/1.99 tff(5806,assumption,(~(s(s(elem!1)) = s(s(s(s(z)))))), introduced(assumption)).
% 1.74/1.99 tff(5807,plain,
% 1.74/1.99 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5232, 69, 5806, 5805])).
% 1.74/1.99 tff(5808,plain,
% 1.74/1.99 (~b(s(z), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3253, 453, 443, 1780, 2497])).
% 1.74/1.99 tff(5809,plain,
% 1.74/1.99 (r(s(z), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1677, 69, 50, 5808])).
% 1.74/1.99 tff(5810,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5811,plain,
% 1.74/1.99 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5812,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5811])).
% 1.74/1.99 tff(5813,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5812, 5810])).
% 1.74/1.99 tff(5814,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(5815,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5814, 5813])).
% 1.74/1.99 tff(5816,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5815, 268, 1033, 5809, 5807])).
% 1.74/1.99 tff(5817,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5818,plain,
% 1.74/1.99 (~r(s(s(elem!1)), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5817, 5797, 2497, 5795, 443, 1780])).
% 1.74/1.99 tff(5819,plain,
% 1.74/1.99 (b(s(s(elem!1)), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1047, 5818])).
% 1.74/1.99 tff(5820,plain,
% 1.74/1.99 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5819, 5790])).
% 1.74/1.99 tff(5821,plain,
% 1.74/1.99 (s(s(s(s(s(z))))) = elem!1),
% 1.74/1.99 inference(symmetry,[status(thm)],[5529])).
% 1.74/1.99 tff(5822,plain,
% 1.74/1.99 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5821])).
% 1.74/1.99 tff(5823,plain,
% 1.74/1.99 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.74/1.99 inference(symmetry,[status(thm)],[5822])).
% 1.74/1.99 tff(5824,plain,
% 1.74/1.99 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5788, 5529])).
% 1.74/1.99 tff(5825,plain,
% 1.74/1.99 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.74/1.99 inference(symmetry,[status(thm)],[5824])).
% 1.74/1.99 tff(5826,plain,
% 1.74/1.99 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.74/1.99 inference(transitivity,[status(thm)],[5796, 5825])).
% 1.74/1.99 tff(5827,plain,
% 1.74/1.99 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[909, 5826])).
% 1.74/1.99 tff(5828,plain,
% 1.74/1.99 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5827, 5823])).
% 1.74/1.99 tff(5829,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(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5830,plain,
% 1.74/1.99 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5831,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5830])).
% 1.74/2.00 tff(5832,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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5831, 5829])).
% 1.74/2.00 tff(5833,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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5834,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5833, 5832])).
% 1.74/2.00 tff(5835,plain,
% 1.74/2.00 ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5834, 453, 443, 1780])).
% 1.74/2.00 tff(5836,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5835, 5828, 5820])).
% 1.74/2.00 tff(5837,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5838,plain,
% 1.74/2.00 (~b(s(s(elem!1)), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5837, 5785, 5549, 5782, 5763])).
% 1.74/2.00 tff(5839,plain,
% 1.74/2.00 (r(s(s(elem!1)), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2240, 5838, 5748])).
% 1.74/2.00 tff(5840,plain,
% 1.74/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5841,plain,
% 1.74/2.00 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5842,plain,
% 1.74/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5841])).
% 1.74/2.00 tff(5843,plain,
% 1.74/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5842, 5840])).
% 1.74/2.00 tff(5844,plain,
% 1.74/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5845,plain,
% 1.74/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5844, 5843])).
% 1.74/2.00 tff(5846,plain,
% 1.74/2.00 (~r(s(s(z)), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5845, 268, 5750, 5839, 5762])).
% 1.74/2.00 tff(5847,plain,
% 1.74/2.00 (s(z) = s(elem!1)),
% 1.74/2.00 inference(symmetry,[status(thm)],[175])).
% 1.74/2.00 tff(5848,plain,
% 1.74/2.00 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5847])).
% 1.74/2.00 tff(5849,plain,
% 1.74/2.00 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5848])).
% 1.74/2.00 tff(5850,plain,
% 1.74/2.00 (s(s(s(s(s(z))))) = z),
% 1.74/2.00 inference(transitivity,[status(thm)],[5168, 86, 5849, 32])).
% 1.74/2.00 tff(5851,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2549, 5850])).
% 1.74/2.00 tff(5852,plain,((~(s(elem!1) = s(z))) | (~(s(s(s(s(s(z))))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5853,plain,
% 1.74/2.00 (~(s(elem!1) = s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5852, 5736])).
% 1.74/2.00 tff(5854,plain,
% 1.74/2.00 (~(s(s(z)) = s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1188, 5853])).
% 1.74/2.00 tff(5855,plain,
% 1.74/2.00 (b(s(s(z)), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4239, 69, 5854, 5846])).
% 1.74/2.00 tff(5856,plain,
% 1.74/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5857,plain,
% 1.74/2.00 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5858,plain,
% 1.74/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5857])).
% 1.74/2.00 tff(5859,plain,
% 1.74/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5858, 5856])).
% 1.74/2.00 tff(5860,plain,
% 1.74/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5861,plain,
% 1.74/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5860, 5859])).
% 1.74/2.00 tff(5862,plain,
% 1.74/2.00 (~r(s(s(s(z))), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5861, 268, 5762, 5515])).
% 1.74/2.00 tff(5863,plain,
% 1.74/2.00 (b(s(s(s(z))), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2534, 69, 160, 5862])).
% 1.74/2.00 tff(5864,plain,
% 1.74/2.00 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5213, 5839, 5515])).
% 1.74/2.00 tff(5865,plain,
% 1.74/2.00 (b(s(s(s(z))), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5203, 5864, 548])).
% 1.74/2.00 tff(5866,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5867,plain,
% 1.74/2.00 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5868,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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5867])).
% 1.74/2.00 tff(5869,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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5868, 5866])).
% 1.74/2.00 tff(5870,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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5871,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5870, 5869])).
% 1.74/2.00 tff(5872,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5871, 453, 5865, 5863, 5855, 5757])).
% 1.74/2.00 tff(5873,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | r(s(z), elem!1) | (~b(s(z), s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))) | (s(s(s(z))) = elem!1) | r(elem!1, s(s(s(s(z))))) | (s(z) = elem!1) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5874,plain,
% 1.74/2.00 (~b(s(s(s(s(z)))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5873, 5548, 5517, 2077, 4541, 2090, 1132, 59, 5527, 492, 5528])).
% 1.74/2.00 tff(5875,plain,
% 1.74/2.00 (r(s(s(s(s(z)))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[254, 5874, 3])).
% 1.74/2.00 tff(5876,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5290, 268, 5515, 5875, 300])).
% 1.74/2.00 tff(5877,plain,((s(s(s(z))) = elem!1) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(z))) | r(s(z), elem!1) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5878,plain,
% 1.74/2.00 (s(s(s(z))) = elem!1),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5877, 5504, 300, 5446, 4541, 5503, 1099, 4495])).
% 1.74/2.00 tff(5879,plain,
% 1.74/2.00 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5878])).
% 1.74/2.00 tff(5880,plain,
% 1.74/2.00 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4123, 249, 5878])).
% 1.74/2.00 tff(5881,plain,
% 1.74/2.00 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[518, 5880])).
% 1.74/2.00 tff(5882,plain,
% 1.74/2.00 (~r(s(s(s(z))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4119, 11, 1099])).
% 1.74/2.00 tff(5883,plain,
% 1.74/2.00 (b(s(s(s(z))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[134, 5882])).
% 1.74/2.00 tff(5884,plain,
% 1.74/2.00 (~r(s(s(s(s(s(z))))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[276, 228, 256])).
% 1.74/2.00 tff(5885,plain,
% 1.74/2.00 (b(s(s(s(s(s(z))))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[297, 5884])).
% 1.74/2.00 tff(5886,plain,
% 1.74/2.00 (b(elem!1, s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4492, 4933, 4545])).
% 1.74/2.00 tff(5887,plain,
% 1.74/2.00 (~b(s(s(s(z))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5465, 5886, 5883, 499])).
% 1.74/2.00 tff(5888,plain,
% 1.74/2.00 (r(s(s(s(z))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[74, 5887, 4544])).
% 1.74/2.00 tff(5889,plain,
% 1.74/2.00 (~r(s(z), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1611, 1099, 11, 228])).
% 1.74/2.00 tff(5890,plain,
% 1.74/2.00 (b(s(z), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[506, 5889, 492])).
% 1.74/2.00 tff(5891,plain,
% 1.74/2.00 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4897, 453, 5890, 1714, 120])).
% 1.74/2.00 tff(5892,plain,
% 1.74/2.00 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4904, 268, 1712, 1545])).
% 1.74/2.00 tff(5893,assumption,(~(s(s(s(z))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.74/2.00 tff(5894,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4908, 69, 5893, 5892, 5891])).
% 1.74/2.00 tff(5895,plain,(b(s(s(s(s(z)))), s(z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (s(z) = elem!1) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | b(s(z), s(s(s(z)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5896,plain,
% 1.74/2.00 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5895, 5888, 1057, 5883, 4495, 221, 11, 10, 4888])).
% 1.74/2.00 tff(5897,plain,
% 1.74/2.00 (s(s(z)) = s(s(elem!1))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4916, 5896])).
% 1.74/2.00 tff(5898,plain,
% 1.74/2.00 (s(elem!1) = s(z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1188, 5897])).
% 1.74/2.00 tff(5899,plain,
% 1.74/2.00 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5898])).
% 1.74/2.00 tff(5900,plain,
% 1.74/2.00 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5899])).
% 1.74/2.00 tff(5901,plain,
% 1.74/2.00 (z = elem!1),
% 1.74/2.00 inference(transitivity,[status(thm)],[4921, 5900, 85])).
% 1.74/2.00 tff(5902,plain,
% 1.74/2.00 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5901])).
% 1.74/2.00 tff(5903,plain,
% 1.74/2.00 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = z)),
% 1.74/2.00 inference(symmetry,[status(thm)],[5902])).
% 1.74/2.00 tff(5904,plain,
% 1.74/2.00 (s(s(s(s(z)))) = elem!1),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5444, 5887, 5883, 221])).
% 1.74/2.00 tff(5905,plain,
% 1.74/2.00 (s(s(s(s(z)))) = z),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5904, 5903])).
% 1.74/2.00 tff(5906,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[287, 5905])).
% 1.74/2.00 tff(5907,plain,(b(elem!1, s(z)) | b(s(s(s(s(z)))), s(z)) | b(s(z), s(s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5908,plain,
% 1.74/2.00 (b(elem!1, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5907, 221, 1057, 11, 499, 1123])).
% 1.74/2.00 tff(5909,plain,
% 1.74/2.00 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5331, 5908, 5885, 499])).
% 1.74/2.00 tff(5910,plain,
% 1.74/2.00 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3216, 268, 11, 256])).
% 1.74/2.00 tff(5911,plain,
% 1.74/2.00 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2463, 69, 5910])).
% 1.74/2.00 tff(5912,plain,
% 1.74/2.00 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5911, 5338])).
% 1.74/2.00 tff(5913,plain,
% 1.74/2.00 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[309, 256, 300])).
% 1.74/2.00 tff(5914,plain,
% 1.74/2.00 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[328, 5913])).
% 1.74/2.00 tff(5915,plain,
% 1.74/2.00 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 1.74/2.00 inference(commutativity,[status(thm)],[])).
% 1.74/2.00 tff(5916,plain,
% 1.74/2.00 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5529, 5787])).
% 1.74/2.00 tff(5917,plain,
% 1.74/2.00 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5916, 5915])).
% 1.74/2.00 tff(5918,plain,
% 1.74/2.00 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(elem!1)))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5917])).
% 1.74/2.00 tff(5919,plain,
% 1.74/2.00 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = elem!1)),
% 1.74/2.00 inference(transitivity,[status(thm)],[5918, 2170])).
% 1.74/2.00 tff(5920,plain,
% 1.74/2.00 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5919])).
% 1.74/2.00 tff(5921,plain,
% 1.74/2.00 (~(s(s(elem!1)) = elem!1)),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2729, 5920])).
% 1.74/2.00 tff(5922,plain,
% 1.74/2.00 (~b(s(s(elem!1)), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5837, 5529, 1780, 443, 2497])).
% 1.74/2.00 tff(5923,plain,
% 1.74/2.00 (r(s(s(elem!1)), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2240, 5922, 5921])).
% 1.74/2.00 tff(5924,plain,
% 1.74/2.00 (~r(s(s(elem!1)), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1970, 5923, 238])).
% 1.74/2.00 tff(5925,plain,
% 1.74/2.00 (b(s(s(elem!1)), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1047, 5924])).
% 1.74/2.00 tff(5926,plain,
% 1.74/2.00 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5925, 5790])).
% 1.74/2.00 tff(5927,plain,
% 1.74/2.00 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(z))))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5787])).
% 1.74/2.00 tff(5928,plain,
% 1.74/2.00 (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(elem!1)))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5927])).
% 1.74/2.00 tff(5929,plain,
% 1.74/2.00 (b(s(s(s(s(s(s(s(s(z)))))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5928])).
% 1.74/2.00 tff(5930,plain,
% 1.74/2.00 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5929])).
% 1.74/2.00 tff(5931,plain,
% 1.74/2.00 (s(s(s(s(s(z))))) = elem!1),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5529, 56])).
% 1.74/2.00 tff(5932,assumption,(~r(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 1.74/2.00 tff(5933,plain,
% 1.74/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5934,plain,
% 1.74/2.00 (((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5935,plain,
% 1.74/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5934])).
% 1.74/2.00 tff(5936,plain,
% 1.74/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5935, 5933])).
% 1.74/2.00 tff(5937,plain,
% 1.74/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5938,plain,
% 1.74/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5937, 5936])).
% 1.74/2.00 tff(5939,plain,
% 1.74/2.00 (~r(elem!1, s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5938, 268, 238, 11, 1132])).
% 1.74/2.00 tff(5940,plain,
% 1.74/2.00 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(z))))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5171])).
% 1.74/2.00 tff(5941,plain,
% 1.74/2.00 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5940])).
% 1.74/2.00 tff(5942,plain,
% 1.74/2.00 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5941])).
% 1.74/2.00 tff(5943,plain,
% 1.74/2.00 (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[563, 5942])).
% 1.74/2.00 tff(5944,plain,
% 1.74/2.00 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5940])).
% 1.74/2.00 tff(5945,plain,
% 1.74/2.00 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5944])).
% 1.74/2.00 tff(5946,plain,
% 1.74/2.00 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5932, 5945])).
% 1.74/2.00 tff(5947,plain,
% 1.74/2.00 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(s(s(z)))))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2709])).
% 1.74/2.00 tff(5948,plain,
% 1.74/2.00 (s(s(s(z))) = s(s(elem!1))),
% 1.74/2.00 inference(transitivity,[status(thm)],[38, 5947, 2335, 5170])).
% 1.74/2.00 tff(5949,plain,
% 1.74/2.00 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = elem!1)),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5168])).
% 1.74/2.00 tff(5950,plain,
% 1.74/2.00 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(z) = elem!1))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5949])).
% 1.74/2.00 tff(5951,plain,
% 1.74/2.00 (~(s(z) = elem!1)),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[289, 5950])).
% 1.74/2.00 tff(5952,plain,
% 1.74/2.00 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[547, 5951])).
% 1.74/2.00 tff(5953,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5952, 5948])).
% 1.74/2.00 tff(5954,plain,((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(s(z)))))))))) | (~(s(s(s(s(s(z))))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5955,plain,
% 1.74/2.00 (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(s(z)))))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5954, 5168])).
% 1.74/2.00 tff(5956,plain,
% 1.74/2.00 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2726, 5955])).
% 1.74/2.00 tff(5957,plain,
% 1.74/2.00 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2862, 5956, 5946])).
% 1.74/2.00 tff(5958,plain,
% 1.74/2.00 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5168])).
% 1.74/2.00 tff(5959,plain,
% 1.74/2.00 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.74/2.00 inference(transitivity,[status(thm)],[5958, 3483])).
% 1.74/2.00 tff(5960,plain,
% 1.74/2.00 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5959])).
% 1.74/2.00 tff(5961,plain,
% 1.74/2.01 (~(s(s(s(s(z)))) = elem!1)),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[319, 5960])).
% 1.74/2.01 tff(5962,plain,
% 1.74/2.01 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[252, 69, 239])).
% 1.74/2.01 tff(5963,plain,
% 1.74/2.01 (b(s(s(s(s(z)))), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5962, 5961])).
% 1.74/2.01 tff(5964,plain,
% 1.74/2.01 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5168])).
% 1.74/2.01 tff(5965,plain,
% 1.74/2.01 (elem!1 = s(s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5538, 5168])).
% 1.74/2.01 tff(5966,plain,
% 1.74/2.01 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5534, 5965, 1085])).
% 1.74/2.01 tff(5967,plain,
% 1.74/2.01 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[328, 5966])).
% 1.74/2.01 tff(5968,plain,
% 1.74/2.01 (b(elem!1, s(s(s(s(z)))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[5967, 5964])).
% 1.74/2.01 tff(5969,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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(5970,plain,
% 1.74/2.01 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(5971,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(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5970])).
% 1.74/2.01 tff(5972,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(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.74/2.01 inference(transitivity,[status(thm)],[5971, 5969])).
% 1.74/2.01 tff(5973,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(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(5974,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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[5973, 5972])).
% 1.74/2.01 tff(5975,plain,
% 1.74/2.01 (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5974, 453, 5968, 5963, 5957])).
% 1.74/2.01 tff(5976,plain,
% 1.74/2.01 (s(s(s(s(s(s(s(s(z)))))))) = elem!1),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5649, 5975, 5943])).
% 1.74/2.01 tff(5977,plain,
% 1.74/2.01 (elem!1 = s(s(s(s(s(s(s(s(z))))))))),
% 1.74/2.01 inference(symmetry,[status(thm)],[5976])).
% 1.74/2.01 tff(5978,plain,
% 1.74/2.01 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(s(z))))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[5168, 5977])).
% 1.74/2.01 tff(5979,plain,
% 1.74/2.01 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(s(z)))))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5978])).
% 1.74/2.01 tff(5980,plain,
% 1.74/2.01 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.74/2.01 inference(transitivity,[status(thm)],[284, 5979, 2335, 5170])).
% 1.74/2.01 tff(5981,plain,
% 1.74/2.01 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5980])).
% 1.74/2.01 tff(5982,plain,
% 1.74/2.01 (s(s(s(z))) = s(elem!1)),
% 1.74/2.01 inference(transitivity,[status(thm)],[38, 5981, 194])).
% 1.74/2.01 tff(5983,plain,
% 1.74/2.01 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5982])).
% 1.74/2.01 tff(5984,plain,
% 1.74/2.01 (s(s(z)) = elem!1),
% 1.74/2.01 inference(transitivity,[status(thm)],[98, 5983, 85])).
% 1.74/2.01 tff(5985,plain,
% 1.74/2.01 ((s(s(s(s(s(z))))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5168])).
% 1.74/2.01 tff(5986,plain,
% 1.74/2.01 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.74/2.01 inference(transitivity,[status(thm)],[5985, 144])).
% 1.74/2.01 tff(5987,plain,
% 1.74/2.01 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5986])).
% 1.74/2.01 tff(5988,plain,
% 1.74/2.01 (~(s(s(z)) = elem!1)),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[52, 5987])).
% 1.74/2.01 tff(5989,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5988, 5984])).
% 1.74/2.01 tff(5990,plain,((~(s(s(s(s(s(z))))) = elem!1)) | r(s(s(s(s(z)))), elem!1) | r(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), elem!1) | r(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(5991,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5990, 5939, 1139, 5932, 563, 5168])).
% 1.74/2.01 tff(5992,plain,((~r(elem!1, s(z))) | r(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), elem!1) | (~(s(s(s(s(s(z))))) = elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(5993,plain,
% 1.74/2.01 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5992, 5931, 1132, 238, 563, 11])).
% 1.74/2.01 tff(5994,assumption,(r(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 1.74/2.01 tff(5995,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), 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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~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)))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(5996,plain,
% 1.74/2.01 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(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(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(5997,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5996])).
% 1.74/2.01 tff(5998,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[5997, 5995])).
% 1.74/2.01 tff(5999,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(6000,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[5999, 5998])).
% 1.74/2.01 tff(6001,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6000, 268, 834, 376, 5994])).
% 1.74/2.01 tff(6002,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(6003,plain,
% 1.74/2.01 (~r(s(s(s(elem!1))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6002, 5993, 376])).
% 1.74/2.01 tff(6004,plain,
% 1.74/2.01 (b(s(s(s(elem!1))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[856, 6003])).
% 1.74/2.01 tff(6005,plain,
% 1.74/2.01 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6004, 5930])).
% 1.74/2.01 tff(6006,plain,
% 1.74/2.01 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5821])).
% 1.74/2.01 tff(6007,plain,
% 1.74/2.01 (b(s(s(s(s(s(s(s(s(z)))))))), elem!1) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 1.74/2.01 inference(symmetry,[status(thm)],[6006])).
% 1.74/2.01 tff(6008,plain,
% 1.74/2.01 ((s(s(s(s(s(s(s(s(z)))))))) = elem!1) <=> (elem!1 = s(s(s(s(s(s(s(s(z)))))))))),
% 1.74/2.01 inference(commutativity,[status(thm)],[])).
% 1.74/2.01 tff(6009,plain,
% 1.74/2.01 ((elem!1 = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(s(z)))))))) = elem!1)),
% 1.74/2.01 inference(symmetry,[status(thm)],[6008])).
% 1.74/2.01 tff(6010,plain,
% 1.74/2.01 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(s(s(s(z)))))))) = elem!1)),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5821])).
% 1.74/2.01 tff(6011,plain,
% 1.74/2.01 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(s(s(s(z)))))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[6010, 6008])).
% 1.74/2.01 tff(6012,plain,
% 1.74/2.01 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(s(s(s(z)))))))) = elem!1)),
% 1.74/2.01 inference(transitivity,[status(thm)],[6011, 6009])).
% 1.74/2.01 tff(6013,plain,
% 1.74/2.01 ((~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(s(s(s(z)))))))) = elem!1))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6012])).
% 1.74/2.01 tff(6014,plain,
% 1.74/2.01 (~(s(s(s(s(s(s(s(s(z)))))))) = elem!1)),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[2688, 6013])).
% 1.74/2.01 tff(6015,plain,
% 1.74/2.01 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5927])).
% 1.74/2.01 tff(6016,plain,
% 1.74/2.01 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6015])).
% 1.74/2.01 tff(6017,plain,
% 1.74/2.01 (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[563, 6016])).
% 1.74/2.01 tff(6018,plain,
% 1.74/2.01 (b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5649, 6017, 6014])).
% 1.74/2.01 tff(6019,plain,
% 1.74/2.01 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6018, 6007])).
% 1.74/2.01 tff(6020,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(6021,plain,
% 1.74/2.01 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))) <=> ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(6022,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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6021])).
% 1.74/2.01 tff(6023,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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[6022, 6020])).
% 1.74/2.01 tff(6024,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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(6025,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6024, 6023])).
% 1.74/2.01 tff(6026,plain,
% 1.74/2.01 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6025, 453, 443, 1780])).
% 1.74/2.01 tff(6027,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6026, 6019, 6005])).
% 1.74/2.01 tff(6028,plain,((~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | r(s(s(s(elem!1))), elem!1) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(6029,plain,
% 1.74/2.01 (r(s(s(s(elem!1))), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6028, 5529, 1780, 5809, 1132, 238, 443, 11])).
% 1.74/2.01 tff(6030,plain,
% 1.74/2.01 (~r(s(s(s(elem!1))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[842, 6029, 238])).
% 1.74/2.01 tff(6031,plain,
% 1.74/2.01 (b(s(s(s(elem!1))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[856, 6030])).
% 1.74/2.01 tff(6032,plain,
% 1.74/2.01 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6031, 5930])).
% 1.74/2.01 tff(6033,plain,
% 1.74/2.01 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5787, 5927])).
% 1.74/2.01 tff(6034,plain,
% 1.74/2.01 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[5918])).
% 1.74/2.01 tff(6035,plain,
% 1.74/2.01 (~(elem!1 = s(s(elem!1)))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[2729, 6034])).
% 1.74/2.01 tff(6036,plain,
% 1.74/2.01 (~(s(elem!1) = elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3351, 6035])).
% 1.74/2.01 tff(6037,plain,
% 1.74/2.01 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[607, 6036])).
% 1.74/2.01 tff(6038,plain,
% 1.74/2.01 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[877, 5923, 6029])).
% 1.74/2.01 tff(6039,plain,
% 1.74/2.01 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[675, 6038, 6037])).
% 1.74/2.01 tff(6040,plain,
% 1.74/2.01 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6039, 6033])).
% 1.74/2.01 tff(6041,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(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(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(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(6042,plain,
% 1.74/2.01 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(6043,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(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(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(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6042])).
% 1.74/2.01 tff(6044,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(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(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(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[6043, 6041])).
% 1.74/2.01 tff(6045,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(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(6046,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6045, 6044])).
% 1.74/2.01 tff(6047,plain,
% 1.74/2.01 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6046, 453, 443, 6040, 6032])).
% 1.74/2.01 tff(6048,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6047, 5926])).
% 1.74/2.01 tff(6049,plain,((~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(6050,plain,
% 1.74/2.01 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6049, 443, 238, 5914, 5912, 1132, 11])).
% 1.74/2.01 tff(6051,plain,
% 1.74/2.01 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5538, 6050])).
% 1.74/2.02 tff(6052,plain,
% 1.74/2.02 (r(s(s(s(s(s(z))))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[643, 6051, 638])).
% 1.74/2.02 tff(6053,plain,
% 1.74/2.02 (~b(s(z), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3253, 453, 443, 5914, 5912])).
% 1.74/2.02 tff(6054,plain,
% 1.74/2.02 (r(s(z), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1677, 69, 50, 6053])).
% 1.74/2.02 tff(6055,plain,
% 1.74/2.02 (~r(s(z), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[384, 6054, 300])).
% 1.74/2.02 tff(6056,plain,
% 1.74/2.02 (b(s(z), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[227, 6055])).
% 1.74/2.02 tff(6057,plain,
% 1.74/2.02 (~b(s(z), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5777, 6052, 6056, 1597, 5913, 59, 256])).
% 1.74/2.02 tff(6058,plain,
% 1.74/2.02 (r(s(z), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[506, 6057, 492])).
% 1.74/2.02 tff(6059,plain,
% 1.74/2.02 (~r(s(s(z)), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[777, 6058, 6052])).
% 1.74/2.02 tff(6060,plain,
% 1.74/2.02 (~r(s(s(s(z))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1566, 6052, 256])).
% 1.74/2.02 tff(6061,plain,
% 1.74/2.02 (b(s(s(s(z))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[74, 6060, 59])).
% 1.74/2.02 tff(6062,plain,
% 1.74/2.02 (~(s(s(s(s(z)))) = elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4469, 6052, 5913])).
% 1.74/2.02 tff(6063,plain,
% 1.74/2.02 (b(s(s(s(s(z)))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[254, 6062, 1139])).
% 1.74/2.02 tff(6064,plain,
% 1.74/2.02 (~(elem!1 = s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[8, 6062])).
% 1.74/2.02 tff(6065,plain,
% 1.74/2.02 (b(elem!1, s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1087, 6064, 1597])).
% 1.74/2.02 tff(6066,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(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6067,plain,
% 1.74/2.02 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6068,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[6067])).
% 1.74/2.02 tff(6069,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.74/2.02 inference(transitivity,[status(thm)],[6068, 6066])).
% 1.74/2.02 tff(6070,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(6071,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[6070, 6069])).
% 1.74/2.02 tff(6072,plain,
% 1.74/2.02 (~b(s(s(s(z))), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6071, 453, 1291, 922, 530])).
% 1.74/2.02 tff(6073,plain,
% 1.74/2.02 (r(s(s(s(z))), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2534, 69, 160, 6072])).
% 1.74/2.02 tff(6074,plain,
% 1.74/2.02 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1735, 453, 922, 530, 299])).
% 1.74/2.02 tff(6075,plain,
% 1.74/2.02 (r(s(s(s(s(z)))), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[795, 69, 153, 6074])).
% 1.74/2.02 tff(6076,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2782, 268, 11, 6075, 6073])).
% 1.74/2.02 tff(6077,plain,((~b(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(6078,plain,
% 1.74/2.02 (~b(s(s(z)), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6077, 6065, 11, 6063, 6061])).
% 1.74/2.02 tff(6079,plain,
% 1.74/2.02 (s(s(z)) = elem!1),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[782, 6078, 6059])).
% 1.74/2.02 tff(6080,plain,
% 1.74/2.02 (elem!1 = s(s(z))),
% 1.74/2.02 inference(symmetry,[status(thm)],[6079])).
% 1.74/2.02 tff(6081,assumption,(r(s(s(s(s(s(s(s(s(z)))))))), elem!1)), introduced(assumption)).
% 1.74/2.02 tff(6082,plain,
% 1.74/2.02 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5656, 268, 722, 6081])).
% 1.74/2.02 tff(6083,plain,
% 1.74/2.02 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2833, 69, 2688, 6082])).
% 1.74/2.02 tff(6084,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6085,plain,
% 1.74/2.02 (((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6086,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[6085])).
% 1.74/2.02 tff(6087,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.74/2.02 inference(transitivity,[status(thm)],[6086, 6084])).
% 1.74/2.02 tff(6088,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(6089,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[6088, 6087])).
% 1.74/2.02 tff(6090,plain,
% 1.74/2.02 (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6089, 268, 701, 6081])).
% 1.74/2.02 tff(6091,plain,
% 1.74/2.02 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2906, 69, 6090, 2886])).
% 1.74/2.02 tff(6092,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6093,plain,
% 1.74/2.02 (((~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6094,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[6093])).
% 1.74/2.02 tff(6095,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.74/2.02 inference(transitivity,[status(thm)],[6094, 6092])).
% 1.74/2.02 tff(6096,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(6097,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[6096, 6095])).
% 1.74/2.02 tff(6098,plain,
% 1.74/2.02 (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6097, 268, 701, 6081])).
% 1.74/2.02 tff(6099,plain,
% 1.74/2.02 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(s(s(z))))))))) | b(s(z), s(s(s(s(s(s(s(s(z))))))))) | r(s(z), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(s(s(z))))))))) | b(s(z), s(s(s(s(s(s(s(s(z))))))))) | r(s(z), s(s(s(s(s(s(s(s(z))))))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6100,plain,
% 1.74/2.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(s(s(z))))))))) | b(s(z), s(s(s(s(s(s(s(s(z))))))))) | r(s(z), s(s(s(s(s(s(s(s(z))))))))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(6101,plain,
% 1.74/2.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(s(s(z))))))))) | b(s(z), s(s(s(s(s(s(s(s(z))))))))) | r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[6100, 6099])).
% 1.74/2.02 tff(6102,plain,
% 1.74/2.02 (b(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6101, 69, 2884, 6098])).
% 1.74/2.02 tff(6103,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(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6104,plain,
% 1.74/2.02 (((~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6105,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(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[6104])).
% 1.74/2.02 tff(6106,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(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[6105, 6103])).
% 1.74/2.02 tff(6107,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(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(6108,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[6107, 6106])).
% 1.74/2.02 tff(6109,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6108, 453, 732, 6102, 6091, 6083])).
% 1.74/2.02 tff(6110,plain,((~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(6111,plain,
% 1.74/2.02 (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6110, 6052, 6058])).
% 1.74/2.02 tff(6112,plain,
% 1.74/2.02 (s(s(s(z))) = s(elem!1)),
% 1.74/2.02 inference(monotonicity,[status(thm)],[6079])).
% 1.74/2.02 tff(6113,plain,
% 1.74/2.02 (s(elem!1) = s(s(s(z)))),
% 1.74/2.02 inference(symmetry,[status(thm)],[6112])).
% 1.74/2.02 tff(6114,plain,
% 1.74/2.02 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.74/2.02 inference(monotonicity,[status(thm)],[6113])).
% 1.74/2.02 tff(6115,plain,
% 1.74/2.02 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.74/2.02 inference(symmetry,[status(thm)],[6114])).
% 1.74/2.02 tff(6116,plain,
% 1.74/2.02 (b(s(elem!1), elem!1)),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[6061, 6115])).
% 1.74/2.02 tff(6117,plain,
% 1.74/2.02 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[6112])).
% 1.74/2.02 tff(6118,plain,
% 1.74/2.02 (b(s(z), s(elem!1))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[6056, 6117])).
% 1.74/2.02 tff(6119,plain,
% 1.74/2.02 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[6112])).
% 1.74/2.02 tff(6120,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6121,plain,
% 1.74/2.02 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6122,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[6121])).
% 1.74/2.02 tff(6123,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[6122, 6120])).
% 1.74/2.02 tff(6124,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(6125,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[6124, 6123])).
% 1.74/2.02 tff(6126,plain,
% 1.74/2.02 (~r(s(s(s(z))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6125, 268, 6058, 300, 6054])).
% 1.74/2.02 tff(6127,plain,
% 1.74/2.02 (b(s(s(s(z))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[134, 6126])).
% 1.74/2.02 tff(6128,plain,
% 1.74/2.02 (b(s(elem!1), s(z))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[6127, 6119])).
% 1.74/2.02 tff(6129,plain,
% 1.74/2.02 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[6112])).
% 1.74/2.02 tff(6130,plain,
% 1.74/2.02 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.74/2.02 inference(symmetry,[status(thm)],[6129])).
% 1.74/2.02 tff(6131,plain,
% 1.74/2.02 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.74/2.02 inference(monotonicity,[status(thm)],[6130])).
% 1.74/2.02 tff(6132,plain,
% 1.74/2.02 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.74/2.02 inference(symmetry,[status(thm)],[6131])).
% 1.74/2.02 tff(6133,plain,
% 1.74/2.02 (b(s(s(elem!1)), elem!1)),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[6063, 6132])).
% 1.74/2.02 tff(6134,plain,
% 1.74/2.02 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[6113])).
% 1.74/2.02 tff(6135,plain,
% 1.74/2.02 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 1.74/2.02 inference(symmetry,[status(thm)],[6134])).
% 1.74/2.02 tff(6136,plain,
% 1.74/2.02 (~r(s(s(s(s(s(z))))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[730, 6058, 6052])).
% 1.74/2.02 tff(6137,plain,
% 1.74/2.02 (b(s(s(s(s(s(z))))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[297, 6136])).
% 1.74/2.02 tff(6138,plain,
% 1.74/2.02 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3141, 453, 443, 6137, 6127])).
% 1.74/2.02 tff(6139,plain,
% 1.74/2.02 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2570, 6138])).
% 1.74/2.02 tff(6140,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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6141,plain,
% 1.74/2.02 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(6142,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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[6141])).
% 1.74/2.02 tff(6143,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[6142, 6140])).
% 1.74/2.02 tff(6144,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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(6145,plain,
% 1.86/2.03 ((~![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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[6144, 6143])).
% 1.86/2.03 tff(6146,plain,
% 1.86/2.03 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6145, 453, 5914, 6065, 6063])).
% 1.86/2.03 tff(6147,plain,
% 1.86/2.03 (r(elem!1, s(s(s(s(s(z))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[466, 6146, 6050])).
% 1.86/2.03 tff(6148,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(6149,plain,
% 1.86/2.03 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(6150,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[6149])).
% 1.86/2.03 tff(6151,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[6150, 6148])).
% 1.86/2.03 tff(6152,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z))))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(6153,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[6152, 6151])).
% 1.86/2.03 tff(6154,plain,
% 1.86/2.03 (~r(elem!1, s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6153, 268, 6147, 6139])).
% 1.86/2.03 tff(6155,plain,
% 1.86/2.03 (b(elem!1, s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[4492, 6154, 5525])).
% 1.86/2.03 tff(6156,plain,
% 1.86/2.03 (b(elem!1, s(elem!1))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[6155, 6135])).
% 1.86/2.03 tff(6157,plain,
% 1.86/2.03 ((s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.03 inference(commutativity,[status(thm)],[])).
% 1.86/2.03 tff(6158,plain,
% 1.86/2.03 ((s(elem!1) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1))),
% 1.86/2.03 inference(symmetry,[status(thm)],[6157])).
% 1.86/2.03 tff(6159,plain,
% 1.86/2.03 ((~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))) <=> (~(s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[6158])).
% 1.86/2.03 tff(6160,plain,
% 1.86/2.03 (~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[3814, 6079])).
% 1.86/2.03 tff(6161,plain,
% 1.86/2.03 (~(s(s(s(s(s(s(s(s(z)))))))) = s(elem!1))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[6160, 6159])).
% 1.86/2.03 tff(6162,plain,
% 1.86/2.03 (~(s(s(elem!1)) = s(s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5612, 6079])).
% 1.86/2.03 tff(6163,plain,
% 1.86/2.03 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[6130])).
% 1.86/2.03 tff(6164,plain,
% 1.86/2.03 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.86/2.03 inference(symmetry,[status(thm)],[6163])).
% 1.86/2.03 tff(6165,plain,
% 1.86/2.03 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[6112])).
% 1.86/2.03 tff(6166,plain,
% 1.86/2.03 (r(s(s(s(s(z)))), s(elem!1))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[11, 6165])).
% 1.86/2.03 tff(6167,plain,
% 1.86/2.03 (r(s(s(elem!1)), s(elem!1))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[6166, 6164])).
% 1.86/2.03 tff(6168,plain,
% 1.86/2.03 (((~![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(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(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(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(6169,plain,
% 1.86/2.03 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(6170,plain,
% 1.86/2.03 (((~![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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(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(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[6169])).
% 1.86/2.03 tff(6171,plain,
% 1.86/2.03 (((~![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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(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(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[6170, 6168])).
% 1.86/2.03 tff(6172,plain,
% 1.86/2.03 ((~![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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(6173,plain,
% 1.86/2.03 ((~![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(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[6172, 6171])).
% 1.86/2.03 tff(6174,plain,
% 1.86/2.03 (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6173, 453, 1071, 909, 5616])).
% 1.86/2.03 tff(6175,plain,
% 1.86/2.03 (r(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5627, 69, 5624, 6174])).
% 1.86/2.03 tff(6176,assumption,(~(s(s(s(s(s(s(s(s(z)))))))) = s(elem!1))), introduced(assumption)).
% 1.86/2.03 tff(6177,plain,
% 1.86/2.03 (((~![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), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(6178,plain,
% 1.86/2.03 (((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(6179,plain,
% 1.86/2.03 (((~![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(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[6178])).
% 1.86/2.03 tff(6180,plain,
% 1.86/2.03 (((~![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(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[6179, 6177])).
% 1.86/2.03 tff(6181,plain,
% 1.86/2.03 ((~![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(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(6182,plain,
% 1.86/2.03 ((~![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), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[6181, 6180])).
% 1.86/2.03 tff(6183,plain,
% 1.86/2.03 (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6182, 453, 1059, 1549, 629, 1071, 5616])).
% 1.86/2.03 tff(6184,plain,
% 1.86/2.03 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)) | r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)) | r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(6185,plain,
% 1.86/2.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)) | r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(6186,plain,
% 1.86/2.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)) | r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[6185, 6184])).
% 1.86/2.03 tff(6187,plain,
% 1.86/2.03 ((s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)) | r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6186, 69])).
% 1.86/2.03 tff(6188,plain,
% 1.86/2.03 (r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6187, 6183, 6176])).
% 1.86/2.03 tff(6189,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(6190,plain,
% 1.86/2.03 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(6191,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[6190])).
% 1.86/2.03 tff(6192,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[6191, 6189])).
% 1.86/2.03 tff(6193,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(6194,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[6193, 6192])).
% 1.86/2.03 tff(6195,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6194, 268, 3406, 6188, 6175])).
% 1.86/2.03 tff(6196,plain,((~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(elem!1)) = s(s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(6197,plain,
% 1.86/2.03 (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6196, 6167, 6162, 6161, 6156, 6133, 6128, 6118, 6116])).
% 1.86/2.03 tff(6198,plain,
% 1.86/2.03 (s(s(s(s(s(s(s(s(z)))))))) = elem!1),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5649, 6197, 6111])).
% 1.86/2.03 tff(6199,plain,
% 1.86/2.03 (s(s(s(s(s(s(s(s(z)))))))) = s(s(z))),
% 1.86/2.03 inference(transitivity,[status(thm)],[6198, 6080])).
% 1.86/2.03 tff(6200,plain,
% 1.86/2.03 (inj_0(s(s(s(s(s(s(s(s(z))))))))) = inj_0(s(s(z)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[6199])).
% 1.86/2.03 tff(6201,plain,
% 1.86/2.03 (s(s(s(s(s(s(s(z))))))) = s(z)),
% 1.86/2.03 inference(transitivity,[status(thm)],[2336, 6200, 28])).
% 1.86/2.03 tff(6202,plain,
% 1.86/2.03 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(z))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[6201])).
% 1.86/2.03 tff(6203,plain,
% 1.86/2.03 (s(s(s(s(s(s(z)))))) = z),
% 1.86/2.03 inference(transitivity,[status(thm)],[1375, 6202, 32])).
% 1.86/2.03 tff(6204,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2341, 6203])).
% 1.86/2.03 tff(6205,plain,((~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (s(z) = elem!1) | (s(s(s(z))) = elem!1) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | b(s(s(s(s(s(z))))), elem!1) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(6206,plain,
% 1.86/2.03 (~b(s(z), s(s(s(s(s(z))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6205, 238, 300, 492, 59, 256, 638, 11, 1132])).
% 1.86/2.03 tff(6207,plain,
% 1.86/2.03 (r(s(z), s(s(s(s(s(z))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[372, 6206])).
% 1.86/2.03 tff(6208,plain,
% 1.86/2.03 (~r(s(z), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2629, 6207, 1132, 11])).
% 1.86/2.03 tff(6209,plain,
% 1.86/2.03 (b(s(z), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[227, 6208])).
% 1.86/2.03 tff(6210,plain,
% 1.86/2.03 (r(s(z), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5780, 6209, 638, 1597, 5913, 59, 256, 6207, 492])).
% 1.86/2.03 tff(6211,plain,
% 1.86/2.03 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[4530, 6210, 6207])).
% 1.86/2.03 tff(6212,plain,
% 1.86/2.03 (s(s(s(s(s(z))))) = elem!1),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[643, 6211, 638])).
% 1.86/2.03 tff(6213,plain,
% 1.86/2.03 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 1.86/2.03 inference(monotonicity,[status(thm)],[6212])).
% 1.86/2.03 tff(6214,plain,
% 1.86/2.03 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[6213])).
% 1.86/2.03 tff(6215,plain,
% 1.86/2.03 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 1.86/2.03 inference(symmetry,[status(thm)],[6214])).
% 1.86/2.03 tff(6216,plain,
% 1.86/2.03 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[6215])).
% 1.86/2.03 tff(6217,plain,
% 1.86/2.03 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.86/2.03 inference(symmetry,[status(thm)],[6216])).
% 1.86/2.03 tff(6218,plain,
% 1.86/2.03 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[6214])).
% 1.86/2.03 tff(6219,plain,
% 1.86/2.03 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.86/2.03 inference(symmetry,[status(thm)],[6218])).
% 1.86/2.03 tff(6220,plain,
% 1.86/2.03 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[6219])).
% 1.86/2.03 tff(6221,plain,
% 1.86/2.03 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.86/2.03 inference(monotonicity,[status(thm)],[6212])).
% 1.86/2.03 tff(6222,plain,
% 1.86/2.03 (b(s(s(s(s(z)))), elem!1)),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[5912, 6221])).
% 1.86/2.03 tff(6223,plain,
% 1.86/2.03 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[6212])).
% 1.86/2.03 tff(6224,plain,
% 1.86/2.03 (b(elem!1, s(s(s(s(z)))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[5914, 6223])).
% 1.86/2.03 tff(6225,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.86/2.03 tff(6226,plain,
% 1.86/2.03 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.86/2.03 inference(monotonicity,[status(thm)],[5168])).
% 1.86/2.03 tff(6227,plain,
% 1.86/2.03 (b(s(s(s(s(z)))), elem!1)),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2497, 6226])).
% 1.86/2.03 tff(6228,plain,
% 1.86/2.03 (b(elem!1, s(s(s(s(z)))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[1780, 5964])).
% 1.86/2.03 tff(6229,plain,
% 1.86/2.03 (r(s(z), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5592, 5168, 2246])).
% 1.86/2.03 tff(6230,plain,
% 1.86/2.03 (r(s(s(elem!1)), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2240, 5180, 6225])).
% 1.86/2.03 tff(6231,plain,
% 1.86/2.03 (~(s(elem!1) = s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5852, 5168])).
% 1.86/2.03 tff(6232,plain,
% 1.86/2.03 (~(s(s(z)) = s(s(elem!1)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1188, 6231])).
% 1.86/2.03 tff(6233,plain,
% 1.86/2.03 (~r(s(s(elem!1)), s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1970, 6230, 238])).
% 1.86/2.03 tff(6234,plain,
% 1.86/2.03 (b(s(s(elem!1)), s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1047, 6233])).
% 1.86/2.03 tff(6235,plain,
% 1.86/2.03 (~r(s(s(z)), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[4248, 6234, 6232, 6230, 6229])).
% 1.86/2.03 tff(6236,plain,
% 1.86/2.03 (b(s(s(z)), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[782, 6235, 5988])).
% 1.86/2.03 tff(6237,plain,
% 1.86/2.03 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1735, 453, 6236, 6228, 6227])).
% 1.86/2.03 tff(6238,plain,
% 1.86/2.03 (r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[795, 69, 153, 6237])).
% 1.86/2.03 tff(6239,plain,
% 1.86/2.03 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.86/2.03 inference(symmetry,[status(thm)],[1])).
% 1.86/2.03 tff(6240,plain,
% 1.86/2.03 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(z))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[6239])).
% 1.86/2.03 tff(6241,plain,
% 1.86/2.03 (~(s(s(z)) = s(s(s(s(z)))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[153, 6240])).
% 1.86/2.03 tff(6242,plain,
% 1.86/2.03 (((~![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(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(6243,plain,
% 1.86/2.03 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(6244,plain,
% 1.86/2.03 (((~![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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[6243])).
% 1.86/2.03 tff(6245,plain,
% 1.86/2.03 (((~![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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.86/2.03 inference(transitivity,[status(thm)],[6244, 6242])).
% 1.86/2.03 tff(6246,plain,
% 1.86/2.03 ((~![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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(6247,plain,
% 1.86/2.04 ((~![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(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[6246, 6245])).
% 1.86/2.04 tff(6248,plain,
% 1.86/2.04 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6247, 453, 6236, 6228, 6227])).
% 1.86/2.04 tff(6249,plain,
% 1.86/2.04 ((s(s(z)) = s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2370, 69, 6248])).
% 1.86/2.04 tff(6250,plain,
% 1.86/2.04 (r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6249, 6241])).
% 1.86/2.04 tff(6251,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(6252,plain,
% 1.86/2.04 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(6253,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[6252])).
% 1.86/2.04 tff(6254,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[6253, 6251])).
% 1.86/2.04 tff(6255,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(6256,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[6255, 6254])).
% 1.86/2.04 tff(6257,plain,
% 1.86/2.04 (~r(s(s(s(z))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6256, 268, 300, 6250])).
% 1.86/2.04 tff(6258,plain,
% 1.86/2.04 (b(s(s(s(z))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2534, 69, 160, 6257])).
% 1.86/2.04 tff(6259,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(6260,plain,
% 1.86/2.04 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(6261,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[6260])).
% 1.86/2.04 tff(6262,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[6261, 6259])).
% 1.86/2.04 tff(6263,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(6264,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[6263, 6262])).
% 1.86/2.04 tff(6265,plain,
% 1.86/2.04 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6264, 268, 300, 6250])).
% 1.86/2.04 tff(6266,plain,
% 1.86/2.04 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1350, 69, 6265])).
% 1.86/2.04 tff(6267,plain,
% 1.86/2.04 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6266, 1243])).
% 1.86/2.04 tff(6268,plain,
% 1.86/2.04 (((~![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(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(6269,plain,
% 1.86/2.04 (((~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(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), 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(z))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(6270,plain,
% 1.86/2.04 (((~![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(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(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(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(z)))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[6269])).
% 1.86/2.04 tff(6271,plain,
% 1.86/2.04 (((~![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(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(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(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(z))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[6270, 6268])).
% 1.86/2.04 tff(6272,plain,
% 1.86/2.04 ((~![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(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(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(6273,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[6272, 6271])).
% 1.86/2.04 tff(6274,plain,
% 1.86/2.04 (~b(s(s(z)), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6273, 453, 2090, 6267, 6258])).
% 1.86/2.04 tff(6275,plain,
% 1.86/2.04 (r(s(s(z)), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[720, 69, 717, 6274])).
% 1.86/2.04 tff(6276,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2385, 268, 1132, 6275, 6238])).
% 1.86/2.04 tff(6277,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | b(s(s(elem!1)), elem!1) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(6278,plain,
% 1.86/2.04 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6277, 6225, 6209, 300, 238, 1132, 5912, 5914, 6207])).
% 1.86/2.04 tff(6279,plain,
% 1.86/2.04 (r(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[643, 6278, 638])).
% 1.86/2.04 tff(6280,plain,
% 1.86/2.04 (~b(s(z), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5777, 6279, 6209, 1597, 5913, 59, 256])).
% 1.86/2.04 tff(6281,plain,
% 1.86/2.04 (r(s(z), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[506, 6280, 492])).
% 1.86/2.04 tff(6282,plain,
% 1.86/2.04 (~r(s(s(z)), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[777, 6281, 6279])).
% 1.86/2.04 tff(6283,plain,
% 1.86/2.04 (~r(s(s(s(z))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1566, 6279, 256])).
% 1.86/2.04 tff(6284,plain,
% 1.86/2.04 (b(s(s(s(z))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[74, 6283, 59])).
% 1.86/2.04 tff(6285,plain,
% 1.86/2.04 (~(s(s(s(s(z)))) = elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[4469, 6279, 5913])).
% 1.86/2.04 tff(6286,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[254, 6285, 1139])).
% 1.86/2.04 tff(6287,plain,
% 1.86/2.04 (~(elem!1 = s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[8, 6285])).
% 1.86/2.04 tff(6288,plain,
% 1.86/2.04 (b(elem!1, s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1087, 6287, 1597])).
% 1.86/2.04 tff(6289,plain,
% 1.86/2.04 (~b(s(s(z)), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6077, 6288, 11, 6286, 6284])).
% 1.86/2.04 tff(6290,plain,
% 1.86/2.04 (s(s(z)) = elem!1),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[782, 6289, 6282])).
% 1.86/2.04 tff(6291,plain,
% 1.86/2.04 (s(s(s(z))) = s(elem!1)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[6290])).
% 1.86/2.04 tff(6292,plain,
% 1.86/2.04 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[6291])).
% 1.86/2.04 tff(6293,plain,
% 1.86/2.04 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.86/2.04 inference(symmetry,[status(thm)],[6292])).
% 1.86/2.04 tff(6294,plain,
% 1.86/2.04 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[6293])).
% 1.86/2.04 tff(6295,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.86/2.04 inference(symmetry,[status(thm)],[6294])).
% 1.86/2.04 tff(6296,plain,
% 1.86/2.04 (b(s(s(elem!1)), elem!1)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[6286, 6295])).
% 1.86/2.04 tff(6297,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6225, 6296])).
% 1.86/2.04 tff(6298,plain,(b(s(s(elem!1)), elem!1) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (s(z) = elem!1) | (s(s(s(z))) = elem!1) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | b(s(s(s(s(s(z))))), elem!1) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(6299,plain,
% 1.86/2.04 (b(s(s(elem!1)), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6298, 238, 492, 59, 256, 638, 300, 11, 1132])).
% 1.86/2.04 tff(6300,plain,
% 1.86/2.04 (((~![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(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(6301,plain,
% 1.86/2.04 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(6302,plain,
% 1.86/2.04 (((~![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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[6301])).
% 1.86/2.04 tff(6303,plain,
% 1.86/2.04 (((~![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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[6302, 6300])).
% 1.86/2.04 tff(6304,plain,
% 1.86/2.04 ((~![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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(6305,plain,
% 1.86/2.04 ((~![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(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[6304, 6303])).
% 1.86/2.04 tff(6306,plain,
% 1.86/2.04 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6305, 453, 6299, 6224, 6222])).
% 1.86/2.04 tff(6307,plain,
% 1.86/2.04 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[6306, 6220])).
% 1.86/2.04 tff(6308,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5250, 2690])).
% 1.86/2.04 tff(6309,plain,
% 1.86/2.04 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6308, 6307])).
% 1.86/2.04 tff(6310,plain,
% 1.86/2.04 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[6309, 6217])).
% 1.86/2.04 tff(6311,plain,
% 1.86/2.04 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[6214])).
% 1.86/2.04 tff(6312,plain,
% 1.86/2.04 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[6215])).
% 1.86/2.04 tff(6313,plain,
% 1.86/2.04 ((~b(s(s(elem!1)), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[6312])).
% 1.86/2.04 tff(6314,plain,
% 1.86/2.04 (((~![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(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(6315,plain,
% 1.86/2.04 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(6316,plain,
% 1.86/2.04 (((~![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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[6315])).
% 1.86/2.04 tff(6317,plain,
% 1.86/2.04 (((~![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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[6316, 6314])).
% 1.86/2.04 tff(6318,plain,
% 1.86/2.04 ((~![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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(6319,plain,
% 1.86/2.04 ((~![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(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[6318, 6317])).
% 1.86/2.04 tff(6320,plain,
% 1.86/2.04 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6319, 453, 6299, 6224, 6222])).
% 1.86/2.04 tff(6321,plain,
% 1.86/2.04 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[6320, 6313])).
% 1.86/2.04 tff(6322,plain,
% 1.86/2.04 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2696, 6321])).
% 1.86/2.04 tff(6323,plain,
% 1.86/2.04 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[6322, 6311])).
% 1.86/2.04 tff(6324,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(6325,plain,
% 1.86/2.04 (((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(6326,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[6325])).
% 1.86/2.04 tff(6327,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[6326, 6324])).
% 1.86/2.04 tff(6328,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(6329,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[6328, 6327])).
% 1.86/2.04 tff(6330,plain,
% 1.86/2.04 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6329, 268, 300, 6323])).
% 1.86/2.04 tff(6331,plain,
% 1.86/2.04 (b(s(s(s(z))), s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5203, 6330, 548])).
% 1.86/2.04 tff(6332,plain,
% 1.86/2.04 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[548, 4163])).
% 1.86/2.04 tff(6333,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(6334,plain,
% 1.86/2.04 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(6335,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[6334])).
% 1.86/2.04 tff(6336,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[6335, 6333])).
% 1.86/2.05 tff(6337,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(6338,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[6337, 6336])).
% 1.86/2.05 tff(6339,plain,
% 1.86/2.05 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6338, 268, 300, 6323])).
% 1.86/2.05 tff(6340,plain,
% 1.86/2.05 ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[4175, 69, 6339])).
% 1.86/2.05 tff(6341,plain,
% 1.86/2.05 (b(s(s(elem!1)), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6340, 6332])).
% 1.86/2.05 tff(6342,plain,
% 1.86/2.05 (((~![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(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(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(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(6343,plain,
% 1.86/2.05 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(6344,plain,
% 1.86/2.05 (((~![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(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[6343])).
% 1.86/2.05 tff(6345,plain,
% 1.86/2.05 (((~![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(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[6344, 6342])).
% 1.86/2.05 tff(6346,plain,
% 1.86/2.05 ((~![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(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(6347,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[6346, 6345])).
% 1.86/2.05 tff(6348,plain,
% 1.86/2.05 (~b(s(s(elem!1)), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6347, 453, 6341, 6331, 6209])).
% 1.86/2.05 tff(6349,plain,
% 1.86/2.05 (r(s(s(elem!1)), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1047, 6348])).
% 1.86/2.05 tff(6350,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[5244, 268, 6349, 1132, 6310])).
% 1.86/2.05 tff(6351,plain,((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | b(s(s(s(s(s(z))))), elem!1) | (s(s(s(z))) = elem!1) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (s(z) = elem!1) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(6352,plain,
% 1.86/2.05 (~r(elem!1, s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6351, 5909, 300, 1099, 4544, 256, 4495, 11])).
% 1.86/2.05 tff(6353,plain,
% 1.86/2.05 (~(s(s(s(s(z)))) = elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[4551, 6352, 1099])).
% 1.86/2.05 tff(6354,plain,
% 1.86/2.05 (b(s(s(s(z))), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[5444, 6353, 5883, 221])).
% 1.86/2.05 tff(6355,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[5452, 453, 499, 5908, 6354, 5883])).
% 1.86/2.05 tff(6356,plain,(b(s(z), s(s(s(z)))) | (~b(s(z), elem!1)) | (~r(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))))) | b(s(s(s(s(z)))), s(z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(6357,plain,
% 1.86/2.05 (b(s(z), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6356, 4542, 300, 256, 11, 1057, 1123])).
% 1.86/2.05 tff(6358,plain,
% 1.86/2.05 (~b(s(s(s(z))), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[5513, 5446, 6357, 4542])).
% 1.86/2.05 tff(6359,plain,
% 1.86/2.05 (r(s(s(s(z))), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[74, 59, 58])).
% 1.86/2.05 tff(6360,plain,
% 1.86/2.05 (~r(s(s(s(s(z)))), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[4961, 6359, 11])).
% 1.86/2.05 tff(6361,plain,
% 1.86/2.05 (b(s(s(s(s(z)))), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[254, 6360, 4552])).
% 1.86/2.05 tff(6362,plain,
% 1.86/2.05 (~(elem!1 = s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[8, 4552])).
% 1.86/2.05 tff(6363,plain,
% 1.86/2.05 (~r(s(s(s(z))), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[4119, 11, 1132])).
% 1.86/2.05 tff(6364,plain,
% 1.86/2.05 (b(s(s(s(z))), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[134, 6363])).
% 1.86/2.05 tff(6365,plain,
% 1.86/2.05 (~b(elem!1, s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[5523, 453, 499, 2077, 6364])).
% 1.86/2.05 tff(6366,plain,
% 1.86/2.05 (r(elem!1, s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[4492, 5525, 6365])).
% 1.86/2.05 tff(6367,plain,
% 1.86/2.05 (~r(elem!1, s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[5432, 6359, 300, 6366])).
% 1.86/2.05 tff(6368,plain,
% 1.86/2.05 (b(elem!1, s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1087, 6367, 6362])).
% 1.86/2.05 tff(6369,plain,
% 1.86/2.05 (b(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[5171])).
% 1.86/2.05 tff(6370,plain,
% 1.86/2.05 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.05 inference(symmetry,[status(thm)],[6369])).
% 1.86/2.05 tff(6371,plain,
% 1.86/2.05 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[5171, 5940])).
% 1.86/2.05 tff(6372,plain,
% 1.86/2.05 ((~(elem!1 = s(s(s(s(s(s(s(z))))))))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[5173])).
% 1.86/2.05 tff(6373,plain,
% 1.86/2.05 (~(elem!1 = s(s(elem!1)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[5179, 6372])).
% 1.86/2.05 tff(6374,plain,
% 1.86/2.05 (~(s(elem!1) = elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3351, 6373])).
% 1.86/2.05 tff(6375,plain,
% 1.86/2.05 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[607, 6374])).
% 1.86/2.05 tff(6376,plain,
% 1.86/2.05 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2463, 69, 433])).
% 1.86/2.05 tff(6377,plain,
% 1.86/2.05 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6376, 5338])).
% 1.86/2.05 tff(6378,plain,
% 1.86/2.05 (~r(s(z), s(s(s(s(s(z))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[5592, 5168, 4541])).
% 1.86/2.05 tff(6379,plain,
% 1.86/2.05 (b(s(z), s(s(s(s(s(z))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[372, 6378])).
% 1.86/2.05 tff(6380,plain,
% 1.86/2.05 (~b(s(s(elem!1)), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[5837, 6379, 1780, 5965, 6377])).
% 1.86/2.05 tff(6381,plain,
% 1.86/2.05 (r(s(s(elem!1)), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2240, 5180, 6380])).
% 1.86/2.05 tff(6382,plain,
% 1.86/2.05 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.86/2.05 inference(monotonicity,[status(thm)],[5168])).
% 1.86/2.05 tff(6383,plain,
% 1.86/2.05 ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~r(s(s(s(s(z)))), elem!1))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[6382])).
% 1.86/2.05 tff(6384,plain,
% 1.86/2.05 (~r(s(s(s(s(z)))), elem!1)),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[433, 6383])).
% 1.86/2.05 tff(6385,plain,
% 1.86/2.05 (b(s(s(s(s(z)))), elem!1)),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[6377, 6226])).
% 1.86/2.05 tff(6386,plain,
% 1.86/2.05 (~b(s(z), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1673, 453, 499, 6228, 6385])).
% 1.86/2.05 tff(6387,plain,
% 1.86/2.05 (r(s(z), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1677, 69, 50, 6386])).
% 1.86/2.05 tff(6388,plain,
% 1.86/2.05 (~r(s(z), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[384, 6387, 300])).
% 1.86/2.05 tff(6389,plain,
% 1.86/2.05 (b(s(z), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[227, 6388])).
% 1.86/2.05 tff(6390,plain,
% 1.86/2.05 (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(elem!1)))),
% 1.86/2.05 inference(symmetry,[status(thm)],[5940])).
% 1.86/2.05 tff(6391,plain,
% 1.86/2.05 (b(s(s(s(s(s(s(s(s(z)))))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[6390])).
% 1.86/2.05 tff(6392,plain,
% 1.86/2.05 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.86/2.05 inference(symmetry,[status(thm)],[6391])).
% 1.86/2.05 tff(6393,plain,
% 1.86/2.05 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(z))),
% 1.86/2.05 inference(transitivity,[status(thm)],[5949, 1120])).
% 1.86/2.05 tff(6394,plain,
% 1.86/2.05 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(z)))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[6393])).
% 1.86/2.05 tff(6395,plain,
% 1.86/2.05 (~(elem!1 = s(z))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[289, 6394])).
% 1.86/2.05 tff(6396,plain,
% 1.86/2.05 (b(elem!1, s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1130, 6395, 2076])).
% 1.86/2.05 tff(6397,plain,
% 1.86/2.05 (r(s(s(s(s(s(s(s(s(z)))))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[6390])).
% 1.86/2.05 tff(6398,plain,
% 1.86/2.05 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.86/2.05 inference(symmetry,[status(thm)],[6397])).
% 1.86/2.05 tff(6399,assumption,(~b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.86/2.05 tff(6400,plain,
% 1.86/2.05 (r(s(s(s(elem!1))), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[856, 6399])).
% 1.86/2.05 tff(6401,plain,
% 1.86/2.05 (r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[6400, 6398])).
% 1.86/2.05 tff(6402,plain,
% 1.86/2.05 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(s(z)))))))))) <=> (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(z))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2720])).
% 1.86/2.05 tff(6403,plain,
% 1.86/2.05 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(z)))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[5955, 6402])).
% 1.86/2.05 tff(6404,plain,
% 1.86/2.05 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.86/2.05 inference(monotonicity,[status(thm)],[5940])).
% 1.86/2.05 tff(6405,plain,
% 1.86/2.05 (b(s(s(s(elem!1))), s(z)) <=> b(elem!1, s(z))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[186])).
% 1.86/2.05 tff(6406,plain,
% 1.86/2.05 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.86/2.05 inference(symmetry,[status(thm)],[6405])).
% 1.86/2.05 tff(6407,plain,
% 1.86/2.05 (b(s(s(s(elem!1))), s(z))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[2077, 6406])).
% 1.86/2.05 tff(6408,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6399, 6407])).
% 1.86/2.05 tff(6409,plain,((~(s(s(s(elem!1))) = elem!1)) | b(s(s(s(elem!1))), s(z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(6410,plain,
% 1.86/2.05 (~(s(s(s(elem!1))) = elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6409, 6399, 2077])).
% 1.86/2.05 tff(6411,plain,
% 1.86/2.05 (b(s(s(s(elem!1))), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[567, 6410, 563])).
% 1.86/2.05 tff(6412,plain,
% 1.86/2.05 (b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[6411, 6404])).
% 1.86/2.05 tff(6413,plain,
% 1.86/2.05 (((~![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(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(6414,plain,
% 1.86/2.05 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(6415,plain,
% 1.86/2.05 (((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[6414])).
% 1.86/2.05 tff(6416,plain,
% 1.86/2.05 (((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.86/2.05 inference(transitivity,[status(thm)],[6415, 6413])).
% 1.86/2.05 tff(6417,plain,
% 1.86/2.05 ((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(6418,plain,
% 1.86/2.05 ((~![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(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[6417, 6416])).
% 1.86/2.05 tff(6419,plain,
% 1.86/2.05 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6418, 453, 2077, 299, 6412])).
% 1.86/2.05 tff(6420,plain,
% 1.86/2.05 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2862, 6419, 6403])).
% 1.86/2.05 tff(6421,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(6422,plain,
% 1.86/2.05 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(6423,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[6422])).
% 1.86/2.05 tff(6424,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[6423, 6421])).
% 1.86/2.05 tff(6425,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(6426,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[6425, 6424])).
% 1.86/2.05 tff(6427,plain,
% 1.86/2.05 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6426, 268, 11, 1132])).
% 1.86/2.05 tff(6428,plain,
% 1.86/2.05 (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6427, 6420])).
% 1.86/2.05 tff(6429,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6428, 6401])).
% 1.86/2.05 tff(6430,plain,(b(s(s(s(elem!1))), s(z)) | (~(s(s(s(s(s(z))))) = elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(6431,plain,
% 1.86/2.05 (b(s(s(s(elem!1))), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6430, 5168, 11, 1132, 6396, 5963, 563])).
% 1.86/2.05 tff(6432,plain,
% 1.86/2.05 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[6431, 6392])).
% 1.86/2.05 tff(6433,plain,
% 1.86/2.05 (((~![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(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(6434,plain,
% 1.86/2.05 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(6435,plain,
% 1.86/2.05 (((~![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(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[6434])).
% 1.86/2.05 tff(6436,plain,
% 1.86/2.05 (((~![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(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.86/2.05 inference(transitivity,[status(thm)],[6435, 6433])).
% 1.86/2.05 tff(6437,plain,
% 1.86/2.05 ((~![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(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(6438,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[6437, 6436])).
% 1.86/2.05 tff(6439,plain,
% 1.86/2.05 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6438, 453, 6396, 2090])).
% 1.86/2.05 tff(6440,plain,
% 1.86/2.05 (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6439, 6432])).
% 1.86/2.05 tff(6441,plain,
% 1.86/2.05 (s(s(s(s(s(s(s(s(z)))))))) = elem!1),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[5649, 6440, 5943])).
% 1.86/2.05 tff(6442,plain,
% 1.86/2.05 (elem!1 = s(s(s(s(s(s(s(s(z))))))))),
% 1.86/2.05 inference(symmetry,[status(thm)],[6441])).
% 1.86/2.05 tff(6443,plain,
% 1.86/2.05 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(s(z))))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[5168, 6442])).
% 1.86/2.05 tff(6444,plain,
% 1.86/2.05 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[6443])).
% 1.86/2.05 tff(6445,plain,
% 1.86/2.05 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.86/2.05 inference(transitivity,[status(thm)],[284, 6444, 2335, 5170])).
% 1.86/2.05 tff(6446,plain,
% 1.86/2.05 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[6445])).
% 1.86/2.05 tff(6447,plain,
% 1.86/2.05 (s(s(s(z))) = s(elem!1)),
% 1.86/2.05 inference(transitivity,[status(thm)],[38, 6446, 194])).
% 1.86/2.05 tff(6448,plain,
% 1.86/2.05 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[6447])).
% 1.86/2.05 tff(6449,plain,
% 1.86/2.05 (s(s(z)) = elem!1),
% 1.86/2.05 inference(transitivity,[status(thm)],[98, 6448, 85])).
% 1.86/2.05 tff(6450,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[5988, 6449])).
% 1.86/2.05 tff(6451,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~b(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(elem!1))), elem!1) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(6452,plain,
% 1.86/2.05 (r(s(s(s(elem!1))), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6451, 6389, 11, 1132, 2076, 5168, 6384])).
% 1.86/2.05 tff(6453,plain,
% 1.86/2.05 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[877, 6452, 6381])).
% 1.86/2.05 tff(6454,plain,
% 1.86/2.05 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[675, 6453, 6375])).
% 1.86/2.05 tff(6455,plain,
% 1.86/2.05 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[6454, 6371])).
% 1.86/2.05 tff(6456,plain,
% 1.86/2.05 (b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[6455, 6370])).
% 1.86/2.05 tff(6457,plain,
% 1.86/2.06 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[5940])).
% 1.86/2.06 tff(6458,plain,
% 1.86/2.06 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[6457, 5661])).
% 1.86/2.06 tff(6459,plain,
% 1.86/2.06 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6458])).
% 1.86/2.06 tff(6460,plain,
% 1.86/2.06 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[4916, 6232])).
% 1.86/2.06 tff(6461,plain,
% 1.86/2.06 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[6460, 6459])).
% 1.86/2.06 tff(6462,plain,
% 1.86/2.06 (r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[6452, 5941])).
% 1.86/2.06 tff(6463,plain,
% 1.86/2.06 (~b(s(s(s(z))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[5513, 6389, 2077, 499])).
% 1.86/2.06 tff(6464,plain,
% 1.86/2.06 (r(s(s(s(z))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[74, 6463, 59])).
% 1.86/2.06 tff(6465,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6466,plain,
% 1.86/2.06 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6467,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6466])).
% 1.86/2.06 tff(6468,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[6467, 6465])).
% 1.86/2.06 tff(6469,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(6470,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[6469, 6468])).
% 1.86/2.06 tff(6471,plain,
% 1.86/2.06 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6470, 268, 6464, 6462])).
% 1.86/2.06 tff(6472,plain,
% 1.86/2.06 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2846, 6471, 6461])).
% 1.86/2.06 tff(6473,plain,
% 1.86/2.06 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6457])).
% 1.86/2.06 tff(6474,plain,
% 1.86/2.06 (~(s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[6460, 6473])).
% 1.86/2.06 tff(6475,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6476,plain,
% 1.86/2.06 (((~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6477,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6476])).
% 1.86/2.06 tff(6478,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[6477, 6475])).
% 1.86/2.06 tff(6479,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(6480,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[6479, 6478])).
% 1.86/2.06 tff(6481,plain,
% 1.86/2.06 (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6480, 268, 6464, 6462])).
% 1.86/2.06 tff(6482,plain,
% 1.86/2.06 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6483,plain,
% 1.86/2.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(6484,plain,
% 1.86/2.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[6483, 6482])).
% 1.86/2.06 tff(6485,plain,
% 1.86/2.06 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6484, 69])).
% 1.86/2.06 tff(6486,plain,
% 1.86/2.06 (b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6485, 6481, 6474])).
% 1.86/2.06 tff(6487,plain,
% 1.86/2.06 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[5213, 6464, 6381])).
% 1.86/2.06 tff(6488,plain,
% 1.86/2.06 (b(s(s(s(z))), s(s(elem!1)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[5203, 6487, 555])).
% 1.86/2.06 tff(6489,plain,
% 1.86/2.06 (((~![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(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(elem!1)), s(s(s(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(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6490,plain,
% 1.86/2.06 (((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6491,plain,
% 1.86/2.06 (((~![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(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6490])).
% 1.86/2.06 tff(6492,plain,
% 1.86/2.06 (((~![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(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[6491, 6489])).
% 1.86/2.06 tff(6493,plain,
% 1.86/2.06 ((~![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(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(6494,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z))))))))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[6493, 6492])).
% 1.86/2.06 tff(6495,plain,
% 1.86/2.06 (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(z)))))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6494, 453, 6488, 6486, 6472])).
% 1.86/2.06 tff(6496,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6495, 6456])).
% 1.86/2.06 tff(6497,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (s(s(s(z))) = elem!1) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | r(elem!1, s(z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(6498,plain,
% 1.86/2.06 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6497, 59, 499, 2076, 555, 11, 1132, 2077, 300, 5910, 5914, 4541])).
% 1.86/2.06 tff(6499,plain,
% 1.86/2.06 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1566, 6359, 256])).
% 1.86/2.06 tff(6500,plain,
% 1.86/2.06 (b(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[643, 6499, 6498])).
% 1.86/2.06 tff(6501,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[5555, 453, 6500, 5914, 6368, 6361])).
% 1.86/2.06 tff(6502,plain,((s(s(s(z))) = elem!1) | (~r(s(s(s(z))), s(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))))) | b(s(s(s(z))), elem!1) | (~b(s(z), elem!1)) | r(elem!1, s(z)) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(6503,plain,
% 1.86/2.06 (s(s(s(z))) = elem!1),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6502, 6358, 11, 256, 300, 4542, 2076, 4877, 1099, 5446, 4541])).
% 1.86/2.06 tff(6504,plain,
% 1.86/2.06 (s(elem!1) = s(s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[81, 6503])).
% 1.86/2.06 tff(6505,plain,
% 1.86/2.06 (~(s(z) = s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[171, 6504])).
% 1.86/2.06 tff(6506,plain,
% 1.86/2.06 (~(s(elem!1) = s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[179, 6505])).
% 1.86/2.06 tff(6507,plain,
% 1.86/2.06 (~(s(s(s(elem!1))) = elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[199, 6506, 6503])).
% 1.86/2.06 tff(6508,plain,
% 1.86/2.06 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6504])).
% 1.86/2.06 tff(6509,plain,
% 1.86/2.06 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6508])).
% 1.86/2.06 tff(6510,plain,
% 1.86/2.06 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.86/2.06 inference(symmetry,[status(thm)],[6509])).
% 1.86/2.06 tff(6511,plain,
% 1.86/2.06 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6510, 6504])).
% 1.86/2.06 tff(6512,plain,
% 1.86/2.06 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.86/2.06 inference(symmetry,[status(thm)],[6511])).
% 1.86/2.06 tff(6513,plain,
% 1.86/2.06 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(s(z)))))) = s(elem!1)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6512])).
% 1.86/2.06 tff(6514,plain,
% 1.86/2.06 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[557, 4877])).
% 1.86/2.06 tff(6515,plain,
% 1.86/2.06 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[6514, 6513])).
% 1.86/2.06 tff(6516,plain,
% 1.86/2.06 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6508, 6504])).
% 1.86/2.06 tff(6517,plain,
% 1.86/2.06 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.86/2.06 inference(symmetry,[status(thm)],[6516])).
% 1.86/2.06 tff(6518,plain,
% 1.86/2.06 (b(s(s(elem!1)), s(elem!1))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[5914, 6517])).
% 1.86/2.06 tff(6519,plain,
% 1.86/2.06 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6504])).
% 1.86/2.06 tff(6520,plain,
% 1.86/2.06 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.86/2.06 inference(symmetry,[status(thm)],[6519])).
% 1.86/2.06 tff(6521,plain,
% 1.86/2.06 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6508])).
% 1.86/2.06 tff(6522,plain,
% 1.86/2.06 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.86/2.06 inference(symmetry,[status(thm)],[6521])).
% 1.86/2.06 tff(6523,plain,
% 1.86/2.06 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.86/2.06 inference(transitivity,[status(thm)],[6522, 6520])).
% 1.86/2.06 tff(6524,plain,
% 1.86/2.06 (b(s(elem!1), s(s(elem!1)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[5912, 6523])).
% 1.86/2.06 tff(6525,plain,
% 1.86/2.06 (~b(s(elem!1), s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1062, 6504, 1057])).
% 1.86/2.06 tff(6526,plain,
% 1.86/2.06 (r(s(elem!1), s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[353, 6506, 6525])).
% 1.86/2.06 tff(6527,plain,
% 1.86/2.06 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6504])).
% 1.86/2.06 tff(6528,plain,
% 1.86/2.06 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.86/2.06 inference(symmetry,[status(thm)],[6527])).
% 1.86/2.06 tff(6529,plain,
% 1.86/2.06 (r(s(s(s(s(z)))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[512, 6504, 11])).
% 1.86/2.06 tff(6530,plain,
% 1.86/2.06 (r(s(elem!1), elem!1)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[6529, 6528])).
% 1.86/2.06 tff(6531,plain,
% 1.86/2.06 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6508])).
% 1.86/2.06 tff(6532,plain,
% 1.86/2.06 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.86/2.06 inference(symmetry,[status(thm)],[6531])).
% 1.86/2.06 tff(6533,plain,
% 1.86/2.06 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6503])).
% 1.86/2.06 tff(6534,plain,
% 1.86/2.06 (r(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[256, 6533])).
% 1.86/2.06 tff(6535,plain,
% 1.86/2.06 (r(s(s(elem!1)), elem!1)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[6534, 6532])).
% 1.86/2.06 tff(6536,plain,
% 1.86/2.06 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.86/2.06 inference(commutativity,[status(thm)],[])).
% 1.86/2.06 tff(6537,plain,
% 1.86/2.06 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[1886])).
% 1.86/2.06 tff(6538,plain,
% 1.86/2.06 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[6537, 6536])).
% 1.86/2.06 tff(6539,plain,
% 1.86/2.06 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 1.86/2.06 inference(symmetry,[status(thm)],[6538])).
% 1.86/2.06 tff(6540,plain,
% 1.86/2.06 ((~(s(s(elem!1)) = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(elem!1))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6539])).
% 1.86/2.06 tff(6541,plain,
% 1.86/2.06 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 1.86/2.06 inference(monotonicity,[status(thm)],[78])).
% 1.86/2.06 tff(6542,plain,
% 1.86/2.06 ((s(s(s(s(z)))) = elem!1) <=> (s(elem!1) = elem!1)),
% 1.86/2.06 inference(symmetry,[status(thm)],[6541])).
% 1.86/2.06 tff(6543,plain,
% 1.86/2.06 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(elem!1) = elem!1))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6542])).
% 1.86/2.06 tff(6544,plain,
% 1.86/2.06 (~(s(elem!1) = elem!1)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[143, 6543])).
% 1.86/2.06 tff(6545,plain,
% 1.86/2.06 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[607, 6544])).
% 1.86/2.06 tff(6546,plain,
% 1.86/2.06 (~(s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[6545, 6540])).
% 1.86/2.06 tff(6547,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6548,plain,
% 1.86/2.06 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6549,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6548])).
% 1.86/2.06 tff(6550,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.86/2.06 inference(transitivity,[status(thm)],[6549, 6547])).
% 1.86/2.06 tff(6551,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(6552,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[6551, 6550])).
% 1.86/2.06 tff(6553,plain,
% 1.86/2.06 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6552, 268, 340, 1892, 997])).
% 1.86/2.06 tff(6554,plain,
% 1.86/2.06 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1903, 69, 955, 6553])).
% 1.86/2.06 tff(6555,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.86/2.06 tff(6556,plain,
% 1.86/2.06 (((~![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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6557,plain,
% 1.86/2.06 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6558,plain,
% 1.86/2.06 (((~![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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6557])).
% 1.86/2.06 tff(6559,plain,
% 1.86/2.06 (((~![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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[6558, 6556])).
% 1.86/2.06 tff(6560,plain,
% 1.86/2.06 ((~![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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(6561,plain,
% 1.86/2.07 ((~![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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[6560, 6559])).
% 1.86/2.07 tff(6562,plain,
% 1.86/2.07 (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6561, 453, 910, 6555, 6554])).
% 1.86/2.07 tff(6563,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6564,plain,
% 1.86/2.07 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6565,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[6564])).
% 1.86/2.07 tff(6566,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[6565, 6563])).
% 1.86/2.07 tff(6567,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(6568,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[6567, 6566])).
% 1.86/2.07 tff(6569,plain,
% 1.86/2.07 (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6568, 268, 869, 997])).
% 1.86/2.07 tff(6570,plain,
% 1.86/2.07 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1))) | r(s(s(s(s(s(s(z)))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1))) | r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6571,plain,
% 1.86/2.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1))) | r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(6572,plain,
% 1.86/2.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1))) | r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[6571, 6570])).
% 1.86/2.07 tff(6573,plain,
% 1.86/2.07 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6572, 69, 6569])).
% 1.86/2.07 tff(6574,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6573, 6562, 6546])).
% 1.86/2.07 tff(6575,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~(s(s(s(z))) = elem!1)) | (s(s(s(s(s(s(z)))))) = s(elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(6576,plain,
% 1.86/2.07 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6575, 6535, 6503, 6530, 6526, 6524, 6518, 6515])).
% 1.86/2.07 tff(6577,plain,
% 1.86/2.07 (~r(s(s(s(elem!1))), elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[992, 6576, 6504])).
% 1.86/2.07 tff(6578,plain,
% 1.86/2.07 (b(s(s(s(elem!1))), elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[567, 6577, 6507])).
% 1.86/2.07 tff(6579,plain,
% 1.86/2.07 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[576, 6578, 6503])).
% 1.86/2.07 tff(6580,plain,
% 1.86/2.07 ((s(s(s(z))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[6503])).
% 1.86/2.07 tff(6581,plain,
% 1.86/2.07 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.86/2.07 inference(transitivity,[status(thm)],[6580, 144])).
% 1.86/2.07 tff(6582,plain,
% 1.86/2.07 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[6581])).
% 1.86/2.07 tff(6583,plain,
% 1.86/2.07 (~(s(s(z)) = elem!1)),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[160, 6582])).
% 1.86/2.07 tff(6584,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6585,plain,
% 1.86/2.07 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6586,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[6585])).
% 1.86/2.07 tff(6587,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.86/2.07 inference(transitivity,[status(thm)],[6586, 6584])).
% 1.86/2.07 tff(6588,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(6589,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[6588, 6587])).
% 1.86/2.07 tff(6590,plain,
% 1.86/2.07 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6589, 268, 700, 1132, 1159])).
% 1.86/2.07 tff(6591,plain,
% 1.86/2.07 ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2370, 69, 6590])).
% 1.86/2.07 tff(6592,plain,
% 1.86/2.07 (b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6591, 6241])).
% 1.86/2.07 tff(6593,plain,
% 1.86/2.07 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[5707, 268, 700, 722])).
% 1.86/2.07 tff(6594,plain,
% 1.86/2.07 ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[5711, 69, 6593])).
% 1.86/2.07 tff(6595,plain,
% 1.86/2.07 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6594, 5578])).
% 1.86/2.07 tff(6596,plain,
% 1.86/2.07 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6597,plain,
% 1.86/2.07 (((~![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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(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(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[6596])).
% 1.86/2.07 tff(6598,plain,
% 1.86/2.07 (((~![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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(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(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[6597, 2742])).
% 1.86/2.07 tff(6599,plain,
% 1.86/2.07 ((~![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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(6600,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[6599, 6598])).
% 1.86/2.07 tff(6601,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6600, 453, 1780, 2497, 6595, 6592])).
% 1.86/2.07 tff(6602,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(6603,plain,
% 1.86/2.07 (~r(s(s(z)), elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6602, 6529, 5912, 1099, 5914, 6534])).
% 1.86/2.07 tff(6604,plain,
% 1.86/2.07 (b(s(s(z)), elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[782, 6603, 6583])).
% 1.86/2.07 tff(6605,plain,
% 1.86/2.07 (((~![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(elem!1, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6606,plain,
% 1.86/2.07 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6607,plain,
% 1.86/2.07 (((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[6606])).
% 1.86/2.07 tff(6608,plain,
% 1.86/2.07 (((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.86/2.07 inference(transitivity,[status(thm)],[6607, 6605])).
% 1.86/2.07 tff(6609,plain,
% 1.86/2.07 ((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(6610,plain,
% 1.86/2.07 ((~![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(elem!1, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[6609, 6608])).
% 1.86/2.07 tff(6611,plain,
% 1.86/2.07 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6610, 453, 5446, 6604, 6579])).
% 1.86/2.07 tff(6612,plain,
% 1.86/2.07 (~(s(s(z)) = s(s(s(s(s(s(z)))))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[818, 6503])).
% 1.86/2.07 tff(6613,plain,
% 1.86/2.07 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[822, 69, 6612, 6611])).
% 1.86/2.07 tff(6614,plain,
% 1.86/2.07 ((s(z) = s(s(s(s(s(s(z))))))) <=> (s(z) = s(s(s(elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[6510])).
% 1.86/2.07 tff(6615,plain,
% 1.86/2.07 ((s(z) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = s(z))),
% 1.86/2.07 inference(transitivity,[status(thm)],[6614, 1470])).
% 1.86/2.07 tff(6616,plain,
% 1.86/2.07 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(s(s(s(z)))))))),
% 1.86/2.07 inference(symmetry,[status(thm)],[6615])).
% 1.86/2.07 tff(6617,plain,
% 1.86/2.07 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = s(s(s(s(s(s(z))))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[6616])).
% 1.86/2.07 tff(6618,plain,
% 1.86/2.07 (~(s(z) = s(s(s(s(s(s(z)))))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[851, 6617])).
% 1.86/2.07 tff(6619,plain,
% 1.86/2.07 (((~![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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6620,plain,
% 1.86/2.07 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6621,plain,
% 1.86/2.07 (((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[6620])).
% 1.86/2.07 tff(6622,plain,
% 1.86/2.07 (((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.86/2.07 inference(transitivity,[status(thm)],[6621, 6619])).
% 1.86/2.07 tff(6623,plain,
% 1.86/2.07 ((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(6624,plain,
% 1.86/2.07 ((~![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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[6623, 6622])).
% 1.86/2.07 tff(6625,plain,
% 1.86/2.07 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6624, 453, 4542, 5446, 6579])).
% 1.86/2.07 tff(6626,plain,
% 1.86/2.07 ((s(z) = s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z)))))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1944, 69, 6625])).
% 1.86/2.07 tff(6627,plain,
% 1.86/2.07 (r(s(z), s(s(s(s(s(s(z)))))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6626, 6618])).
% 1.86/2.07 tff(6628,plain,
% 1.86/2.07 (((~![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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6629,plain,
% 1.86/2.07 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6630,plain,
% 1.86/2.07 (((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[6629])).
% 1.86/2.07 tff(6631,plain,
% 1.86/2.07 (((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.07 inference(transitivity,[status(thm)],[6630, 6628])).
% 1.86/2.07 tff(6632,plain,
% 1.86/2.07 ((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(6633,plain,
% 1.86/2.07 ((~![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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[6632, 6631])).
% 1.86/2.07 tff(6634,plain,
% 1.86/2.07 (~b(s(z), s(s(z)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6633, 453, 4542, 5446, 6604])).
% 1.86/2.07 tff(6635,plain,
% 1.86/2.07 (r(s(z), s(s(z)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[757, 6634])).
% 1.86/2.07 tff(6636,plain,
% 1.86/2.07 (~b(s(s(z)), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[5570, 453, 4542, 5446, 6604])).
% 1.86/2.07 tff(6637,plain,
% 1.86/2.07 (r(s(s(z)), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[720, 69, 717, 6636])).
% 1.86/2.07 tff(6638,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6639,plain,
% 1.86/2.07 (((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6640,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[6639])).
% 1.86/2.07 tff(6641,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[6640, 6638])).
% 1.86/2.07 tff(6642,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(6643,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6642, 6641])).
% 1.86/2.08 tff(6644,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6643, 268, 6637, 6635, 6627, 6613])).
% 1.86/2.08 tff(6645,plain,(r(elem!1, s(z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(s(s(z)))), s(z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | r(s(z), elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(6646,plain,
% 1.86/2.08 (r(elem!1, s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6645, 4541, 11, 1057, 300, 256, 1123])).
% 1.86/2.08 tff(6647,plain,
% 1.86/2.08 (~r(s(s(s(s(z)))), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1138, 268, 6646, 1099])).
% 1.86/2.08 tff(6648,plain,
% 1.86/2.08 (~r(elem!1, s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[5938, 268, 6646, 11, 1099])).
% 1.86/2.08 tff(6649,plain,
% 1.86/2.08 (r(elem!1, s(z)) <=> r(s(s(s(z))), s(z))),
% 1.86/2.08 inference(symmetry,[status(thm)],[232])).
% 1.86/2.08 tff(6650,plain,
% 1.86/2.08 (r(s(s(s(z))), s(z))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[238, 6649])).
% 1.86/2.08 tff(6651,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[129, 6650])).
% 1.86/2.08 tff(6652,plain,((~(s(s(s(z))) = elem!1)) | r(s(s(s(z))), s(z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(6653,plain,
% 1.86/2.08 (~(s(s(s(z))) = elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6652, 6646, 5882])).
% 1.86/2.08 tff(6654,plain,
% 1.86/2.08 (b(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6351, 6653, 300, 1099, 6646, 256, 4495, 11])).
% 1.86/2.08 tff(6655,plain,
% 1.86/2.08 (b(s(s(s(s(z)))), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[254, 3, 239])).
% 1.86/2.08 tff(6656,plain,
% 1.86/2.08 (b(elem!1, s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1087, 9, 1085])).
% 1.86/2.08 tff(6657,plain,
% 1.86/2.08 (((~![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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6658,plain,
% 1.86/2.08 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6659,plain,
% 1.86/2.08 (((~![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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[6658])).
% 1.86/2.08 tff(6660,plain,
% 1.86/2.08 (((~![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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.08 inference(transitivity,[status(thm)],[6659, 6657])).
% 1.86/2.08 tff(6661,plain,
% 1.86/2.08 ((~![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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(6662,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6661, 6660])).
% 1.86/2.08 tff(6663,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6662, 453, 646, 1780, 6656, 6655, 2497])).
% 1.86/2.08 tff(6664,plain,((s(s(s(s(z)))) = elem!1) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | r(elem!1, s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(6665,plain,
% 1.86/2.08 (s(s(s(s(z)))) = elem!1),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6664, 6654, 5914, 5912, 6648, 6647])).
% 1.86/2.08 tff(6666,plain,
% 1.86/2.08 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), elem!1)),
% 1.86/2.08 inference(monotonicity,[status(thm)],[6665])).
% 1.86/2.08 tff(6667,plain,
% 1.86/2.08 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.08 inference(symmetry,[status(thm)],[6666])).
% 1.86/2.08 tff(6668,plain,
% 1.86/2.08 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[6667])).
% 1.86/2.08 tff(6669,plain,
% 1.86/2.08 (r(s(s(s(s(s(s(z)))))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[1172])).
% 1.86/2.08 tff(6670,plain,
% 1.86/2.08 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.08 inference(symmetry,[status(thm)],[6669])).
% 1.86/2.08 tff(6671,assumption,(~r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.86/2.08 tff(6672,plain,
% 1.86/2.08 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.86/2.08 inference(symmetry,[status(thm)],[1172])).
% 1.86/2.08 tff(6673,plain,
% 1.86/2.08 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[6672])).
% 1.86/2.08 tff(6674,plain,
% 1.86/2.08 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[6673])).
% 1.86/2.08 tff(6675,plain,
% 1.86/2.08 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[6674, 1307])).
% 1.86/2.08 tff(6676,plain,
% 1.86/2.08 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.86/2.08 inference(symmetry,[status(thm)],[6675])).
% 1.86/2.08 tff(6677,plain,
% 1.86/2.08 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[6676])).
% 1.86/2.08 tff(6678,plain,
% 1.86/2.08 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1273, 1170])).
% 1.86/2.08 tff(6679,plain,
% 1.86/2.08 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1436, 6678])).
% 1.86/2.08 tff(6680,plain,
% 1.86/2.08 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6679, 6677])).
% 1.86/2.08 tff(6681,plain,
% 1.86/2.08 (~(elem!1 = s(s(elem!1)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[4223, 6680])).
% 1.86/2.08 tff(6682,plain,
% 1.86/2.08 (~(s(s(elem!1)) = elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3359, 6681])).
% 1.86/2.08 tff(6683,plain,
% 1.86/2.08 (b(s(s(elem!1)), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2240, 6682, 6671])).
% 1.86/2.08 tff(6684,plain,
% 1.86/2.08 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(elem!1))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[1171])).
% 1.86/2.08 tff(6685,plain,
% 1.86/2.08 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[1170])).
% 1.86/2.08 tff(6686,plain,
% 1.86/2.08 (b(elem!1, s(s(s(s(s(z))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[2497, 6685])).
% 1.86/2.08 tff(6687,plain,
% 1.86/2.08 (b(elem!1, s(elem!1))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6686, 6684])).
% 1.86/2.08 tff(6688,plain,
% 1.86/2.08 (((~![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(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6689,plain,
% 1.86/2.08 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6690,plain,
% 1.86/2.08 (((~![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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[6689])).
% 1.86/2.08 tff(6691,plain,
% 1.86/2.08 (((~![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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.86/2.08 inference(transitivity,[status(thm)],[6690, 6688])).
% 1.86/2.08 tff(6692,plain,
% 1.86/2.08 ((~![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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(6693,plain,
% 1.86/2.08 ((~![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(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6692, 6691])).
% 1.86/2.08 tff(6694,plain,
% 1.86/2.08 (~b(s(s(elem!1)), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6693, 453, 499, 6687, 6683])).
% 1.86/2.08 tff(6695,plain,
% 1.86/2.08 (r(s(s(elem!1)), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1047, 6694])).
% 1.86/2.08 tff(6696,plain,
% 1.86/2.08 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6695, 6670])).
% 1.86/2.08 tff(6697,plain,
% 1.86/2.08 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(elem!1), s(z))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[1171])).
% 1.86/2.08 tff(6698,plain,
% 1.86/2.08 (r(s(elem!1), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.86/2.08 inference(symmetry,[status(thm)],[6697])).
% 1.86/2.08 tff(6699,plain,
% 1.86/2.08 (b(s(elem!1), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1336, 1170, 646])).
% 1.86/2.08 tff(6700,plain,
% 1.86/2.08 (((~![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(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), 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(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6701,plain,
% 1.86/2.08 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6702,plain,
% 1.86/2.08 (((~![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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[6701])).
% 1.86/2.08 tff(6703,plain,
% 1.86/2.08 (((~![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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)))),
% 1.86/2.08 inference(transitivity,[status(thm)],[6702, 6700])).
% 1.86/2.08 tff(6704,plain,
% 1.86/2.08 ((~![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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(6705,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6704, 6703])).
% 1.86/2.08 tff(6706,plain,
% 1.86/2.08 (~b(s(elem!1), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6705, 453, 499, 6699, 6687])).
% 1.86/2.08 tff(6707,plain,
% 1.86/2.08 (r(s(elem!1), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[353, 1182, 6706])).
% 1.86/2.08 tff(6708,plain,
% 1.86/2.08 (r(s(s(s(s(s(z))))), s(z))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6707, 6698])).
% 1.86/2.08 tff(6709,plain,
% 1.86/2.08 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[1171, 1172])).
% 1.86/2.08 tff(6710,plain,
% 1.86/2.08 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.86/2.08 inference(symmetry,[status(thm)],[6709])).
% 1.86/2.08 tff(6711,plain,
% 1.86/2.08 (~(s(elem!1) = s(s(elem!1)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1861, 6681])).
% 1.86/2.08 tff(6712,plain,
% 1.86/2.08 (~b(s(elem!1), s(s(elem!1)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1079, 6683, 6687, 6699])).
% 1.86/2.08 tff(6713,plain,
% 1.86/2.08 (r(s(elem!1), s(s(elem!1)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[440, 6712, 6711])).
% 1.86/2.08 tff(6714,plain,
% 1.86/2.08 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6713, 6710])).
% 1.86/2.08 tff(6715,plain,
% 1.86/2.08 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[4805, 6714, 6708])).
% 1.86/2.08 tff(6716,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6715, 6696])).
% 1.86/2.08 tff(6717,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(s(z), elem!1)) | r(s(s(elem!1)), elem!1) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(6718,plain,
% 1.86/2.08 (r(s(s(elem!1)), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6717, 6665, 4542, 5912, 6654])).
% 1.86/2.08 tff(6719,plain,
% 1.86/2.08 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[5213, 869, 1545])).
% 1.86/2.08 tff(6720,plain,
% 1.86/2.08 (b(s(s(s(z))), s(s(elem!1)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[5203, 6719, 555])).
% 1.86/2.08 tff(6721,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[5195, 453, 499, 2223, 6720, 120])).
% 1.86/2.08 tff(6722,plain,((~r(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(6723,plain,
% 1.86/2.08 (~r(s(s(s(z))), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6722, 6718, 5883, 4877, 4542, 6646])).
% 1.86/2.08 tff(6724,plain,
% 1.86/2.08 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6723, 6668])).
% 1.86/2.08 tff(6725,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[300, 6724])).
% 1.86/2.08 tff(6726,plain,(r(s(z), elem!1) | (~r(s(s(s(z))), s(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))))) | b(s(s(s(s(z)))), s(z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(6727,plain,
% 1.86/2.08 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6726, 5881, 300, 4541, 1057, 1123])).
% 1.86/2.08 tff(6728,plain,
% 1.86/2.08 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[687, 6727])).
% 1.86/2.08 tff(6729,plain,
% 1.86/2.08 (b(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6728, 5879])).
% 1.86/2.08 tff(6730,plain,
% 1.86/2.08 ((s(s(s(z))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[5878])).
% 1.86/2.08 tff(6731,plain,
% 1.86/2.08 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.86/2.08 inference(transitivity,[status(thm)],[6730, 144])).
% 1.86/2.08 tff(6732,plain,
% 1.86/2.08 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[6731])).
% 1.86/2.08 tff(6733,plain,
% 1.86/2.08 (~(s(s(z)) = elem!1)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[160, 6732])).
% 1.86/2.08 tff(6734,plain,
% 1.86/2.08 (r(s(s(s(s(z)))), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[254, 249, 5504])).
% 1.86/2.08 tff(6735,plain,
% 1.86/2.08 (s(elem!1) = s(s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[81, 5878])).
% 1.86/2.08 tff(6736,plain,
% 1.86/2.08 (r(s(z), s(s(s(z)))) <=> r(s(z), elem!1)),
% 1.86/2.08 inference(monotonicity,[status(thm)],[5878])).
% 1.86/2.08 tff(6737,plain,
% 1.86/2.08 (r(s(z), elem!1) <=> r(s(z), s(s(s(z))))),
% 1.86/2.08 inference(symmetry,[status(thm)],[6736])).
% 1.86/2.08 tff(6738,plain,
% 1.86/2.08 ((~r(s(z), elem!1)) <=> (~r(s(z), s(s(s(z)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[6737])).
% 1.86/2.08 tff(6739,plain,
% 1.86/2.08 (~r(s(z), s(s(s(z))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[4541, 6738])).
% 1.86/2.08 tff(6740,plain,
% 1.86/2.08 (r(s(s(s(z))), elem!1) <=> r(elem!1, elem!1)),
% 1.86/2.08 inference(monotonicity,[status(thm)],[5878])).
% 1.86/2.08 tff(6741,plain,
% 1.86/2.08 (r(elem!1, elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.86/2.08 inference(symmetry,[status(thm)],[6740])).
% 1.86/2.08 tff(6742,plain,
% 1.86/2.08 ((~r(elem!1, elem!1)) <=> (~r(s(s(s(z))), elem!1))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[6741])).
% 1.86/2.08 tff(6743,plain,
% 1.86/2.08 (^[X: $i] : refl((~r(X, X)) <=> (~r(X, X)))),
% 1.86/2.08 inference(bind,[status(th)],[])).
% 1.86/2.08 tff(6744,plain,
% 1.86/2.08 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.86/2.08 inference(quant_intro,[status(thm)],[6743])).
% 1.86/2.08 tff(6745,plain,
% 1.86/2.08 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6746,axiom,(![X: $i] : (~r(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ri')).
% 1.86/2.08 tff(6747,plain,
% 1.86/2.08 (![X: $i] : (~r(X, X))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6746, 6745])).
% 1.86/2.08 tff(6748,plain,(
% 1.86/2.08 ![X: $i] : (~r(X, X))),
% 1.86/2.08 inference(skolemize,[status(sab)],[6747])).
% 1.86/2.08 tff(6749,plain,
% 1.86/2.08 (![X: $i] : (~r(X, X))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6748, 6744])).
% 1.86/2.08 tff(6750,plain,
% 1.86/2.08 ((~![X: $i] : (~r(X, X))) | (~r(elem!1, elem!1))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(6751,plain,
% 1.86/2.08 (~r(elem!1, elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6750, 6749])).
% 1.86/2.08 tff(6752,plain,
% 1.86/2.08 (~r(s(s(s(z))), elem!1)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6751, 6742])).
% 1.86/2.08 tff(6753,plain,
% 1.86/2.08 (b(s(z), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[227, 222])).
% 1.86/2.08 tff(6754,plain,
% 1.86/2.08 (b(elem!1, s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1130, 1123, 2076])).
% 1.86/2.08 tff(6755,plain,
% 1.86/2.08 (~(s(s(s(elem!1))) = elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6409, 6754, 6399])).
% 1.86/2.08 tff(6756,plain,
% 1.86/2.08 (b(s(s(s(elem!1))), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[567, 6755, 563])).
% 1.86/2.08 tff(6757,plain,
% 1.86/2.08 (((~![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))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6758,plain,
% 1.86/2.08 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6759,plain,
% 1.86/2.08 (((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[6758])).
% 1.86/2.08 tff(6760,plain,
% 1.86/2.08 (((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.08 inference(transitivity,[status(thm)],[6759, 6757])).
% 1.86/2.08 tff(6761,plain,
% 1.86/2.08 ((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(6762,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6761, 6760])).
% 1.86/2.08 tff(6763,plain,
% 1.86/2.08 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6762, 453, 6754, 6756, 646])).
% 1.86/2.08 tff(6764,plain,
% 1.86/2.08 ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[2025])).
% 1.86/2.08 tff(6765,assumption,(~b(s(s(s(s(s(z))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.86/2.08 tff(6766,plain,
% 1.86/2.08 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6765, 6764])).
% 1.86/2.08 tff(6767,plain,
% 1.86/2.08 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[675, 2218, 6766])).
% 1.86/2.08 tff(6768,plain,
% 1.86/2.08 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6767, 2023])).
% 1.86/2.09 tff(6769,plain,
% 1.86/2.09 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6768, 2022])).
% 1.86/2.09 tff(6770,plain,
% 1.86/2.09 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[834, 4561])).
% 1.86/2.09 tff(6771,plain,
% 1.86/2.09 (r(s(z), elem!1) <=> r(s(z), s(s(s(z))))),
% 1.86/2.09 inference(symmetry,[status(thm)],[220])).
% 1.86/2.09 tff(6772,plain,
% 1.86/2.09 (r(s(z), s(s(s(z))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[701, 6771])).
% 1.86/2.09 tff(6773,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[222, 6772])).
% 1.86/2.09 tff(6774,plain,((~r(s(z), elem!1)) | r(s(z), s(s(s(z)))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(6775,plain,
% 1.86/2.09 (~r(s(z), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6774, 76, 222])).
% 1.86/2.09 tff(6776,plain,
% 1.86/2.09 (b(s(z), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[506, 6775, 492])).
% 1.86/2.09 tff(6777,plain,
% 1.86/2.09 (~b(s(s(s(s(s(z))))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[5329, 453, 6776, 2077, 646])).
% 1.86/2.09 tff(6778,plain,
% 1.86/2.09 (r(s(s(s(s(s(z))))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[297, 6777])).
% 1.86/2.09 tff(6779,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[4803, 268, 6778, 6770, 6769])).
% 1.86/2.09 tff(6780,plain,((~(s(s(s(z))) = elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | (s(z) = elem!1) | r(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(6781,plain,
% 1.86/2.09 (~(s(s(s(z))) = elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6780, 6754, 646, 6400, 6763, 4495, 222])).
% 1.86/2.09 tff(6782,plain,
% 1.86/2.09 (b(s(s(s(z))), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[74, 6781, 2])).
% 1.86/2.09 tff(6783,plain,
% 1.86/2.09 (((~![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(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(6784,plain,
% 1.86/2.09 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(6785,plain,
% 1.86/2.09 (((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6784])).
% 1.86/2.09 tff(6786,plain,
% 1.86/2.09 (((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.09 inference(transitivity,[status(thm)],[6785, 6783])).
% 1.86/2.09 tff(6787,plain,
% 1.86/2.09 ((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(6788,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6787, 6786])).
% 1.86/2.09 tff(6789,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6788, 453, 6754, 6782, 646, 1779])).
% 1.86/2.09 tff(6790,plain,((elem!1 = s(z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | r(s(s(s(z))), elem!1) | r(s(z), s(s(s(z)))) | r(s(s(s(elem!1))), elem!1) | b(s(s(s(elem!1))), s(z)) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(6791,plain,
% 1.86/2.09 (elem!1 = s(z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6790, 6399, 1779, 2, 222, 563, 646, 2076])).
% 1.86/2.09 tff(6792,plain,
% 1.86/2.09 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6791])).
% 1.86/2.09 tff(6793,plain,
% 1.86/2.09 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 1.86/2.09 inference(symmetry,[status(thm)],[6792])).
% 1.86/2.09 tff(6794,plain,
% 1.86/2.09 (r(s(s(s(elem!1))), elem!1)),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6400, 6793])).
% 1.86/2.09 tff(6795,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[563, 6794])).
% 1.86/2.09 tff(6796,plain,(b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), elem!1) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | r(s(s(s(z))), elem!1) | r(s(z), s(s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(6797,plain,
% 1.86/2.09 (b(s(s(s(elem!1))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6796, 646, 1779, 2, 222, 563, 2076])).
% 1.86/2.09 tff(6798,plain,
% 1.86/2.09 (~(elem!1 = s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1112, 6797, 1057])).
% 1.86/2.09 tff(6799,plain,
% 1.86/2.09 (b(elem!1, s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1130, 6798, 2076])).
% 1.86/2.09 tff(6800,plain,
% 1.86/2.09 (((~![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(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(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))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(6801,plain,
% 1.86/2.09 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(6802,plain,
% 1.86/2.09 (((~![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(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6801])).
% 1.86/2.09 tff(6803,plain,
% 1.86/2.09 (((~![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(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[6802, 6800])).
% 1.86/2.09 tff(6804,plain,
% 1.86/2.09 ((~![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(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(6805,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6804, 6803])).
% 1.86/2.09 tff(6806,plain,
% 1.86/2.09 (~b(s(s(s(elem!1))), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6805, 453, 2077, 1110, 2090])).
% 1.86/2.09 tff(6807,plain,
% 1.86/2.09 (s(s(s(elem!1))) = elem!1),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[567, 6806, 563])).
% 1.86/2.09 tff(6808,plain,
% 1.86/2.09 (~(s(s(s(z))) = elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[199, 6807, 197])).
% 1.86/2.09 tff(6809,plain,
% 1.86/2.09 (b(s(s(s(z))), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[74, 6808, 2])).
% 1.86/2.09 tff(6810,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6788, 453, 2077, 6809, 646, 1779])).
% 1.86/2.09 tff(6811,plain,((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | r(s(s(s(z))), elem!1) | (s(elem!1) = s(z)) | r(s(s(s(elem!1))), elem!1) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(6812,plain,
% 1.86/2.09 (s(elem!1) = s(z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6811, 6799, 1779, 2, 646, 563, 6797, 6753])).
% 1.86/2.09 tff(6813,plain,
% 1.86/2.09 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6812])).
% 1.86/2.09 tff(6814,plain,
% 1.86/2.09 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.86/2.09 inference(symmetry,[status(thm)],[6813])).
% 1.86/2.09 tff(6815,plain,
% 1.86/2.09 (z = elem!1),
% 1.86/2.09 inference(transitivity,[status(thm)],[4921, 6814, 85])).
% 1.86/2.09 tff(6816,plain,
% 1.86/2.09 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6815])).
% 1.86/2.09 tff(6817,plain,
% 1.86/2.09 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.86/2.09 inference(symmetry,[status(thm)],[6816])).
% 1.86/2.09 tff(6818,plain,
% 1.86/2.09 (b(z, s(z))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6799, 6817])).
% 1.86/2.09 tff(6819,plain,
% 1.86/2.09 (elem!1 = z),
% 1.86/2.09 inference(transitivity,[status(thm)],[86, 6813, 32])).
% 1.86/2.09 tff(6820,plain,
% 1.86/2.09 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6819])).
% 1.86/2.09 tff(6821,plain,
% 1.86/2.09 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), z)),
% 1.86/2.09 inference(monotonicity,[status(thm)],[5032, 5035])).
% 1.86/2.09 tff(6822,plain,
% 1.86/2.09 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.86/2.09 inference(symmetry,[status(thm)],[6821])).
% 1.86/2.09 tff(6823,plain,
% 1.86/2.09 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 1.86/2.09 inference(monotonicity,[status(thm)],[5035])).
% 1.86/2.09 tff(6824,plain,
% 1.86/2.09 (s(z) = s(elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[179, 175])).
% 1.86/2.09 tff(6825,plain,
% 1.86/2.09 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[171, 6824])).
% 1.86/2.09 tff(6826,plain,
% 1.86/2.09 (~(s(s(s(z))) = elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[81, 6825])).
% 1.86/2.09 tff(6827,plain,
% 1.86/2.09 (b(s(s(s(z))), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[74, 6826, 2])).
% 1.86/2.09 tff(6828,plain,
% 1.86/2.09 (b(s(s(s(z))), z)),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6827, 6823])).
% 1.86/2.09 tff(6829,plain,
% 1.86/2.09 (b(s(s(s(elem!1))), elem!1)),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6828, 6822])).
% 1.86/2.09 tff(6830,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3333, 6829])).
% 1.86/2.09 tff(6831,plain,((~(s(elem!1) = s(z))) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(6832,plain,
% 1.86/2.09 (b(s(s(s(elem!1))), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6831, 6812, 2])).
% 1.86/2.09 tff(6833,plain,
% 1.86/2.09 (s(z) = s(elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[179, 6812])).
% 1.86/2.09 tff(6834,plain,
% 1.86/2.09 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.86/2.09 inference(symmetry,[status(thm)],[4982])).
% 1.86/2.09 tff(6835,plain,
% 1.86/2.09 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6834])).
% 1.86/2.09 tff(6836,plain,
% 1.86/2.09 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.86/2.09 inference(symmetry,[status(thm)],[6835])).
% 1.86/2.09 tff(6837,plain,
% 1.86/2.09 (b(s(s(s(z))), elem!1)),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[572, 6836])).
% 1.86/2.09 tff(6838,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[58, 6837])).
% 1.86/2.09 tff(6839,plain,(b(s(s(s(z))), elem!1) | (~b(s(s(s(elem!1))), elem!1)) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(6840,plain,
% 1.86/2.09 (b(s(s(s(z))), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6839, 6833, 6832])).
% 1.86/2.09 tff(6841,plain,
% 1.86/2.09 (b(s(s(s(z))), z)),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6840, 6820])).
% 1.86/2.09 tff(6842,plain,
% 1.86/2.09 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6812])).
% 1.86/2.09 tff(6843,plain,
% 1.86/2.09 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[4982, 163])).
% 1.86/2.09 tff(6844,plain,
% 1.86/2.09 (b(s(s(s(z))), s(elem!1))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[1110, 6843])).
% 1.86/2.09 tff(6845,assumption,(~b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.86/2.09 tff(6846,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6845, 6844])).
% 1.86/2.09 tff(6847,plain,((~b(s(s(s(elem!1))), s(z))) | b(s(s(s(z))), s(elem!1)) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(6848,plain,
% 1.86/2.09 (b(s(s(s(z))), s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6847, 6833, 6797])).
% 1.86/2.09 tff(6849,plain,
% 1.86/2.09 (b(s(s(s(z))), s(z))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6848, 6842])).
% 1.86/2.09 tff(6850,plain,
% 1.86/2.09 (((~![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(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))), z)) | (~b(z, s(z))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(6851,plain,
% 1.86/2.09 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(6852,plain,
% 1.86/2.09 (((~![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(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z)))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6851])).
% 1.86/2.09 tff(6853,plain,
% 1.86/2.09 (((~![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(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[6852, 6850])).
% 1.86/2.09 tff(6854,plain,
% 1.86/2.09 ((~![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(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)))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(6855,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z)))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6854, 6853])).
% 1.86/2.09 tff(6856,plain,
% 1.86/2.09 (~b(z, s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6855, 453, 6849, 6841, 6753])).
% 1.86/2.09 tff(6857,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6856, 6818])).
% 1.86/2.09 tff(6858,plain,((~b(s(s(s(s(s(z))))), elem!1)) | r(s(s(s(z))), elem!1) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | r(s(s(s(elem!1))), elem!1) | r(elem!1, s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(6859,plain,
% 1.86/2.09 (r(s(s(s(elem!1))), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6858, 6729, 1057, 2076, 6752, 6728, 6739])).
% 1.86/2.09 tff(6860,plain,
% 1.86/2.09 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[992, 6859, 6735])).
% 1.86/2.09 tff(6861,plain,
% 1.86/2.09 (~(s(s(z)) = s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[818, 5878])).
% 1.86/2.09 tff(6862,plain,
% 1.86/2.09 (s(s(s(s(z)))) = s(elem!1)),
% 1.86/2.09 inference(symmetry,[status(thm)],[6735])).
% 1.86/2.09 tff(6863,plain,
% 1.86/2.09 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6862])).
% 1.86/2.09 tff(6864,plain,
% 1.86/2.09 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.86/2.09 inference(symmetry,[status(thm)],[6863])).
% 1.86/2.09 tff(6865,plain,
% 1.86/2.09 ((~(s(s(s(s(s(s(z)))))) = s(elem!1))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6864])).
% 1.86/2.09 tff(6866,plain,
% 1.86/2.09 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6735])).
% 1.86/2.09 tff(6867,plain,
% 1.86/2.09 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6866])).
% 1.86/2.09 tff(6868,plain,
% 1.86/2.09 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.86/2.09 inference(symmetry,[status(thm)],[6867])).
% 1.86/2.09 tff(6869,plain,
% 1.86/2.09 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6868, 6735])).
% 1.86/2.09 tff(6870,plain,
% 1.86/2.09 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.86/2.09 inference(symmetry,[status(thm)],[6869])).
% 1.86/2.09 tff(6871,plain,
% 1.86/2.09 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(s(z)))))) = s(elem!1)))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6870])).
% 1.86/2.09 tff(6872,plain,
% 1.86/2.09 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6514, 6871])).
% 1.86/2.09 tff(6873,plain,
% 1.86/2.09 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6872, 6865])).
% 1.86/2.09 tff(6874,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(6875,plain,
% 1.86/2.09 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(6876,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6875])).
% 1.86/2.09 tff(6877,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[6876, 6874])).
% 1.86/2.09 tff(6878,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(6879,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6878, 6877])).
% 1.86/2.09 tff(6880,plain,
% 1.86/2.09 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6879, 268, 1099, 6734, 6860])).
% 1.86/2.09 tff(6881,plain,
% 1.86/2.09 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2210, 69, 6880])).
% 1.86/2.09 tff(6882,plain,
% 1.86/2.09 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6881, 6873])).
% 1.86/2.09 tff(6883,plain,
% 1.86/2.09 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(elem!1) = s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6862])).
% 1.86/2.09 tff(6884,plain,
% 1.86/2.09 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 1.86/2.09 inference(transitivity,[status(thm)],[6883, 533])).
% 1.86/2.09 tff(6885,plain,
% 1.86/2.09 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(symmetry,[status(thm)],[6884])).
% 1.86/2.09 tff(6886,plain,
% 1.86/2.09 ((~(s(s(s(s(s(s(z)))))) = s(elem!1))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6885])).
% 1.86/2.09 tff(6887,plain,
% 1.86/2.09 (~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6872, 6886])).
% 1.86/2.09 tff(6888,plain,
% 1.86/2.09 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[4419, 268, 6734, 6860])).
% 1.86/2.09 tff(6889,plain,
% 1.86/2.09 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[591, 69, 6888])).
% 1.86/2.09 tff(6890,plain,
% 1.86/2.09 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6889, 6887])).
% 1.86/2.09 tff(6891,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.86/2.09 tff(6892,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.86/2.09 tff(6893,plain,
% 1.86/2.09 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2058, 268, 700, 1159])).
% 1.86/2.09 tff(6894,plain,
% 1.86/2.09 (b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[795, 69, 153, 6893])).
% 1.86/2.09 tff(6895,plain,
% 1.86/2.09 (((~![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(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(6896,plain,
% 1.86/2.09 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(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(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6897,plain,
% 1.86/2.10 (((~![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(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6896])).
% 1.86/2.10 tff(6898,plain,
% 1.86/2.10 (((~![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(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[6897, 6895])).
% 1.86/2.10 tff(6899,plain,
% 1.86/2.10 ((~![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(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(6900,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[6899, 6898])).
% 1.86/2.10 tff(6901,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6900, 453, 6894, 6892, 6891, 1006])).
% 1.86/2.10 tff(6902,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (s(s(z)) = s(s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(6903,plain,
% 1.86/2.10 (~r(s(s(z)), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6902, 6890, 6882, 6861, 6860, 6734])).
% 1.86/2.10 tff(6904,plain,
% 1.86/2.10 (b(s(s(z)), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[782, 6903, 6733])).
% 1.86/2.10 tff(6905,plain,
% 1.86/2.10 (((~![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(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6906,plain,
% 1.86/2.10 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6907,plain,
% 1.86/2.10 (((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6906])).
% 1.86/2.10 tff(6908,plain,
% 1.86/2.10 (((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.86/2.10 inference(transitivity,[status(thm)],[6907, 6905])).
% 1.86/2.10 tff(6909,plain,
% 1.86/2.10 ((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(6910,plain,
% 1.86/2.10 ((~![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(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[6909, 6908])).
% 1.86/2.10 tff(6911,plain,
% 1.86/2.10 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6910, 453, 5446, 6904, 6729])).
% 1.86/2.10 tff(6912,plain,
% 1.86/2.10 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[768, 69, 52, 6911])).
% 1.86/2.10 tff(6913,plain,
% 1.86/2.10 (~b(s(s(z)), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[5570, 453, 4542, 5446, 6904])).
% 1.86/2.10 tff(6914,plain,
% 1.86/2.10 (r(s(s(z)), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[720, 69, 717, 6913])).
% 1.86/2.10 tff(6915,plain,
% 1.86/2.10 (~b(s(s(s(s(s(z))))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[5329, 453, 4542, 5446, 6729])).
% 1.86/2.10 tff(6916,plain,
% 1.86/2.10 (r(s(s(s(s(s(z))))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[297, 6915])).
% 1.86/2.10 tff(6917,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6918,plain,
% 1.86/2.10 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6919,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6918])).
% 1.86/2.10 tff(6920,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[6919, 6917])).
% 1.86/2.10 tff(6921,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(6922,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[6921, 6920])).
% 1.86/2.10 tff(6923,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6922, 268, 6916, 6914, 6912])).
% 1.86/2.10 tff(6924,plain,(b(s(s(s(s(z)))), elem!1) | b(s(s(s(s(z)))), s(z)) | r(elem!1, s(z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | r(s(z), elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(6925,plain,
% 1.86/2.10 (b(s(s(s(s(z)))), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6924, 2076, 1057, 300, 4541, 1123])).
% 1.86/2.10 tff(6926,plain,
% 1.86/2.10 (~b(s(s(z)), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[5574, 6925, 5446, 1099, 4542])).
% 1.86/2.10 tff(6927,plain,
% 1.86/2.10 (r(s(s(z)), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[782, 6926, 6733])).
% 1.86/2.10 tff(6928,plain,
% 1.86/2.10 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.86/2.10 inference(transitivity,[status(thm)],[206, 56])).
% 1.86/2.10 tff(6929,plain,
% 1.86/2.10 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6928])).
% 1.86/2.10 tff(6930,plain,
% 1.86/2.10 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[111, 6929])).
% 1.86/2.10 tff(6931,plain,
% 1.86/2.10 (r(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[643, 638, 6930])).
% 1.86/2.10 tff(6932,plain,
% 1.86/2.10 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[775, 268, 700, 6931])).
% 1.86/2.10 tff(6933,plain,
% 1.86/2.10 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[768, 69, 52, 6932])).
% 1.86/2.10 tff(6934,assumption,(r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.86/2.10 tff(6935,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6936,plain,
% 1.86/2.10 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6937,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6936])).
% 1.86/2.10 tff(6938,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[6937, 6935])).
% 1.86/2.10 tff(6939,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(6940,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[6939, 6938])).
% 1.86/2.10 tff(6941,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6940, 268, 700, 419, 6934])).
% 1.86/2.10 tff(6942,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(6943,plain,
% 1.86/2.10 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6942, 700, 333])).
% 1.86/2.10 tff(6944,plain,
% 1.86/2.10 ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2370, 69, 6943])).
% 1.86/2.10 tff(6945,plain,
% 1.86/2.10 (b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6944, 6241])).
% 1.86/2.10 tff(6946,plain,
% 1.86/2.10 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[4457, 638, 76])).
% 1.86/2.10 tff(6947,plain,
% 1.86/2.10 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[687, 6946])).
% 1.86/2.10 tff(6948,plain,
% 1.86/2.10 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[309, 6947, 300])).
% 1.86/2.10 tff(6949,plain,
% 1.86/2.10 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[328, 6948])).
% 1.86/2.10 tff(6950,plain,
% 1.86/2.10 (((~![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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6951,plain,
% 1.86/2.10 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6952,plain,
% 1.86/2.10 (((~![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(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6951])).
% 1.86/2.10 tff(6953,plain,
% 1.86/2.10 (((~![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(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[6952, 6950])).
% 1.86/2.10 tff(6954,plain,
% 1.86/2.10 ((~![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(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(6955,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[6954, 6953])).
% 1.86/2.10 tff(6956,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6955, 453, 6949, 299, 6945, 6933])).
% 1.86/2.10 tff(6957,plain,(b(s(s(s(s(s(z))))), elem!1) | (~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(6958,plain,
% 1.86/2.10 (b(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6957, 6925, 6927, 300, 5878])).
% 1.86/2.10 tff(6959,plain,
% 1.86/2.10 (~b(s(s(s(s(s(z))))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[5331, 6958, 4542, 5446])).
% 1.86/2.10 tff(6960,plain,
% 1.86/2.10 (r(s(s(s(s(s(z))))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[297, 6959])).
% 1.86/2.10 tff(6961,plain,
% 1.86/2.10 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2414, 6960, 1099])).
% 1.86/2.10 tff(6962,plain,
% 1.86/2.10 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[328, 6961])).
% 1.86/2.10 tff(6963,plain,
% 1.86/2.10 (((~![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(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6964,plain,
% 1.86/2.10 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6965,plain,
% 1.86/2.10 (((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~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(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6964])).
% 1.86/2.10 tff(6966,plain,
% 1.86/2.10 (((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~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(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.10 inference(transitivity,[status(thm)],[6965, 6963])).
% 1.86/2.10 tff(6967,plain,
% 1.86/2.10 ((~![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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(6968,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[6967, 6966])).
% 1.86/2.10 tff(6969,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6968, 453, 5446, 6958, 6962, 6925])).
% 1.86/2.10 tff(6970,plain,(r(elem!1, s(z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(z)) | r(s(z), elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(6971,plain,
% 1.86/2.10 (r(elem!1, s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6970, 4541, 1057, 300, 1123])).
% 1.86/2.10 tff(6972,plain,
% 1.86/2.10 (~(s(s(s(z))) = elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6652, 6971, 4539])).
% 1.86/2.10 tff(6973,plain,
% 1.86/2.10 (~r(elem!1, s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1596, 268, 6971, 1099])).
% 1.86/2.10 tff(6974,plain,
% 1.86/2.10 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.86/2.10 inference(symmetry,[status(thm)],[6685])).
% 1.86/2.10 tff(6975,plain,
% 1.86/2.10 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.86/2.10 inference(symmetry,[status(thm)],[6684])).
% 1.86/2.10 tff(6976,plain,
% 1.86/2.10 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[6975, 6974])).
% 1.86/2.10 tff(6977,plain,
% 1.86/2.10 ((elem!1 = s(s(s(s(s(z)))))) <=> (elem!1 = s(elem!1))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[1171])).
% 1.86/2.10 tff(6978,plain,
% 1.86/2.10 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(elem!1) = elem!1)),
% 1.86/2.10 inference(transitivity,[status(thm)],[6977, 1027])).
% 1.86/2.10 tff(6979,plain,
% 1.86/2.10 ((elem!1 = s(s(s(s(s(z)))))) <=> (elem!1 = s(elem!1))),
% 1.86/2.10 inference(transitivity,[status(thm)],[6978, 1028])).
% 1.86/2.10 tff(6980,plain,
% 1.86/2.10 ((~(elem!1 = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(elem!1)))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6979])).
% 1.86/2.10 tff(6981,plain,
% 1.86/2.10 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[1541])).
% 1.86/2.10 tff(6982,plain,
% 1.86/2.10 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[319, 6981])).
% 1.86/2.10 tff(6983,plain,
% 1.86/2.10 (~(elem!1 = s(elem!1))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[6982, 6980])).
% 1.86/2.10 tff(6984,plain,
% 1.86/2.10 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 1.86/2.10 inference(transitivity,[status(thm)],[1180, 174])).
% 1.86/2.10 tff(6985,plain,
% 1.86/2.10 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(z) = s(elem!1)))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6984])).
% 1.86/2.10 tff(6986,plain,
% 1.86/2.10 (~(s(z) = s(elem!1))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[289, 6985])).
% 1.86/2.10 tff(6987,plain,
% 1.86/2.10 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), elem!1)),
% 1.86/2.10 inference(monotonicity,[status(thm)],[1170])).
% 1.86/2.10 tff(6988,plain,
% 1.86/2.10 (r(s(s(s(z))), elem!1)),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[300, 6987])).
% 1.86/2.10 tff(6989,plain,
% 1.86/2.10 (~r(s(s(elem!1)), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6722, 6988, 120, 555, 499, 238])).
% 1.86/2.10 tff(6990,plain,
% 1.86/2.10 (b(s(s(elem!1)), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2240, 6682, 6989])).
% 1.86/2.10 tff(6991,plain,
% 1.86/2.10 ((s(elem!1) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[1258])).
% 1.86/2.10 tff(6992,plain,
% 1.86/2.10 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 1.86/2.10 inference(symmetry,[status(thm)],[6991])).
% 1.86/2.10 tff(6993,plain,
% 1.86/2.10 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(elem!1) = s(s(z))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6992])).
% 1.86/2.10 tff(6994,plain,
% 1.86/2.10 (~(s(elem!1) = s(s(z)))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[52, 6993])).
% 1.86/2.10 tff(6995,plain,
% 1.86/2.10 ((s(s(s(s(z)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[1170])).
% 1.86/2.10 tff(6996,plain,
% 1.86/2.10 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.86/2.10 inference(transitivity,[status(thm)],[6995, 144])).
% 1.86/2.10 tff(6997,plain,
% 1.86/2.10 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6996])).
% 1.86/2.10 tff(6998,plain,
% 1.86/2.10 (~(s(s(z)) = elem!1)),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[153, 6997])).
% 1.86/2.10 tff(6999,plain,
% 1.86/2.10 (r(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[643, 638, 1544])).
% 1.86/2.10 tff(7000,plain,
% 1.86/2.10 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1566, 6999, 1545])).
% 1.86/2.11 tff(7001,plain,
% 1.86/2.11 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[687, 7000])).
% 1.86/2.11 tff(7002,plain,
% 1.86/2.11 ((~(elem!1 = s(s(s(s(s(z))))))) <=> (~(s(elem!1) = elem!1))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[6978])).
% 1.86/2.11 tff(7003,plain,
% 1.86/2.11 (~(s(elem!1) = elem!1)),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[6982, 7002])).
% 1.86/2.11 tff(7004,plain,
% 1.86/2.11 (b(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[629, 1332])).
% 1.86/2.11 tff(7005,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[638, 7004])).
% 1.86/2.11 tff(7006,plain,((~b(s(elem!1), elem!1)) | b(s(s(s(s(s(z))))), elem!1) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(7007,plain,
% 1.86/2.11 (~b(s(elem!1), elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7006, 638, 1170])).
% 1.86/2.11 tff(7008,plain,
% 1.86/2.11 (r(s(elem!1), elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2440, 7007, 7003])).
% 1.86/2.11 tff(7009,assumption,(r(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.86/2.11 tff(7010,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(7011,plain,
% 1.86/2.11 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(7012,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[7011])).
% 1.86/2.11 tff(7013,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 1.86/2.11 inference(transitivity,[status(thm)],[7012, 7010])).
% 1.86/2.11 tff(7014,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(7015,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[7014, 7013])).
% 1.86/2.11 tff(7016,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7015, 268, 1892, 1545, 7009])).
% 1.86/2.11 tff(7017,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(7018,plain,
% 1.86/2.11 (~r(s(s(s(z))), s(elem!1))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7017, 7008, 1545])).
% 1.86/2.11 tff(7019,plain,
% 1.86/2.11 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[1258])).
% 1.86/2.11 tff(7020,plain,
% 1.86/2.11 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(elem!1))),
% 1.86/2.11 inference(symmetry,[status(thm)],[7019])).
% 1.86/2.11 tff(7021,plain,
% 1.86/2.11 (r(s(s(s(z))), s(elem!1))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[4621, 7020])).
% 1.86/2.11 tff(7022,assumption,(~r(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.86/2.11 tff(7023,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7022, 7021])).
% 1.86/2.11 tff(7024,plain,(r(s(s(s(z))), s(elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(7025,plain,
% 1.86/2.11 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7024, 7018, 1170])).
% 1.86/2.11 tff(7026,plain,
% 1.86/2.11 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2570, 7025])).
% 1.86/2.11 tff(7027,plain,
% 1.86/2.11 (~b(s(z), s(s(s(s(s(z))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2619, 2611, 120, 1779])).
% 1.86/2.11 tff(7028,plain,
% 1.86/2.11 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(elem!1))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[1171])).
% 1.86/2.11 tff(7029,plain,
% 1.86/2.11 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.86/2.11 inference(symmetry,[status(thm)],[7028])).
% 1.86/2.11 tff(7030,plain,
% 1.86/2.11 (b(s(z), s(s(s(s(s(z))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[1549, 7029])).
% 1.86/2.11 tff(7031,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[366, 7030])).
% 1.86/2.11 tff(7032,plain,((~b(s(z), s(elem!1))) | b(s(z), s(s(s(s(s(z)))))) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(7033,plain,
% 1.86/2.11 (~b(s(z), s(elem!1))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7032, 7027, 1170])).
% 1.86/2.11 tff(7034,plain,
% 1.86/2.11 (r(s(z), s(elem!1))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[397, 7033, 6986])).
% 1.86/2.11 tff(7035,plain,
% 1.86/2.11 (~r(elem!1, s(elem!1))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1496, 7034, 238])).
% 1.86/2.11 tff(7036,plain,
% 1.86/2.11 (b(elem!1, s(elem!1))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1069, 7035, 6983])).
% 1.86/2.11 tff(7037,plain,
% 1.86/2.11 (((~![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(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(7038,plain,
% 1.86/2.11 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(7039,plain,
% 1.86/2.11 (((~![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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), 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(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[7038])).
% 1.86/2.11 tff(7040,plain,
% 1.86/2.11 (((~![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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), 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(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.11 inference(transitivity,[status(thm)],[7039, 7037])).
% 1.86/2.11 tff(7041,plain,
% 1.86/2.11 ((~![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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(7042,plain,
% 1.86/2.11 ((~![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(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[7041, 7040])).
% 1.86/2.11 tff(7043,plain,
% 1.86/2.11 (~b(s(s(z)), s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7042, 453, 7036, 909, 922])).
% 1.86/2.11 tff(7044,plain,
% 1.86/2.11 (r(s(s(z)), s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[4239, 69, 1189, 7043])).
% 1.86/2.11 tff(7045,plain,
% 1.86/2.11 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(elem!1))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[1171])).
% 1.86/2.11 tff(7046,plain,
% 1.86/2.11 (b(s(s(s(z))), s(elem!1))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[2611, 7045])).
% 1.86/2.11 tff(7047,plain,
% 1.86/2.11 (((~![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(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(7048,plain,
% 1.86/2.11 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(7049,plain,
% 1.86/2.11 (((~![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(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[7048])).
% 1.86/2.11 tff(7050,plain,
% 1.86/2.11 (((~![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(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.11 inference(transitivity,[status(thm)],[7049, 7047])).
% 1.86/2.11 tff(7051,plain,
% 1.86/2.11 ((~![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(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(7052,plain,
% 1.86/2.11 ((~![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(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[7051, 7050])).
% 1.86/2.11 tff(7053,plain,
% 1.86/2.11 (~b(s(s(z)), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7052, 453, 499, 7036, 7046, 922, 2090])).
% 1.86/2.11 tff(7054,plain,
% 1.86/2.11 (r(s(s(z)), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[720, 69, 717, 7053])).
% 1.86/2.11 tff(7055,plain,
% 1.86/2.11 (((~![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(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), 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(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(7056,plain,
% 1.86/2.11 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(7057,plain,
% 1.86/2.11 (((~![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(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z)))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[7056])).
% 1.86/2.11 tff(7058,plain,
% 1.86/2.11 (((~![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(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[7057, 7055])).
% 1.86/2.11 tff(7059,plain,
% 1.86/2.11 ((~![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(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(7060,plain,
% 1.86/2.11 ((~![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(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(z)))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[7059, 7058])).
% 1.86/2.11 tff(7061,plain,
% 1.86/2.11 (~b(s(s(elem!1)), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7060, 453, 499, 7036, 909, 7046, 2090])).
% 1.86/2.11 tff(7062,plain,
% 1.86/2.11 (r(s(s(elem!1)), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1047, 7061])).
% 1.86/2.11 tff(7063,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(7064,plain,
% 1.86/2.11 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(7065,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[7064])).
% 1.86/2.11 tff(7066,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[7065, 7063])).
% 1.86/2.11 tff(7067,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(7068,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[7067, 7066])).
% 1.86/2.11 tff(7069,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7068, 268, 7062, 7054, 7044])).
% 1.86/2.11 tff(7070,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~(s(s(s(s(z)))) = elem!1)) | (~r(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(7071,plain,
% 1.86/2.11 (~b(s(s(z)), elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7070, 7026, 909, 499, 2090, 1170, 238, 120, 7001])).
% 1.86/2.11 tff(7072,plain,
% 1.86/2.11 (r(s(s(z)), elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[782, 7071, 6998])).
% 1.86/2.11 tff(7073,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(7074,plain,
% 1.86/2.11 (((~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(7075,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[7074])).
% 1.86/2.11 tff(7076,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[7075, 7073])).
% 1.86/2.11 tff(7077,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(7078,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[7077, 7076])).
% 1.86/2.11 tff(7079,plain,
% 1.86/2.11 (~r(s(elem!1), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7078, 268, 7008, 7072])).
% 1.86/2.11 tff(7080,plain,
% 1.86/2.11 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(7081,plain,
% 1.86/2.11 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(7082,plain,
% 1.86/2.11 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z)))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[7081, 7080])).
% 1.86/2.11 tff(7083,plain,
% 1.86/2.11 ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7082, 69, 7079])).
% 1.86/2.11 tff(7084,plain,
% 1.86/2.11 (b(s(elem!1), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7083, 6994])).
% 1.86/2.11 tff(7085,plain,
% 1.86/2.11 (~r(s(s(s(z))), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[5861, 268, 7072, 1545])).
% 1.86/2.11 tff(7086,plain,
% 1.86/2.11 (b(s(s(s(z))), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2534, 69, 160, 7085])).
% 1.86/2.11 tff(7087,plain,
% 1.86/2.11 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[5719, 268, 7072, 1545])).
% 1.86/2.11 tff(7088,plain,
% 1.86/2.11 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1350, 69, 7087])).
% 1.86/2.11 tff(7089,plain,
% 1.86/2.11 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7088, 1243])).
% 1.86/2.11 tff(7090,plain,
% 1.86/2.11 (b(s(elem!1), s(s(s(z))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[7001, 1546])).
% 1.86/2.11 tff(7091,plain,
% 1.86/2.11 (b(s(s(s(z))), s(elem!1))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[7026, 7045])).
% 1.86/2.11 tff(7092,plain,
% 1.86/2.11 (((~![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(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(7093,plain,
% 1.86/2.11 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(7094,plain,
% 1.86/2.11 (((~![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(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(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(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[7093])).
% 1.86/2.11 tff(7095,plain,
% 1.86/2.11 (((~![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(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(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(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[7094, 7092])).
% 1.86/2.12 tff(7096,plain,
% 1.86/2.12 ((~![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(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(7097,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[7096, 7095])).
% 1.86/2.12 tff(7098,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7097, 453, 7091, 7090, 7089, 7086, 7084])).
% 1.86/2.12 tff(7099,plain,(b(s(s(s(s(s(z))))), elem!1) | (~(s(s(s(s(z)))) = elem!1)) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(7100,plain,
% 1.86/2.12 (b(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7099, 1170, 6988, 6990, 499, 2090, 238, 120])).
% 1.86/2.12 tff(7101,plain,
% 1.86/2.12 (b(s(elem!1), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1336, 7100, 1170])).
% 1.86/2.12 tff(7102,plain,
% 1.86/2.12 (~r(s(elem!1), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[348, 339, 238])).
% 1.86/2.12 tff(7103,plain,
% 1.86/2.12 (b(s(elem!1), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[353, 7102, 197])).
% 1.86/2.12 tff(7104,plain,
% 1.86/2.12 (~b(elem!1, s(s(elem!1)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2121, 7103, 499, 629])).
% 1.86/2.12 tff(7105,plain,
% 1.86/2.12 (r(elem!1, s(s(elem!1)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1024, 7104, 216])).
% 1.86/2.12 tff(7106,plain,
% 1.86/2.12 (~r(s(s(elem!1)), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1041, 7105, 238])).
% 1.86/2.12 tff(7107,plain,
% 1.86/2.12 (b(s(s(elem!1)), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1047, 7106])).
% 1.86/2.12 tff(7108,plain,
% 1.86/2.12 (~r(s(z), s(elem!1))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1496, 339, 238])).
% 1.86/2.12 tff(7109,plain,
% 1.86/2.12 (b(s(z), s(elem!1))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[397, 7108, 177])).
% 1.86/2.12 tff(7110,plain,
% 1.86/2.12 (((~![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(z), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(7111,plain,
% 1.86/2.12 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(7112,plain,
% 1.86/2.12 (((~![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(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z)))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[7111])).
% 1.86/2.12 tff(7113,plain,
% 1.86/2.12 (((~![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(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[7112, 7110])).
% 1.86/2.12 tff(7114,plain,
% 1.86/2.12 ((~![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(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(7115,plain,
% 1.86/2.12 ((~![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(z), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z)))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[7114, 7113])).
% 1.86/2.12 tff(7116,plain,
% 1.86/2.12 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7115, 453, 7109, 7107, 120])).
% 1.86/2.12 tff(7117,plain,
% 1.86/2.12 (r(s(s(s(z))), s(s(elem!1)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[5203, 7116, 555])).
% 1.86/2.12 tff(7118,plain,
% 1.86/2.12 (~(s(elem!1) = s(s(elem!1)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1861, 216])).
% 1.86/2.12 tff(7119,plain,
% 1.86/2.12 (~b(s(elem!1), s(s(elem!1)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2015, 453, 7103, 7109, 7107])).
% 1.86/2.12 tff(7120,plain,
% 1.86/2.12 (r(s(elem!1), s(s(elem!1)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[440, 7119, 7118])).
% 1.86/2.12 tff(7121,plain,
% 1.86/2.12 (~b(s(elem!1), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1555, 453, 7103, 7109, 120])).
% 1.86/2.12 tff(7122,plain,
% 1.86/2.12 (r(s(elem!1), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1305, 7121, 1290])).
% 1.86/2.12 tff(7123,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(7124,plain,
% 1.86/2.12 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(7125,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[7124])).
% 1.86/2.12 tff(7126,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[7125, 7123])).
% 1.86/2.12 tff(7127,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(7128,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[7127, 7126])).
% 1.86/2.12 tff(7129,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7128, 268, 431, 5205, 3047])).
% 1.86/2.12 tff(7130,plain,((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(7131,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7130, 7122, 7120, 7117])).
% 1.86/2.12 tff(7132,plain,((~r(elem!1, s(elem!1))) | (s(elem!1) = s(s(s(z)))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (elem!1 = s(s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (s(elem!1) = s(z)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(7133,plain,
% 1.86/2.12 (~r(elem!1, s(elem!1))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7132, 1271, 555, 120, 238, 6681, 499, 7101, 1182, 6986])).
% 1.86/2.12 tff(7134,plain,
% 1.86/2.12 (b(elem!1, s(elem!1))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1069, 7133, 6983])).
% 1.86/2.12 tff(7135,plain,
% 1.86/2.12 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[7134, 6976])).
% 1.86/2.12 tff(7136,plain,
% 1.86/2.12 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6717, 7100, 499, 1170, 6989])).
% 1.86/2.12 tff(7137,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7136, 7135])).
% 1.86/2.12 tff(7138,plain,((~(s(s(s(s(z)))) = elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(7139,plain,
% 1.86/2.12 (~(s(s(s(s(z)))) = elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7138, 6971, 4540, 4877, 4542, 5503, 300])).
% 1.86/2.12 tff(7140,plain,
% 1.86/2.12 (~(elem!1 = s(s(s(s(z)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8, 7139])).
% 1.86/2.12 tff(7141,plain,
% 1.86/2.12 (b(elem!1, s(s(s(s(z)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1087, 7140, 6973])).
% 1.86/2.12 tff(7142,plain,
% 1.86/2.12 (((~![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(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(7143,plain,
% 1.86/2.12 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(7144,plain,
% 1.86/2.12 (((~![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(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[7143])).
% 1.86/2.12 tff(7145,plain,
% 1.86/2.12 (((~![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(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[7144, 7142])).
% 1.86/2.12 tff(7146,plain,
% 1.86/2.12 ((~![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(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(7147,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[7146, 7145])).
% 1.86/2.12 tff(7148,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7147, 453, 499, 1291, 530, 120])).
% 1.86/2.12 tff(7149,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(7150,plain,
% 1.86/2.12 (~b(s(s(s(z))), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7149, 4542, 7141, 4540])).
% 1.86/2.12 tff(7151,plain,
% 1.86/2.12 (r(s(s(s(z))), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[74, 7150, 6972])).
% 1.86/2.12 tff(7152,plain,
% 1.86/2.12 (~r(s(s(s(s(z)))), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1138, 268, 6971, 1099])).
% 1.86/2.12 tff(7153,plain,
% 1.86/2.12 (b(s(s(s(s(z)))), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[254, 7139, 7152])).
% 1.86/2.12 tff(7154,plain,
% 1.86/2.12 (((~![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(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(7155,plain,
% 1.86/2.12 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(7156,plain,
% 1.86/2.12 (((~![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(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), 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), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[7155])).
% 1.86/2.12 tff(7157,plain,
% 1.86/2.12 (((~![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(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), 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), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.12 inference(transitivity,[status(thm)],[7156, 7154])).
% 1.86/2.12 tff(7158,plain,
% 1.86/2.12 ((~![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(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(7159,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[7158, 7157])).
% 1.86/2.12 tff(7160,plain,
% 1.86/2.12 (~b(s(s(z)), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7159, 453, 499, 922, 530])).
% 1.86/2.12 tff(7161,plain,
% 1.86/2.12 (r(s(s(z)), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[720, 69, 717, 7160])).
% 1.86/2.12 tff(7162,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2385, 268, 1132, 7161, 6075])).
% 1.86/2.12 tff(7163,plain,((~b(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(7164,plain,
% 1.86/2.12 (~b(s(s(z)), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7163, 7141, 1099, 7153, 4542])).
% 1.86/2.12 tff(7165,plain,
% 1.86/2.12 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[5719, 268, 700, 1545])).
% 1.86/2.12 tff(7166,plain,
% 1.86/2.12 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1350, 69, 7165])).
% 1.86/2.12 tff(7167,plain,
% 1.86/2.12 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7166, 1243])).
% 1.86/2.12 tff(7168,plain,
% 1.86/2.12 (((~![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(z)), s(s(s(z))))) | (~b(s(s(s(z))), 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(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(7169,plain,
% 1.86/2.12 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(7170,plain,
% 1.86/2.12 (((~![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(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[7169])).
% 1.86/2.12 tff(7171,plain,
% 1.86/2.12 (((~![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(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[7170, 7168])).
% 1.86/2.12 tff(7172,plain,
% 1.86/2.12 ((~![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(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(7173,plain,
% 1.86/2.12 ((~![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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[7172, 7171])).
% 1.86/2.12 tff(7174,plain,
% 1.86/2.12 (~b(s(s(z)), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7173, 453, 120, 2090, 7167])).
% 1.86/2.12 tff(7175,plain,
% 1.86/2.12 (r(s(s(z)), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[720, 69, 717, 7174])).
% 1.86/2.12 tff(7176,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(7177,plain,
% 1.86/2.12 (((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(7178,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[7177])).
% 1.86/2.12 tff(7179,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.86/2.12 inference(transitivity,[status(thm)],[7178, 7176])).
% 1.86/2.12 tff(7180,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(7181,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[7180, 7179])).
% 1.86/2.12 tff(7182,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7181, 268, 238, 700, 7175])).
% 1.86/2.12 tff(7183,plain,((~r(s(s(z)), elem!1)) | (~r(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(7184,plain,
% 1.86/2.12 (~r(s(s(z)), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7183, 6971, 4540, 5503, 7151])).
% 1.86/2.12 tff(7185,plain,
% 1.86/2.12 (s(s(z)) = elem!1),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[782, 7184, 7164])).
% 1.86/2.12 tff(7186,plain,
% 1.86/2.12 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3537])).
% 1.86/2.12 tff(7187,plain,
% 1.86/2.12 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.12 inference(symmetry,[status(thm)],[7186])).
% 1.86/2.12 tff(7188,plain,
% 1.86/2.12 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.12 inference(transitivity,[status(thm)],[3553, 7187])).
% 1.86/2.12 tff(7189,plain,
% 1.86/2.12 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.86/2.12 inference(transitivity,[status(thm)],[3590, 56])).
% 1.86/2.12 tff(7190,plain,
% 1.86/2.12 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[7189])).
% 1.86/2.12 tff(7191,plain,
% 1.86/2.12 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[52, 7190])).
% 1.86/2.12 tff(7192,plain,
% 1.86/2.12 (r(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[643, 7191, 638])).
% 1.86/2.12 tff(7193,plain,
% 1.86/2.12 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1566, 7192, 1545])).
% 1.86/2.12 tff(7194,plain,
% 1.86/2.12 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[687, 7193])).
% 1.86/2.12 tff(7195,plain,
% 1.86/2.12 (b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[7194, 7188])).
% 1.86/2.12 tff(7196,plain,
% 1.86/2.12 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.97/2.13 inference(symmetry,[status(thm)],[1391])).
% 1.97/2.13 tff(7197,plain,
% 1.97/2.13 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.97/2.13 inference(transitivity,[status(thm)],[3734, 7196])).
% 1.97/2.13 tff(7198,plain,
% 1.97/2.13 ((~(elem!1 = s(s(s(s(s(z))))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7197])).
% 1.97/2.13 tff(7199,plain,
% 1.97/2.13 (~(s(s(s(elem!1))) = elem!1)),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[3592, 7198])).
% 1.97/2.13 tff(7200,plain,
% 1.97/2.13 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.13 inference(monotonicity,[status(thm)],[3537])).
% 1.97/2.13 tff(7201,plain,
% 1.97/2.13 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.97/2.13 inference(symmetry,[status(thm)],[7200])).
% 1.97/2.13 tff(7202,plain,
% 1.97/2.13 ((~b(s(s(s(s(s(z))))), elem!1)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7201])).
% 1.97/2.13 tff(7203,plain,
% 1.97/2.13 (~b(s(s(s(elem!1))), elem!1)),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[638, 7202])).
% 1.97/2.13 tff(7204,plain,
% 1.97/2.13 (r(s(s(s(elem!1))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[567, 7203, 7199])).
% 1.97/2.13 tff(7205,plain,
% 1.97/2.13 (~r(s(s(s(elem!1))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[842, 7204, 238])).
% 1.97/2.13 tff(7206,plain,
% 1.97/2.13 (b(s(s(s(elem!1))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[856, 7205])).
% 1.97/2.13 tff(7207,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.97/2.13 tff(7208,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(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7209,plain,
% 1.97/2.13 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7210,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(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7209])).
% 1.97/2.13 tff(7211,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(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7210, 7208])).
% 1.97/2.13 tff(7212,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(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(7213,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7212, 7211])).
% 1.97/2.13 tff(7214,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7213, 453, 1059, 1549, 1110, 7207])).
% 1.97/2.13 tff(7215,plain,((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7216,plain,
% 1.97/2.13 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7215, 7206, 5604, 5606])).
% 1.97/2.13 tff(7217,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7216, 7195])).
% 1.97/2.13 tff(7218,plain,((~(s(s(z)) = elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | b(s(s(s(s(s(z))))), elem!1) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7219,plain,
% 1.97/2.13 (b(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7218, 7185, 7151, 6971, 5503, 4540])).
% 1.97/2.13 tff(7220,plain,
% 1.97/2.13 (s(s(s(z))) = s(elem!1)),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7185])).
% 1.97/2.13 tff(7221,plain,
% 1.97/2.13 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7220])).
% 1.97/2.13 tff(7222,plain,
% 1.97/2.13 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7221])).
% 1.97/2.13 tff(7223,plain,
% 1.97/2.13 (b(elem!1, s(s(elem!1)))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7141, 7222])).
% 1.97/2.13 tff(7224,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), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7225,plain,
% 1.97/2.13 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7226,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7225])).
% 1.97/2.13 tff(7227,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7226, 7224])).
% 1.97/2.13 tff(7228,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(7229,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), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7228, 7227])).
% 1.97/2.13 tff(7230,plain,
% 1.97/2.13 (~b(s(z), s(s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7229, 453, 4542, 7223, 7219])).
% 1.97/2.13 tff(7231,plain,
% 1.97/2.13 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.97/2.13 inference(symmetry,[status(thm)],[7221])).
% 1.97/2.13 tff(7232,plain,
% 1.97/2.13 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7231])).
% 1.97/2.13 tff(7233,plain,
% 1.97/2.13 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7231, 7232])).
% 1.97/2.13 tff(7234,plain,
% 1.97/2.13 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7221])).
% 1.97/2.13 tff(7235,plain,
% 1.97/2.13 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7234, 6536])).
% 1.97/2.13 tff(7236,plain,
% 1.97/2.13 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7235])).
% 1.97/2.13 tff(7237,plain,
% 1.97/2.13 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[6514, 7236])).
% 1.97/2.13 tff(7238,plain,
% 1.97/2.13 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7232])).
% 1.97/2.13 tff(7239,plain,
% 1.97/2.13 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.97/2.13 inference(symmetry,[status(thm)],[7238])).
% 1.97/2.13 tff(7240,plain,
% 1.97/2.13 ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7239])).
% 1.97/2.13 tff(7241,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7221])).
% 1.97/2.13 tff(7242,plain,
% 1.97/2.13 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7241])).
% 1.97/2.13 tff(7243,plain,
% 1.97/2.13 (~b(s(s(s(s(s(z))))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3620, 7219, 4542, 7141])).
% 1.97/2.13 tff(7244,plain,
% 1.97/2.13 (r(s(s(s(s(s(z))))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[297, 7243])).
% 1.97/2.13 tff(7245,plain,
% 1.97/2.13 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2414, 7244, 1099])).
% 1.97/2.13 tff(7246,plain,
% 1.97/2.13 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[328, 7245])).
% 1.97/2.13 tff(7247,plain,
% 1.97/2.13 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6664, 7246, 6973, 7139, 7219, 7152])).
% 1.97/2.13 tff(7248,plain,
% 1.97/2.13 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7247, 7242])).
% 1.97/2.13 tff(7249,plain,
% 1.97/2.13 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7248, 7240])).
% 1.97/2.13 tff(7250,plain,
% 1.97/2.13 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[675, 7249, 7237])).
% 1.97/2.13 tff(7251,plain,
% 1.97/2.13 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7250, 7233])).
% 1.97/2.13 tff(7252,plain,
% 1.97/2.13 (~r(s(z), s(s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2254, 7251, 1099])).
% 1.97/2.13 tff(7253,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[372, 7252, 7230])).
% 1.97/2.13 tff(7254,plain,(r(s(z), elem!1) | (~r(s(s(s(z))), s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7255,plain,
% 1.97/2.13 (r(s(z), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7254, 1057, 300, 1123])).
% 1.97/2.13 tff(7256,plain,
% 1.97/2.13 (~r(s(s(s(z))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4885, 228, 701])).
% 1.97/2.13 tff(7257,plain,
% 1.97/2.13 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1611, 228, 1132, 701])).
% 1.97/2.13 tff(7258,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[518, 7257])).
% 1.97/2.13 tff(7259,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[254, 4552, 239])).
% 1.97/2.13 tff(7260,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(s(z)))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7261,plain,
% 1.97/2.13 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7262,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7261])).
% 1.97/2.13 tff(7263,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7262, 7260])).
% 1.97/2.13 tff(7264,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(7265,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7264, 7263])).
% 1.97/2.13 tff(7266,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7265, 453, 5446, 523, 5445, 7259])).
% 1.97/2.13 tff(7267,plain,(r(elem!1, s(z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | b(s(z), s(s(s(z)))) | r(s(s(s(s(z)))), elem!1) | (~r(s(s(s(s(z)))), s(z))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7268,plain,
% 1.97/2.13 (r(elem!1, s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7267, 7258, 5517, 221, 1168, 1132, 1123])).
% 1.97/2.13 tff(7269,plain,
% 1.97/2.13 (~(s(s(s(z))) = elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[6652, 7268, 5516])).
% 1.97/2.13 tff(7270,plain,
% 1.97/2.13 (b(s(s(s(z))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[74, 7269, 7256])).
% 1.97/2.13 tff(7271,plain,
% 1.97/2.13 (~(elem!1 = s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4487, 7269])).
% 1.97/2.13 tff(7272,plain,
% 1.97/2.13 (~r(elem!1, s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1157, 7268, 228])).
% 1.97/2.13 tff(7273,plain,
% 1.97/2.13 (b(elem!1, s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4492, 7272, 7271])).
% 1.97/2.13 tff(7274,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7275,plain,
% 1.97/2.13 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7276,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(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7275])).
% 1.97/2.13 tff(7277,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(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7276, 7274])).
% 1.97/2.13 tff(7278,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(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(7279,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7278, 7277])).
% 1.97/2.13 tff(7280,plain,
% 1.97/2.13 (~b(s(s(s(s(z)))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7279, 453, 523, 1291, 1275])).
% 1.97/2.13 tff(7281,plain,
% 1.97/2.13 (r(s(s(s(s(z)))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[254, 7280, 3])).
% 1.97/2.13 tff(7282,plain,
% 1.97/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7283,plain,
% 1.97/2.13 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(7284,plain,
% 1.97/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7283])).
% 1.97/2.13 tff(7285,plain,
% 1.97/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.97/2.13 inference(transitivity,[status(thm)],[7284, 7282])).
% 1.97/2.13 tff(7286,plain,
% 1.97/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(7287,plain,
% 1.97/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7286, 7285])).
% 1.97/2.13 tff(7288,plain,
% 1.97/2.13 (~r(s(z), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7287, 268, 701, 7281])).
% 1.97/2.13 tff(7289,plain,
% 1.97/2.13 (b(s(z), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1677, 69, 7288, 50])).
% 1.97/2.13 tff(7290,plain,
% 1.97/2.13 (~r(s(s(s(s(z)))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1167, 7281, 701])).
% 1.97/2.13 tff(7291,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1098, 7290])).
% 1.97/2.13 tff(7292,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4715, 453, 523, 7291, 7289, 120])).
% 1.97/2.13 tff(7293,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7294,plain,
% 1.97/2.13 (s(s(s(s(z)))) = elem!1),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7293, 7273, 5517, 701, 7258, 7270])).
% 1.97/2.13 tff(7295,plain,
% 1.97/2.13 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), elem!1)),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7294])).
% 1.97/2.13 tff(7296,plain,
% 1.97/2.13 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.13 inference(symmetry,[status(thm)],[7295])).
% 1.97/2.13 tff(7297,plain,
% 1.97/2.13 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7296])).
% 1.97/2.13 tff(7298,plain,
% 1.97/2.13 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[7256, 7297])).
% 1.97/2.13 tff(7299,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[300, 7298])).
% 1.97/2.13 tff(7300,plain,(b(s(z), s(s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(7301,plain,
% 1.97/2.13 (b(s(z), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7300, 7255, 300, 1099, 1123])).
% 1.97/2.13 tff(7302,plain,
% 1.97/2.13 (~r(s(s(s(s(z)))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1167, 7255, 1099])).
% 1.97/2.13 tff(7303,plain,
% 1.97/2.13 (r(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[643, 1544, 638])).
% 1.97/2.13 tff(7304,plain,
% 1.97/2.13 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1566, 7303, 6988])).
% 1.97/2.13 tff(7305,plain,
% 1.97/2.13 (r(s(z), s(s(s(s(z))))) <=> r(s(z), elem!1)),
% 1.97/2.13 inference(monotonicity,[status(thm)],[1170])).
% 1.97/2.13 tff(7306,plain,
% 1.97/2.13 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(z)))))),
% 1.97/2.13 inference(symmetry,[status(thm)],[7305])).
% 1.97/2.13 tff(7307,plain,
% 1.97/2.13 (r(s(z), s(s(s(s(z)))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[701, 7306])).
% 1.97/2.13 tff(7308,plain,
% 1.97/2.13 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.13 inference(monotonicity,[status(thm)],[1170])).
% 1.97/2.13 tff(7309,plain,
% 1.97/2.13 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.13 inference(symmetry,[status(thm)],[7308])).
% 1.97/2.13 tff(7310,plain,
% 1.97/2.13 ((~b(s(s(s(s(s(z))))), elem!1)) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[7309])).
% 1.97/2.13 tff(7311,plain,
% 1.97/2.13 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[638, 7310])).
% 1.97/2.13 tff(7312,plain,
% 1.97/2.14 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[328, 7311])).
% 1.97/2.14 tff(7313,plain,
% 1.97/2.14 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[5380, 7312, 120, 7307])).
% 1.97/2.14 tff(7314,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[687, 7313, 7304])).
% 1.97/2.14 tff(7315,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(s(s(s(z))), s(z))) | b(s(s(s(s(s(z))))), elem!1) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(7316,plain,
% 1.97/2.14 (~(s(s(s(s(z)))) = elem!1)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7315, 638, 4540, 7255, 300])).
% 1.97/2.14 tff(7317,plain,
% 1.97/2.14 (b(s(s(s(s(z)))), elem!1)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[254, 7316, 7302])).
% 1.97/2.14 tff(7318,plain,
% 1.97/2.14 (b(s(s(s(s(z)))), elem!1)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[254, 5504, 7302])).
% 1.97/2.14 tff(7319,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7320,plain,
% 1.97/2.14 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7321,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7320])).
% 1.97/2.14 tff(7322,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.97/2.14 inference(transitivity,[status(thm)],[7321, 7319])).
% 1.97/2.14 tff(7323,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(7324,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[7323, 7322])).
% 1.97/2.14 tff(7325,plain,
% 1.97/2.14 (~b(s(s(s(z))), s(s(z)))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7324, 453, 2077, 1291, 922])).
% 1.97/2.14 tff(7326,plain,
% 1.97/2.14 (r(s(s(s(z))), s(s(z)))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[2534, 69, 160, 7325])).
% 1.97/2.14 tff(7327,plain,
% 1.97/2.14 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7265, 453, 2077, 1291, 299])).
% 1.97/2.14 tff(7328,plain,
% 1.97/2.14 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[518, 7327])).
% 1.97/2.14 tff(7329,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[2782, 268, 7328, 7326, 5564])).
% 1.97/2.14 tff(7330,plain,((~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(7331,plain,
% 1.97/2.14 (~b(s(s(z)), elem!1)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7330, 1291, 5446, 7318])).
% 1.97/2.14 tff(7332,plain,
% 1.97/2.14 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7265, 453, 5446, 1291, 7318])).
% 1.97/2.14 tff(7333,plain,
% 1.97/2.14 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[518, 7332])).
% 1.97/2.14 tff(7334,plain,
% 1.97/2.14 (s(s(s(s(s(z))))) = elem!1),
% 1.97/2.14 inference(symmetry,[status(thm)],[5965])).
% 1.97/2.14 tff(7335,plain,
% 1.97/2.14 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7334])).
% 1.97/2.14 tff(7336,plain,
% 1.97/2.14 (r(s(s(s(s(s(s(s(s(z)))))))), elem!1) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 1.97/2.14 inference(symmetry,[status(thm)],[7335])).
% 1.97/2.14 tff(7337,plain,
% 1.97/2.14 (s(elem!1) = s(s(s(s(s(s(z))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[5965])).
% 1.97/2.14 tff(7338,plain,
% 1.97/2.14 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7337])).
% 1.97/2.14 tff(7339,plain,
% 1.97/2.14 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(z))))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7338])).
% 1.97/2.14 tff(7340,plain,
% 1.97/2.14 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7339])).
% 1.97/2.14 tff(7341,plain,
% 1.97/2.14 (~r(s(z), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1611, 701, 1132, 11])).
% 1.97/2.14 tff(7342,plain,
% 1.97/2.14 (b(s(z), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[227, 7341])).
% 1.97/2.14 tff(7343,plain,
% 1.97/2.14 (r(s(s(s(elem!1))), elem!1)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6451, 5168, 11, 1132, 7342, 2076, 1168])).
% 1.97/2.14 tff(7344,plain,
% 1.97/2.14 (r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[7343, 7340])).
% 1.97/2.14 tff(7345,plain,
% 1.97/2.14 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[7344, 7336])).
% 1.97/2.14 tff(7346,plain,
% 1.97/2.14 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7339])).
% 1.97/2.14 tff(7347,plain,
% 1.97/2.14 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[7346, 5661])).
% 1.97/2.14 tff(7348,plain,
% 1.97/2.14 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7347])).
% 1.97/2.14 tff(7349,plain,
% 1.97/2.14 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[6460, 7348])).
% 1.97/2.14 tff(7350,plain,
% 1.97/2.14 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(s(z))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[5965])).
% 1.97/2.14 tff(7351,plain,
% 1.97/2.14 (r(s(z), s(s(s(s(s(z))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[701, 7350])).
% 1.97/2.14 tff(7352,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7353,plain,
% 1.97/2.14 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7354,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7353])).
% 1.97/2.14 tff(7355,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[7354, 7352])).
% 1.97/2.14 tff(7356,plain,
% 1.97/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(7357,plain,
% 1.97/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[7356, 7355])).
% 1.97/2.14 tff(7358,plain,
% 1.97/2.14 ((~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7357, 268, 7351])).
% 1.97/2.14 tff(7359,plain,
% 1.97/2.14 (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7358, 7345])).
% 1.97/2.14 tff(7360,plain,
% 1.97/2.14 (b(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6101, 69, 2884, 7359])).
% 1.97/2.14 tff(7361,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7362,plain,
% 1.97/2.14 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))) <=> ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7363,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7362])).
% 1.97/2.14 tff(7364,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[7363, 7361])).
% 1.97/2.14 tff(7365,plain,
% 1.97/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(7366,plain,
% 1.97/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[7365, 7364])).
% 1.97/2.14 tff(7367,plain,
% 1.97/2.14 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7366, 268, 7351])).
% 1.97/2.14 tff(7368,plain,
% 1.97/2.14 (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7367, 7345])).
% 1.97/2.14 tff(7369,plain,
% 1.97/2.14 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[2906, 69, 7368, 2886])).
% 1.97/2.14 tff(7370,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(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7371,plain,
% 1.97/2.14 (((~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7372,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(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7371])).
% 1.97/2.14 tff(7373,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(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[7372, 7370])).
% 1.97/2.14 tff(7374,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(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(7375,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(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[7374, 7373])).
% 1.97/2.14 tff(7376,plain,
% 1.97/2.14 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7375, 453, 6364, 7369, 7360])).
% 1.97/2.14 tff(7377,plain,
% 1.97/2.14 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[2846, 7376, 7349])).
% 1.97/2.14 tff(7378,plain,
% 1.97/2.14 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7346])).
% 1.97/2.14 tff(7379,plain,
% 1.97/2.14 (~(s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[6460, 7378])).
% 1.97/2.14 tff(7380,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(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(s(s(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(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7381,plain,
% 1.97/2.14 (((~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7382,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(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(s(s(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(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7381])).
% 1.97/2.14 tff(7383,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(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(s(s(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(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[7382, 7380])).
% 1.97/2.14 tff(7384,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(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(7385,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(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[7384, 7383])).
% 1.97/2.14 tff(7386,plain,
% 1.97/2.14 (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7385, 453, 6364, 7369, 7360])).
% 1.97/2.14 tff(7387,plain,
% 1.97/2.14 (r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6485, 7386, 7379])).
% 1.97/2.14 tff(7388,plain,
% 1.97/2.14 (b(elem!1, s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[5965])).
% 1.97/2.14 tff(7389,plain,
% 1.97/2.14 (b(s(s(s(s(s(z))))), s(z))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[2077, 7388])).
% 1.97/2.14 tff(7390,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(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7391,plain,
% 1.97/2.14 (((~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(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(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(7392,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(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(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(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[7391])).
% 1.97/2.14 tff(7393,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(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(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(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[7392, 7390])).
% 1.97/2.14 tff(7394,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(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(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(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(7395,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(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[7394, 7393])).
% 1.97/2.14 tff(7396,plain,
% 1.97/2.14 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7395, 453, 7389, 6364, 7360])).
% 1.97/2.14 tff(7397,plain,
% 1.97/2.14 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[2570, 7396])).
% 1.97/2.14 tff(7398,plain,
% 1.97/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7399,plain,
% 1.97/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(7400,plain,
% 1.97/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[7399, 7398])).
% 1.97/2.15 tff(7401,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7400, 268, 7397, 7387, 7377, 7345])).
% 1.97/2.15 tff(7402,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(7403,plain,
% 1.97/2.15 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7402, 7333, 7255, 5446, 1099, 2076])).
% 1.97/2.15 tff(7404,plain,
% 1.97/2.15 (r(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[643, 7403, 638])).
% 1.97/2.15 tff(7405,plain,
% 1.97/2.15 (~r(s(s(z)), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[777, 7404, 7255])).
% 1.97/2.15 tff(7406,plain,
% 1.97/2.15 (s(s(z)) = elem!1),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[782, 7405, 7331])).
% 1.97/2.15 tff(7407,plain,
% 1.97/2.15 (s(s(s(z))) = s(elem!1)),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7406])).
% 1.97/2.15 tff(7408,plain,
% 1.97/2.15 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7407])).
% 1.97/2.15 tff(7409,plain,
% 1.97/2.15 (b(s(elem!1), s(z))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[4540, 7408])).
% 1.97/2.15 tff(7410,plain,
% 1.97/2.15 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7407])).
% 1.97/2.15 tff(7411,plain,
% 1.97/2.15 (b(s(z), s(elem!1))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[7301, 7410])).
% 1.97/2.15 tff(7412,plain,
% 1.97/2.15 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7407])).
% 1.97/2.15 tff(7413,plain,
% 1.97/2.15 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.97/2.15 inference(symmetry,[status(thm)],[7412])).
% 1.97/2.15 tff(7414,plain,
% 1.97/2.15 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7413])).
% 1.97/2.15 tff(7415,plain,
% 1.97/2.15 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7414])).
% 1.97/2.15 tff(7416,plain,
% 1.97/2.15 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.97/2.15 inference(symmetry,[status(thm)],[7415])).
% 1.97/2.15 tff(7417,plain,
% 1.97/2.15 (~r(s(s(s(s(s(z))))), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[730, 7404, 7255])).
% 1.97/2.15 tff(7418,plain,
% 1.97/2.15 (b(s(s(s(s(s(z))))), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[297, 7417])).
% 1.97/2.15 tff(7419,plain,
% 1.97/2.15 (b(s(s(s(elem!1))), s(z))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[7418, 7416])).
% 1.97/2.15 tff(7420,plain,
% 1.97/2.15 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7414])).
% 1.97/2.15 tff(7421,plain,
% 1.97/2.15 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.15 inference(symmetry,[status(thm)],[7420])).
% 1.97/2.15 tff(7422,plain,
% 1.97/2.15 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7407])).
% 1.97/2.15 tff(7423,plain,
% 1.97/2.15 (r(s(z), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6726, 11, 300, 256, 1057, 1123])).
% 1.97/2.15 tff(7424,plain,
% 1.97/2.15 (~r(s(z), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1611, 7423, 1099, 11])).
% 1.97/2.15 tff(7425,plain,
% 1.97/2.15 (b(s(z), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[227, 7424])).
% 1.97/2.15 tff(7426,plain,
% 1.97/2.15 (~r(s(s(s(s(z)))), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1167, 7423, 1099])).
% 1.97/2.15 tff(7427,plain,
% 1.97/2.15 (~(s(s(s(z))) = elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6774, 7424, 7423])).
% 1.97/2.15 tff(7428,plain,
% 1.97/2.15 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7402, 5446, 701, 11, 1132, 2076])).
% 1.97/2.15 tff(7429,plain,
% 1.97/2.15 (~(s(s(s(z))) = elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6774, 7341, 701])).
% 1.97/2.15 tff(7430,plain,
% 1.97/2.15 (b(s(s(s(s(z)))), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[254, 4552, 1168])).
% 1.97/2.15 tff(7431,plain,
% 1.97/2.15 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[7428, 2924])).
% 1.97/2.15 tff(7432,plain,
% 1.97/2.15 (~r(s(s(z)), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[777, 722, 701])).
% 1.97/2.15 tff(7433,plain,
% 1.97/2.15 (~b(s(s(z)), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7330, 5769, 2077, 299])).
% 1.97/2.15 tff(7434,plain,
% 1.97/2.15 (s(s(z)) = elem!1),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[782, 7433, 7432])).
% 1.97/2.15 tff(7435,plain,
% 1.97/2.15 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7434])).
% 1.97/2.15 tff(7436,plain,
% 1.97/2.15 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 1.97/2.15 inference(symmetry,[status(thm)],[7435])).
% 1.97/2.15 tff(7437,plain,
% 1.97/2.15 (s(s(s(z))) = s(elem!1)),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7434])).
% 1.97/2.15 tff(7438,plain,
% 1.97/2.15 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7437])).
% 1.97/2.15 tff(7439,plain,
% 1.97/2.15 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.97/2.15 inference(symmetry,[status(thm)],[7438])).
% 1.97/2.15 tff(7440,plain,
% 1.97/2.15 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7439])).
% 1.97/2.15 tff(7441,plain,
% 1.97/2.15 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7440])).
% 1.97/2.15 tff(7442,plain,
% 1.97/2.15 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[7441, 7436])).
% 1.97/2.15 tff(7443,plain,
% 1.97/2.15 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7440])).
% 1.97/2.15 tff(7444,plain,
% 1.97/2.15 ((elem!1 = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.97/2.15 inference(symmetry,[status(thm)],[7443])).
% 1.97/2.15 tff(7445,plain,
% 1.97/2.15 ((~(elem!1 = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7444])).
% 1.97/2.15 tff(7446,plain,
% 1.97/2.15 (~(elem!1 = s(s(s(elem!1))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[2073, 7445])).
% 1.97/2.15 tff(7447,plain,
% 1.97/2.15 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7440])).
% 1.97/2.15 tff(7448,plain,
% 1.97/2.15 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.97/2.15 inference(symmetry,[status(thm)],[7447])).
% 1.97/2.15 tff(7449,plain,
% 1.97/2.15 (b(s(s(s(elem!1))), s(z))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[3677, 7448])).
% 1.97/2.15 tff(7450,plain,
% 1.97/2.15 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7437])).
% 1.97/2.15 tff(7451,plain,
% 1.97/2.15 (b(s(z), s(elem!1))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[2090, 7450])).
% 1.97/2.15 tff(7452,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.97/2.15 tff(7453,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(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7454,plain,
% 1.97/2.15 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7455,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(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7454])).
% 1.97/2.15 tff(7456,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(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[7455, 7453])).
% 1.97/2.15 tff(7457,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(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(7458,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[7457, 7456])).
% 1.97/2.15 tff(7459,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7458, 453, 1549, 2077, 1110, 7452])).
% 1.97/2.15 tff(7460,plain,((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(7461,plain,
% 1.97/2.15 (~b(elem!1, s(s(s(elem!1))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7460, 7451, 2077, 7449])).
% 1.97/2.15 tff(7462,plain,
% 1.97/2.15 (r(elem!1, s(s(s(elem!1))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1428, 7461, 7446])).
% 1.97/2.15 tff(7463,plain,
% 1.97/2.15 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[7462, 7442])).
% 1.97/2.15 tff(7464,plain,
% 1.97/2.15 (r(s(s(z)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7434])).
% 1.97/2.15 tff(7465,plain,
% 1.97/2.15 (r(elem!1, s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.97/2.15 inference(symmetry,[status(thm)],[7464])).
% 1.97/2.15 tff(7466,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(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, 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(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7467,plain,
% 1.97/2.15 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7468,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(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(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(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7467])).
% 1.97/2.15 tff(7469,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(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(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(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[7468, 7466])).
% 1.97/2.15 tff(7470,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(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(7471,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[7470, 7469])).
% 1.97/2.15 tff(7472,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7471, 453, 2077, 1291, 2090, 1275])).
% 1.97/2.15 tff(7473,plain,((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(7474,plain,
% 1.97/2.15 (~b(elem!1, s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7473, 5769, 2090, 2077])).
% 1.97/2.15 tff(7475,plain,
% 1.97/2.15 (r(elem!1, s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4492, 7474, 5525])).
% 1.97/2.15 tff(7476,plain,
% 1.97/2.15 (r(s(s(z)), s(s(s(z))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[7475, 7465])).
% 1.97/2.15 tff(7477,plain,
% 1.97/2.15 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2795, 7476, 256])).
% 1.97/2.15 tff(7478,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7477, 7463])).
% 1.97/2.15 tff(7479,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (s(s(s(z))) = elem!1) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(7480,plain,
% 1.97/2.15 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7479, 5446, 256, 7431, 7342, 7430, 7429, 701])).
% 1.97/2.15 tff(7481,plain,
% 1.97/2.15 (b(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[643, 7480, 7428])).
% 1.97/2.15 tff(7482,plain,
% 1.97/2.15 (r(elem!1, s(s(s(s(z)))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6664, 7481, 5914, 5912, 4552, 1168])).
% 1.97/2.15 tff(7483,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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7484,plain,
% 1.97/2.15 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7485,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(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7484])).
% 1.97/2.15 tff(7486,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(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[7485, 7483])).
% 1.97/2.15 tff(7487,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(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(7488,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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[7487, 7486])).
% 1.97/2.15 tff(7489,plain,
% 1.97/2.15 (~b(s(s(s(z))), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7488, 453, 5446, 6364, 7342])).
% 1.97/2.15 tff(7490,plain,
% 1.97/2.15 (r(s(s(s(z))), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[74, 7489, 7429])).
% 1.97/2.15 tff(7491,plain,
% 1.97/2.15 (~(elem!1 = s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4487, 7429])).
% 1.97/2.15 tff(7492,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(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, 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(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7493,plain,
% 1.97/2.15 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(7494,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(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(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(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7493])).
% 1.97/2.15 tff(7495,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(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(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(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[7494, 7492])).
% 1.97/2.15 tff(7496,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(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(7497,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[7496, 7495])).
% 1.97/2.15 tff(7498,plain,
% 1.97/2.15 (~b(elem!1, s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7497, 453, 5446, 6364, 7342])).
% 1.97/2.15 tff(7499,plain,
% 1.97/2.15 (r(elem!1, s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4492, 7498, 7491])).
% 1.97/2.15 tff(7500,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[5432, 7499, 7490, 300, 7482])).
% 1.97/2.15 tff(7501,plain,(r(elem!1, s(z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(7502,plain,
% 1.97/2.15 (r(elem!1, s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7501, 7423, 256, 300, 11, 1099, 1123])).
% 1.97/2.15 tff(7503,plain,
% 1.97/2.15 (b(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6351, 7502, 300, 1099, 7427, 256, 4495, 11])).
% 1.97/2.15 tff(7504,plain,
% 1.97/2.15 (~r(elem!1, s(s(s(s(z)))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[5938, 268, 7502, 11, 1099])).
% 1.97/2.15 tff(7505,plain,
% 1.97/2.15 (s(s(s(s(z)))) = elem!1),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6664, 7504, 5914, 5912, 7503, 7426])).
% 1.97/2.15 tff(7506,plain,
% 1.97/2.15 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), elem!1)),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7505])).
% 1.97/2.15 tff(7507,plain,
% 1.97/2.15 (r(s(s(s(z))), elem!1)),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[300, 7506])).
% 1.97/2.15 tff(7508,plain,
% 1.97/2.15 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7505])).
% 1.97/2.15 tff(7509,plain,
% 1.97/2.15 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7508])).
% 1.97/2.15 tff(7510,plain,
% 1.97/2.15 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.97/2.15 inference(symmetry,[status(thm)],[7509])).
% 1.97/2.15 tff(7511,plain,
% 1.97/2.15 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7510])).
% 1.97/2.15 tff(7512,plain,
% 1.97/2.15 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7511])).
% 1.97/2.15 tff(7513,plain,
% 1.97/2.15 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[7512, 1307])).
% 1.97/2.15 tff(7514,plain,
% 1.97/2.15 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.97/2.15 inference(symmetry,[status(thm)],[7513])).
% 1.97/2.15 tff(7515,plain,
% 1.97/2.15 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7514])).
% 1.97/2.15 tff(7516,plain,
% 1.97/2.15 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1273, 7505])).
% 1.97/2.15 tff(7517,plain,
% 1.97/2.15 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1436, 7516])).
% 1.97/2.15 tff(7518,plain,
% 1.97/2.15 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[7517, 7515])).
% 1.97/2.15 tff(7519,plain,
% 1.97/2.15 (~(elem!1 = s(s(elem!1)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4223, 7518])).
% 1.97/2.15 tff(7520,plain,
% 1.97/2.15 (~(s(s(elem!1)) = elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3359, 7519])).
% 1.97/2.15 tff(7521,plain,
% 1.97/2.15 (b(s(elem!1), elem!1)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1336, 7505, 7503])).
% 1.97/2.15 tff(7522,plain,
% 1.97/2.15 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(elem!1))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7508])).
% 1.97/2.15 tff(7523,plain,
% 1.97/2.15 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[7505])).
% 1.97/2.15 tff(7524,plain,
% 1.97/2.15 (b(elem!1, s(s(s(s(s(z))))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[5912, 7523])).
% 1.97/2.15 tff(7525,plain,
% 1.97/2.15 (b(elem!1, s(elem!1))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[7524, 7522])).
% 1.97/2.15 tff(7526,plain,
% 1.97/2.15 ((s(s(s(s(z)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7505])).
% 1.97/2.16 tff(7527,plain,
% 1.97/2.16 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.97/2.16 inference(transitivity,[status(thm)],[7526, 144])).
% 1.97/2.16 tff(7528,plain,
% 1.97/2.16 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7527])).
% 1.97/2.16 tff(7529,plain,
% 1.97/2.16 (~(s(s(z)) = elem!1)),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[153, 7528])).
% 1.97/2.16 tff(7530,plain,
% 1.97/2.16 (~r(s(s(s(z))), s(s(z)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5861, 268, 700, 1545])).
% 1.97/2.16 tff(7531,plain,
% 1.97/2.16 (b(s(s(s(z))), s(s(z)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[2534, 69, 160, 7530])).
% 1.97/2.16 tff(7532,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(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7533,plain,
% 1.97/2.16 (((~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(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7534,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(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(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7533])).
% 1.97/2.16 tff(7535,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(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(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[7534, 7532])).
% 1.97/2.16 tff(7536,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(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))))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(7537,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[7536, 7535])).
% 1.97/2.16 tff(7538,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7537, 453, 758, 2090, 7531, 721])).
% 1.97/2.16 tff(7539,plain,((~r(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(7540,plain,
% 1.97/2.16 (~r(s(s(z)), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7539, 7425, 7423, 7507])).
% 1.97/2.16 tff(7541,plain,
% 1.97/2.16 (b(s(s(z)), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[782, 7540, 7529])).
% 1.97/2.16 tff(7542,plain,
% 1.97/2.16 ((s(s(z)) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[1258])).
% 1.97/2.16 tff(7543,plain,
% 1.97/2.16 ((s(s(z)) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.97/2.16 inference(transitivity,[status(thm)],[7542, 4133])).
% 1.97/2.16 tff(7544,plain,
% 1.97/2.16 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = s(elem!1))),
% 1.97/2.16 inference(symmetry,[status(thm)],[7543])).
% 1.97/2.16 tff(7545,plain,
% 1.97/2.16 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = s(elem!1)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7544])).
% 1.97/2.16 tff(7546,plain,
% 1.97/2.16 (~(s(s(z)) = s(elem!1))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[52, 7545])).
% 1.97/2.16 tff(7547,plain,
% 1.97/2.16 (~b(s(s(z)), s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7042, 453, 1071, 909, 922])).
% 1.97/2.16 tff(7548,plain,
% 1.97/2.16 (r(s(s(z)), s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4239, 69, 1189, 7547])).
% 1.97/2.16 tff(7549,plain,
% 1.97/2.16 (~b(s(elem!1), s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1079, 909, 1071, 629])).
% 1.97/2.16 tff(7550,plain,
% 1.97/2.16 (r(s(elem!1), s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[440, 7549, 6711])).
% 1.97/2.16 tff(7551,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7552,plain,
% 1.97/2.16 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7553,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1)))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7552])).
% 1.97/2.16 tff(7554,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[7553, 7551])).
% 1.97/2.16 tff(7555,plain,
% 1.97/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(7556,plain,
% 1.97/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1)))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[7555, 7554])).
% 1.97/2.16 tff(7557,plain,
% 1.97/2.16 (~r(s(s(z)), s(elem!1))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7556, 268, 7550, 7548])).
% 1.97/2.16 tff(7558,plain,
% 1.97/2.16 (~b(s(s(z)), s(elem!1))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4257, 453, 629, 1071, 922])).
% 1.97/2.16 tff(7559,plain,
% 1.97/2.16 ((s(s(z)) = s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4261, 69, 7558])).
% 1.97/2.16 tff(7560,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7559, 7557, 7546])).
% 1.97/2.16 tff(7561,plain,((~b(s(s(z)), elem!1)) | (~(s(s(s(s(z)))) = elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(7562,plain,
% 1.97/2.16 (~b(s(s(elem!1)), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7561, 7541, 7525, 7505, 7521])).
% 1.97/2.16 tff(7563,plain,
% 1.97/2.16 (r(s(s(elem!1)), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[2240, 7562, 7520])).
% 1.97/2.16 tff(7564,plain,
% 1.97/2.16 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5213, 7563, 7507])).
% 1.97/2.16 tff(7565,plain,
% 1.97/2.16 (b(s(s(s(z))), s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5203, 7564, 4877])).
% 1.97/2.16 tff(7566,plain,
% 1.97/2.16 (~r(s(s(elem!1)), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1970, 7563, 7502])).
% 1.97/2.16 tff(7567,plain,
% 1.97/2.16 (b(s(s(elem!1)), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1047, 7566])).
% 1.97/2.16 tff(7568,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(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), 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(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7569,plain,
% 1.97/2.16 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7570,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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7569])).
% 1.97/2.16 tff(7571,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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[7570, 7568])).
% 1.97/2.16 tff(7572,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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(7573,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[7572, 7571])).
% 1.97/2.16 tff(7574,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7573, 453, 7567, 7565, 5883, 7425])).
% 1.97/2.16 tff(7575,plain,((~r(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(z))))) | (elem!1 = s(z)) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(7576,plain,
% 1.97/2.16 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7575, 7333, 300, 1123, 1057])).
% 1.97/2.16 tff(7577,plain,
% 1.97/2.16 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[687, 7576])).
% 1.97/2.16 tff(7578,plain,
% 1.97/2.16 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[7577, 7422])).
% 1.97/2.16 tff(7579,plain,
% 1.97/2.16 (b(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[7578, 7421])).
% 1.97/2.16 tff(7580,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7215, 7579, 7419, 7411, 7409])).
% 1.97/2.16 tff(7581,plain,((~b(s(s(s(z))), elem!1)) | b(s(s(s(s(s(z))))), elem!1) | r(elem!1, s(z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (elem!1 = s(z)) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(7582,plain,
% 1.97/2.16 (~b(s(s(s(z))), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7581, 638, 2076, 300, 1123, 1057])).
% 1.97/2.16 tff(7583,plain,
% 1.97/2.16 (r(elem!1, s(elem!1))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[337, 76, 300])).
% 1.97/2.16 tff(7584,plain,
% 1.97/2.16 (~r(s(z), s(elem!1))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1751, 7583, 701])).
% 1.97/2.16 tff(7585,plain,
% 1.97/2.16 (r(s(z), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6774, 76, 701])).
% 1.97/2.16 tff(7586,plain,
% 1.97/2.16 (~b(s(z), s(elem!1))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4774, 7585, 300, 76, 4459, 2077])).
% 1.97/2.16 tff(7587,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[397, 7586, 7584, 172])).
% 1.97/2.16 tff(7588,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~r(s(z), elem!1)) | b(s(s(s(s(s(z))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(7589,plain,
% 1.97/2.16 (~(s(s(s(z))) = elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7588, 638, 5446, 7255, 300])).
% 1.97/2.16 tff(7590,plain,
% 1.97/2.16 (r(s(s(s(z))), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[74, 7589, 7582])).
% 1.97/2.16 tff(7591,plain,
% 1.97/2.16 (~r(s(s(z)), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7539, 7590, 7255, 7301])).
% 1.97/2.16 tff(7592,plain,
% 1.97/2.16 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[730, 3699, 701])).
% 1.97/2.16 tff(7593,plain,
% 1.97/2.16 (s(s(s(s(s(z))))) = elem!1),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[643, 7592, 638])).
% 1.97/2.16 tff(7594,plain,
% 1.97/2.16 (elem!1 = s(s(s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5538, 7593])).
% 1.97/2.16 tff(7595,plain,
% 1.97/2.16 (b(elem!1, s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7594])).
% 1.97/2.16 tff(7596,plain,
% 1.97/2.16 (b(s(s(s(s(s(z))))), s(z)) <=> b(elem!1, s(z))),
% 1.97/2.16 inference(symmetry,[status(thm)],[7595])).
% 1.97/2.16 tff(7597,plain,
% 1.97/2.16 ((~b(s(s(s(s(s(z))))), s(z))) <=> (~b(elem!1, s(z)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7596])).
% 1.97/2.16 tff(7598,plain,
% 1.97/2.16 (~b(elem!1, s(z))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[278, 7597])).
% 1.97/2.16 tff(7599,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[2077, 7598])).
% 1.97/2.16 tff(7600,plain,(b(s(s(s(s(s(z))))), s(z)) | (~b(elem!1, s(z))) | b(s(s(s(s(s(z))))), elem!1) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(7601,plain,
% 1.97/2.16 (b(s(s(s(s(s(z))))), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7600, 638, 5446, 7255])).
% 1.97/2.16 tff(7602,plain,
% 1.97/2.16 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3300, 453, 7601, 4540, 7301])).
% 1.97/2.16 tff(7603,plain,
% 1.97/2.16 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[687, 7602])).
% 1.97/2.16 tff(7604,plain,
% 1.97/2.16 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1566, 7603, 7590])).
% 1.97/2.16 tff(7605,plain,
% 1.97/2.16 (s(s(s(s(s(z))))) = elem!1),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[643, 7604, 638])).
% 1.97/2.16 tff(7606,plain,
% 1.97/2.16 ((s(s(s(s(s(z))))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7605])).
% 1.97/2.16 tff(7607,plain,
% 1.97/2.16 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.97/2.16 inference(transitivity,[status(thm)],[7606, 144])).
% 1.97/2.16 tff(7608,plain,
% 1.97/2.16 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7607])).
% 1.97/2.16 tff(7609,plain,
% 1.97/2.16 (~(s(s(z)) = elem!1)),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[52, 7608])).
% 1.97/2.16 tff(7610,plain,
% 1.97/2.16 (b(s(s(z)), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[782, 7609, 7591])).
% 1.97/2.16 tff(7611,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(elem!1, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7612,plain,
% 1.97/2.16 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7613,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7612])).
% 1.97/2.16 tff(7614,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.97/2.16 inference(transitivity,[status(thm)],[7613, 7611])).
% 1.97/2.16 tff(7615,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(7616,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(elem!1, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[7615, 7614])).
% 1.97/2.16 tff(7617,plain,
% 1.97/2.16 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7616, 453, 5446, 7610, 7318])).
% 1.97/2.16 tff(7618,plain,
% 1.97/2.16 ((s(s(z)) = s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[2370, 69, 7617])).
% 1.97/2.16 tff(7619,plain,
% 1.97/2.16 (r(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7618, 6241])).
% 1.97/2.16 tff(7620,plain,
% 1.97/2.16 (~r(s(s(s(z))), s(s(z)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6256, 268, 300, 7619])).
% 1.97/2.16 tff(7621,plain,
% 1.97/2.16 (b(s(s(s(z))), s(s(z)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[2534, 69, 160, 7620])).
% 1.97/2.16 tff(7622,plain,
% 1.97/2.16 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7575, 7603, 300, 1123, 1057])).
% 1.97/2.16 tff(7623,plain,
% 1.97/2.16 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[518, 7622])).
% 1.97/2.16 tff(7624,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(z)))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7625,plain,
% 1.97/2.16 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7626,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(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7625])).
% 1.97/2.16 tff(7627,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(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[7626, 7624])).
% 1.97/2.16 tff(7628,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(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(7629,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(z)))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[7628, 7627])).
% 1.97/2.16 tff(7630,plain,
% 1.97/2.16 (~b(s(z), s(s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7629, 453, 5446, 7623, 7318, 4540, 7301])).
% 1.97/2.16 tff(7631,plain,
% 1.97/2.16 (r(s(z), s(s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1677, 69, 50, 7630])).
% 1.97/2.16 tff(7632,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7633,plain,
% 1.97/2.16 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(7634,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[7633])).
% 1.97/2.16 tff(7635,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[7634, 7632])).
% 1.97/2.17 tff(7636,plain,
% 1.97/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(7637,plain,
% 1.97/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[7636, 7635])).
% 1.97/2.17 tff(7638,plain,
% 1.97/2.17 (~r(s(z), s(s(z)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7637, 268, 7631, 7619])).
% 1.97/2.17 tff(7639,plain,
% 1.97/2.17 (b(s(z), s(s(z)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[757, 7638])).
% 1.97/2.17 tff(7640,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(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7641,plain,
% 1.97/2.17 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), 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(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7642,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)), elem!1)) | (~b(s(s(z)), 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(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7641])).
% 1.97/2.17 tff(7643,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)), elem!1)) | (~b(s(s(z)), 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(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.97/2.17 inference(transitivity,[status(thm)],[7642, 7640])).
% 1.97/2.17 tff(7644,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)), elem!1)) | (~b(s(s(z)), 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))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(7645,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[7644, 7643])).
% 1.97/2.17 tff(7646,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7645, 453, 7610, 7639, 4540, 7621])).
% 1.97/2.17 tff(7647,plain,(b(s(s(s(s(s(z))))), elem!1) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (elem!1 = s(z)) | b(s(s(s(s(z)))), s(z)) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(7648,plain,
% 1.97/2.17 (b(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7647, 2076, 1123, 1057, 300])).
% 1.97/2.17 tff(7649,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(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7650,plain,
% 1.97/2.17 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7651,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7650])).
% 1.97/2.17 tff(7652,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.97/2.17 inference(transitivity,[status(thm)],[7651, 7649])).
% 1.97/2.17 tff(7653,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(7654,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(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[7653, 7652])).
% 1.97/2.17 tff(7655,plain,
% 1.97/2.17 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7654, 453, 5446, 7648, 7318])).
% 1.97/2.17 tff(7656,plain,
% 1.97/2.17 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2463, 69, 7655])).
% 1.97/2.17 tff(7657,plain,
% 1.97/2.17 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7656, 5338])).
% 1.97/2.17 tff(7658,plain,
% 1.97/2.17 (~r(s(z), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2254, 7657, 1099])).
% 1.97/2.17 tff(7659,plain,
% 1.97/2.17 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6968, 453, 5446, 7648, 7318])).
% 1.97/2.17 tff(7660,plain,
% 1.97/2.17 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[328, 7659])).
% 1.97/2.17 tff(7661,plain,
% 1.97/2.17 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[309, 7660, 300])).
% 1.97/2.17 tff(7662,plain,
% 1.97/2.17 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[687, 7661])).
% 1.97/2.17 tff(7663,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7664,plain,
% 1.97/2.17 (((~r(s(s(s(s(s(z))))), s(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(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7665,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(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(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7664])).
% 1.97/2.17 tff(7666,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(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(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[7665, 7663])).
% 1.97/2.17 tff(7667,plain,
% 1.97/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(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(z))), s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(7668,plain,
% 1.97/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[7667, 7666])).
% 1.97/2.17 tff(7669,plain,
% 1.97/2.17 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7668, 268, 7660, 300])).
% 1.97/2.17 tff(7670,plain,
% 1.97/2.17 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2570, 7669])).
% 1.97/2.17 tff(7671,plain,
% 1.97/2.17 (~b(s(z), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2619, 7670, 4540, 7662])).
% 1.97/2.17 tff(7672,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[372, 7671, 7658])).
% 1.97/2.17 tff(7673,plain,(r(elem!1, s(z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (elem!1 = s(z)) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(7674,plain,
% 1.97/2.17 (r(elem!1, s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7673, 1057, 1123, 300])).
% 1.97/2.17 tff(7675,plain,
% 1.97/2.17 (~r(elem!1, s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1596, 268, 7674, 1099])).
% 1.97/2.17 tff(7676,plain,
% 1.97/2.17 (~(elem!1 = s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8, 7316])).
% 1.97/2.17 tff(7677,plain,
% 1.97/2.17 (b(elem!1, s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1087, 7676, 7675])).
% 1.97/2.17 tff(7678,plain,
% 1.97/2.17 (~b(s(z), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5584, 453, 1779, 5517, 2090])).
% 1.97/2.17 tff(7679,plain,
% 1.97/2.17 (r(s(z), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[372, 7678])).
% 1.97/2.17 tff(7680,plain,
% 1.97/2.17 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4530, 7679, 701])).
% 1.97/2.17 tff(7681,plain,
% 1.97/2.17 (s(s(s(s(s(z))))) = elem!1),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[643, 7680, 638])).
% 1.97/2.17 tff(7682,plain,
% 1.97/2.17 (elem!1 = s(s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5538, 7681])).
% 1.97/2.17 tff(7683,plain,
% 1.97/2.17 (s(s(s(s(s(z))))) = elem!1),
% 1.97/2.17 inference(symmetry,[status(thm)],[7682])).
% 1.97/2.17 tff(7684,plain,
% 1.97/2.17 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(s(z)), elem!1)),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7683])).
% 1.97/2.17 tff(7685,plain,
% 1.97/2.17 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(symmetry,[status(thm)],[7684])).
% 1.97/2.17 tff(7686,plain,
% 1.97/2.17 (~(s(s(s(z))) = elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6652, 238, 5516])).
% 1.97/2.17 tff(7687,plain,
% 1.97/2.17 (~(s(s(s(s(z)))) = elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7315, 638, 5517, 701, 300])).
% 1.97/2.17 tff(7688,plain,
% 1.97/2.17 (b(s(s(s(s(z)))), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[254, 7687, 1168])).
% 1.97/2.17 tff(7689,plain,
% 1.97/2.17 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7334])).
% 1.97/2.17 tff(7690,plain,
% 1.97/2.17 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(symmetry,[status(thm)],[7689])).
% 1.97/2.17 tff(7691,plain,
% 1.97/2.17 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 1.97/2.17 inference(symmetry,[status(thm)],[7338])).
% 1.97/2.17 tff(7692,plain,
% 1.97/2.17 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7691, 5965])).
% 1.97/2.17 tff(7693,plain,
% 1.97/2.17 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.97/2.17 inference(symmetry,[status(thm)],[7692])).
% 1.97/2.17 tff(7694,plain,
% 1.97/2.17 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[5965])).
% 1.97/2.17 tff(7695,plain,
% 1.97/2.17 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.97/2.17 inference(transitivity,[status(thm)],[7694, 7693])).
% 1.97/2.17 tff(7696,plain,
% 1.97/2.17 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[5965])).
% 1.97/2.17 tff(7697,plain,
% 1.97/2.17 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[299, 7696])).
% 1.97/2.17 tff(7698,plain,
% 1.97/2.17 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5534, 5965, 1597])).
% 1.97/2.17 tff(7699,plain,
% 1.97/2.17 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[328, 7698])).
% 1.97/2.17 tff(7700,plain,
% 1.97/2.17 (b(s(s(elem!1)), elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6277, 7351, 2090, 300, 238, 1132, 5168, 7699, 7697])).
% 1.97/2.17 tff(7701,plain,
% 1.97/2.17 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[7700, 7695])).
% 1.97/2.17 tff(7702,plain,
% 1.97/2.17 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[7701, 7690])).
% 1.97/2.17 tff(7703,plain,
% 1.97/2.17 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[5965])).
% 1.97/2.17 tff(7704,plain,
% 1.97/2.17 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[1291, 7703])).
% 1.97/2.17 tff(7705,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7706,plain,
% 1.97/2.17 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7707,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7706])).
% 1.97/2.17 tff(7708,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[7707, 7705])).
% 1.97/2.17 tff(7709,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(7710,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[7709, 7708])).
% 1.97/2.17 tff(7711,plain,
% 1.97/2.17 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7710, 453, 7699, 7704])).
% 1.97/2.17 tff(7712,plain,
% 1.97/2.17 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7711, 7702])).
% 1.97/2.17 tff(7713,plain,
% 1.97/2.17 ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 1.97/2.17 inference(symmetry,[status(thm)],[3473])).
% 1.97/2.17 tff(7714,plain,
% 1.97/2.17 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7338])).
% 1.97/2.17 tff(7715,plain,
% 1.97/2.17 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[7714, 7713])).
% 1.97/2.17 tff(7716,plain,
% 1.97/2.17 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z)))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7715])).
% 1.97/2.17 tff(7717,plain,
% 1.97/2.17 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[555, 7716])).
% 1.97/2.17 tff(7718,plain,
% 1.97/2.17 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1238, 69, 7717, 7712])).
% 1.97/2.17 tff(7719,plain,
% 1.97/2.17 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7720,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7719])).
% 1.97/2.17 tff(7721,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[7720, 2698])).
% 1.97/2.17 tff(7722,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(7723,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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[7722, 7721])).
% 1.97/2.17 tff(7724,plain,
% 1.97/2.17 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7723, 453, 7699, 7697])).
% 1.97/2.17 tff(7725,plain,
% 1.97/2.17 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7724, 7702])).
% 1.97/2.17 tff(7726,plain,
% 1.97/2.17 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2696, 7725])).
% 1.97/2.17 tff(7727,plain,
% 1.97/2.17 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(s(s(s(z))) = s(s(s(s(s(s(s(z)))))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[7714])).
% 1.97/2.17 tff(7728,plain,
% 1.97/2.17 (~(s(s(s(z))) = s(s(s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[555, 7727])).
% 1.97/2.17 tff(7729,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(7730,plain,
% 1.97/2.17 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7731,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(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(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7730])).
% 1.97/2.18 tff(7732,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(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(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[7731, 7729])).
% 1.97/2.18 tff(7733,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7734,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7733, 7732])).
% 1.97/2.18 tff(7735,plain,
% 1.97/2.18 ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7734, 453, 7699, 7704])).
% 1.97/2.18 tff(7736,plain,
% 1.97/2.18 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7735, 7702])).
% 1.97/2.18 tff(7737,plain,
% 1.97/2.18 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7738,plain,
% 1.97/2.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7739,plain,
% 1.97/2.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7738, 7737])).
% 1.97/2.18 tff(7740,plain,
% 1.97/2.18 ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7739, 69])).
% 1.97/2.18 tff(7741,plain,
% 1.97/2.18 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7740, 7736, 7728])).
% 1.97/2.18 tff(7742,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7743,plain,
% 1.97/2.18 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7744,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7743])).
% 1.97/2.18 tff(7745,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[7744, 7742])).
% 1.97/2.18 tff(7746,plain,
% 1.97/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7747,plain,
% 1.97/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7746, 7745])).
% 1.97/2.18 tff(7748,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7747, 268, 300, 7741, 7726, 7718])).
% 1.97/2.18 tff(7749,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(7750,plain,
% 1.97/2.18 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7749, 1291, 2090, 238, 1132, 555, 7688, 300, 701])).
% 1.97/2.18 tff(7751,plain,
% 1.97/2.18 (r(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[643, 7750, 638])).
% 1.97/2.18 tff(7752,plain,
% 1.97/2.18 (~r(s(s(z)), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[777, 7751, 701])).
% 1.97/2.18 tff(7753,plain,
% 1.97/2.18 (~(elem!1 = s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[8, 7687])).
% 1.97/2.18 tff(7754,plain,
% 1.97/2.18 (b(elem!1, s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1087, 7753, 1597])).
% 1.97/2.18 tff(7755,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7756,plain,
% 1.97/2.18 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7757,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7756])).
% 1.97/2.18 tff(7758,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.97/2.18 inference(transitivity,[status(thm)],[7757, 7755])).
% 1.97/2.18 tff(7759,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7760,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7759, 7758])).
% 1.97/2.18 tff(7761,plain,
% 1.97/2.18 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7760, 453, 1291, 7754, 7688])).
% 1.97/2.18 tff(7762,plain,
% 1.97/2.18 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[518, 7761])).
% 1.97/2.18 tff(7763,plain,
% 1.97/2.18 (~b(s(s(z)), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[6077, 7762, 1291, 7688, 7754])).
% 1.97/2.18 tff(7764,plain,
% 1.97/2.18 (s(s(z)) = elem!1),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[782, 7763, 7752])).
% 1.97/2.18 tff(7765,plain,
% 1.97/2.18 (s(s(s(z))) = s(elem!1)),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7764])).
% 1.97/2.18 tff(7766,plain,
% 1.97/2.18 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7765])).
% 1.97/2.18 tff(7767,plain,
% 1.97/2.18 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[1779, 7766])).
% 1.97/2.18 tff(7768,plain,
% 1.97/2.18 (~r(s(s(s(s(s(z))))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[730, 7751, 701])).
% 1.97/2.18 tff(7769,plain,
% 1.97/2.18 (b(s(s(s(s(s(z))))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[297, 7768])).
% 1.97/2.18 tff(7770,plain,
% 1.97/2.18 (~r(s(z), s(s(s(s(s(z))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4530, 7751, 701])).
% 1.97/2.18 tff(7771,plain,
% 1.97/2.18 (b(s(z), s(s(s(s(s(z))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[372, 7770])).
% 1.97/2.18 tff(7772,plain,
% 1.97/2.18 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7765])).
% 1.97/2.18 tff(7773,plain,
% 1.97/2.18 (b(s(elem!1), s(z))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[5517, 7772])).
% 1.97/2.18 tff(7774,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(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7775,plain,
% 1.97/2.18 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7776,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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7775])).
% 1.97/2.18 tff(7777,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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[7776, 7774])).
% 1.97/2.18 tff(7778,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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7779,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7778, 7777])).
% 1.97/2.18 tff(7780,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7779, 453, 7773, 7771, 7769, 7767])).
% 1.97/2.18 tff(7781,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), elem!1)) | b(s(s(s(s(s(z))))), elem!1) | (~b(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(7782,plain,
% 1.97/2.18 (~b(s(s(s(z))), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7781, 1779, 701, 638, 2090, 238, 1132, 555, 300])).
% 1.97/2.18 tff(7783,plain,
% 1.97/2.18 (r(s(s(s(z))), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[74, 7782, 7686])).
% 1.97/2.18 tff(7784,plain,
% 1.97/2.18 (~r(s(s(z)), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7539, 7783, 701, 2090])).
% 1.97/2.18 tff(7785,plain,
% 1.97/2.18 (~(s(s(z)) = elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7218, 7783, 238, 638, 2090, 5517])).
% 1.97/2.18 tff(7786,plain,
% 1.97/2.18 (b(s(s(z)), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[782, 7785, 7784])).
% 1.97/2.18 tff(7787,plain,
% 1.97/2.18 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7786, 7685])).
% 1.97/2.18 tff(7788,plain,
% 1.97/2.18 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[6247, 453, 7786, 7754, 7688])).
% 1.97/2.18 tff(7789,plain,
% 1.97/2.18 ((s(s(z)) = s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2370, 69, 7788])).
% 1.97/2.18 tff(7790,plain,
% 1.97/2.18 (r(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7789, 6241])).
% 1.97/2.18 tff(7791,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7792,plain,
% 1.97/2.18 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7793,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7792])).
% 1.97/2.18 tff(7794,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[7793, 7791])).
% 1.97/2.18 tff(7795,plain,
% 1.97/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7796,plain,
% 1.97/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7795, 7794])).
% 1.97/2.18 tff(7797,plain,
% 1.97/2.18 (~r(s(s(z)), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7796, 268, 7783, 300, 7790])).
% 1.97/2.18 tff(7798,plain,
% 1.97/2.18 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1350, 69, 7797])).
% 1.97/2.18 tff(7799,plain,
% 1.97/2.18 (b(s(s(z)), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7798, 1243])).
% 1.97/2.18 tff(7800,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(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(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(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7801,plain,
% 1.97/2.18 (((~b(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(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(7802,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(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(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(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[7801])).
% 1.97/2.18 tff(7803,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(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(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(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[7802, 7800])).
% 1.97/2.18 tff(7804,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(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(7805,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[7804, 7803])).
% 1.97/2.18 tff(7806,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7805, 453, 1779, 5517, 7799, 7787])).
% 1.97/2.18 tff(7807,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | b(s(s(s(s(s(z))))), elem!1) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(7808,plain,
% 1.97/2.18 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7807, 638, 7255, 300, 7301, 7674, 1099, 4877])).
% 1.97/2.18 tff(7809,plain,
% 1.97/2.18 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[687, 7808])).
% 1.97/2.18 tff(7810,plain,
% 1.97/2.18 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7575, 7809, 300, 1123, 1057])).
% 1.97/2.18 tff(7811,plain,
% 1.97/2.18 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[518, 7810])).
% 1.97/2.18 tff(7812,plain,
% 1.97/2.18 (~b(s(z), s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3063, 453, 7811, 4540, 7301])).
% 1.97/2.18 tff(7813,plain,
% 1.97/2.18 (r(s(z), s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1677, 69, 50, 7812])).
% 1.97/2.18 tff(7814,plain,
% 1.97/2.18 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[6247, 453, 922, 530, 299])).
% 1.97/2.18 tff(7815,plain,
% 1.97/2.18 ((s(s(z)) = s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2370, 69, 7814])).
% 1.97/2.18 tff(7816,plain,
% 1.97/2.18 (r(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7815, 6241])).
% 1.97/2.18 tff(7817,plain,
% 1.97/2.18 (~r(s(s(s(z))), s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[6256, 268, 300, 7816])).
% 1.97/2.18 tff(7818,plain,
% 1.97/2.18 (b(s(s(s(z))), s(s(z)))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2534, 69, 160, 7817])).
% 1.97/2.19 tff(7819,plain,
% 1.97/2.19 (~r(s(z), s(s(z)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7637, 268, 376, 7816])).
% 1.97/2.19 tff(7820,plain,
% 1.97/2.19 (b(s(z), s(s(z)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[757, 7819])).
% 1.97/2.19 tff(7821,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7645, 453, 922, 7820, 120, 7818])).
% 1.97/2.19 tff(7822,plain,((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(7823,plain,
% 1.97/2.19 (~b(s(s(z)), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7822, 7813, 4540, 300, 7677, 7317])).
% 1.97/2.19 tff(7824,plain,
% 1.97/2.19 (~(s(s(s(z))) = elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[6652, 7674, 4539])).
% 1.97/2.19 tff(7825,plain,
% 1.97/2.19 (s(s(z)) = elem!1),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[782, 7432, 4])).
% 1.97/2.19 tff(7826,plain,
% 1.97/2.19 (s(s(s(z))) = s(elem!1)),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7825])).
% 1.97/2.19 tff(7827,plain,
% 1.97/2.19 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7826])).
% 1.97/2.19 tff(7828,plain,
% 1.97/2.19 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.97/2.19 inference(symmetry,[status(thm)],[7827])).
% 1.97/2.19 tff(7829,plain,
% 1.97/2.19 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7828])).
% 1.97/2.19 tff(7830,plain,
% 1.97/2.19 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.97/2.19 inference(symmetry,[status(thm)],[7829])).
% 1.97/2.19 tff(7831,plain,
% 1.97/2.19 (b(s(s(elem!1)), elem!1)),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[299, 7830])).
% 1.97/2.19 tff(7832,plain,
% 1.97/2.19 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7827])).
% 1.97/2.19 tff(7833,plain,
% 1.97/2.19 (b(elem!1, s(s(elem!1)))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[530, 7832])).
% 1.97/2.19 tff(7834,plain,
% 1.97/2.19 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7826])).
% 1.97/2.19 tff(7835,plain,
% 1.97/2.19 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.97/2.19 inference(symmetry,[status(thm)],[7834])).
% 1.97/2.19 tff(7836,plain,
% 1.97/2.19 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7827])).
% 1.97/2.19 tff(7837,plain,
% 1.97/2.19 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7836, 7835])).
% 1.97/2.19 tff(7838,plain,
% 1.97/2.19 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7826])).
% 1.97/2.19 tff(7839,plain,
% 1.97/2.19 (b(s(s(s(s(z)))), s(elem!1))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[523, 7838])).
% 1.97/2.19 tff(7840,plain,
% 1.97/2.19 (b(s(s(elem!1)), s(s(s(z))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7839, 7837])).
% 1.97/2.19 tff(7841,assumption,(b(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.97/2.19 tff(7842,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(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7843,plain,
% 1.97/2.19 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7844,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7843])).
% 1.97/2.19 tff(7845,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7844, 7842])).
% 1.97/2.19 tff(7846,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(7847,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7846, 7845])).
% 1.97/2.19 tff(7848,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7847, 453, 907, 909, 7841, 1291])).
% 1.97/2.19 tff(7849,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(7850,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7849, 7840, 7833, 5769, 7831])).
% 1.97/2.19 tff(7851,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(z)), elem!1) | (s(s(s(z))) = elem!1) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(7852,plain,
% 1.97/2.19 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7851, 7317, 7677, 7811, 7823, 7824, 7255, 7809])).
% 1.97/2.19 tff(7853,plain,
% 1.97/2.19 (s(s(s(s(s(z))))) = elem!1),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[643, 7852, 638])).
% 1.97/2.19 tff(7854,plain,
% 1.97/2.19 (~b(s(s(s(z))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7749, 7853, 7301, 7674, 1099, 4877, 7317, 300, 7255])).
% 1.97/2.19 tff(7855,plain,
% 1.97/2.19 (r(s(s(s(z))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[74, 7854, 7824])).
% 1.97/2.19 tff(7856,plain,
% 1.97/2.19 (~r(s(s(z)), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7539, 7855, 7255, 7301])).
% 1.97/2.19 tff(7857,plain,
% 1.97/2.19 (~(s(s(z)) = elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7218, 7855, 7674, 638, 7301, 4540])).
% 1.97/2.19 tff(7858,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[782, 7857, 7856, 7823])).
% 1.97/2.19 tff(7859,plain,(b(s(s(s(s(s(z))))), elem!1) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (elem!1 = s(z)) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(7860,plain,
% 1.97/2.19 (b(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7859, 1057, 1123, 300])).
% 1.97/2.19 tff(7861,plain,
% 1.97/2.19 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.19 inference(symmetry,[status(thm)],[7045])).
% 1.97/2.19 tff(7862,plain,
% 1.97/2.19 ((~b(s(s(s(z))), s(elem!1))) <=> (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7861])).
% 1.97/2.19 tff(7863,plain,
% 1.97/2.19 (~r(s(s(z)), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7539, 6988, 701, 2090])).
% 1.97/2.19 tff(7864,plain,
% 1.97/2.19 (b(s(s(z)), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[782, 7863, 6998])).
% 1.97/2.19 tff(7865,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7573, 453, 2223, 6720, 120, 2090])).
% 1.97/2.19 tff(7866,plain,((~r(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(7867,plain,
% 1.97/2.19 (~r(s(s(elem!1)), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7866, 6988, 2090, 555, 120, 238])).
% 1.97/2.19 tff(7868,plain,
% 1.97/2.19 (b(s(s(elem!1)), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2240, 7867, 6682])).
% 1.97/2.19 tff(7869,plain,
% 1.97/2.19 (~b(elem!1, s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7561, 7868, 1170, 7864, 6699])).
% 1.97/2.19 tff(7870,plain,
% 1.97/2.19 (r(elem!1, s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1069, 7869, 6983])).
% 1.97/2.19 tff(7871,plain,
% 1.97/2.19 (~r(s(z), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1751, 7870, 701])).
% 1.97/2.19 tff(7872,plain,
% 1.97/2.19 (b(s(z), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[397, 7871, 6986])).
% 1.97/2.19 tff(7873,plain,
% 1.97/2.19 (~r(s(elem!1), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[348, 7870, 238])).
% 1.97/2.19 tff(7874,plain,
% 1.97/2.19 (b(s(elem!1), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[353, 7873, 1182])).
% 1.97/2.19 tff(7875,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(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7876,plain,
% 1.97/2.19 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7877,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(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z)))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7876])).
% 1.97/2.19 tff(7878,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(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7877, 7875])).
% 1.97/2.19 tff(7879,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(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(7880,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(z)))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7879, 7878])).
% 1.97/2.19 tff(7881,plain,
% 1.97/2.19 (~b(s(s(s(z))), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7880, 453, 7874, 7872, 120])).
% 1.97/2.19 tff(7882,plain,
% 1.97/2.19 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7881, 7862])).
% 1.97/2.19 tff(7883,plain,
% 1.97/2.19 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(elem!1))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[1171])).
% 1.97/2.19 tff(7884,plain,
% 1.97/2.19 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.97/2.19 inference(symmetry,[status(thm)],[7883])).
% 1.97/2.19 tff(7885,plain,
% 1.97/2.19 (r(elem!1, s(s(s(s(s(z))))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7870, 7884])).
% 1.97/2.19 tff(7886,plain,
% 1.97/2.19 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5151, 7885, 6988, 7870])).
% 1.97/2.19 tff(7887,plain,
% 1.97/2.19 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2570, 7886])).
% 1.97/2.19 tff(7888,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7887, 7882])).
% 1.97/2.19 tff(7889,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(7890,plain,
% 1.97/2.19 (~(s(s(s(s(z)))) = elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7889, 4540, 7674, 7255, 7301, 4877, 300, 7860])).
% 1.97/2.19 tff(7891,plain,
% 1.97/2.19 (b(s(s(s(s(z)))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[254, 7890, 7302])).
% 1.97/2.19 tff(7892,plain,
% 1.97/2.19 (~(elem!1 = s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[8, 7890])).
% 1.97/2.19 tff(7893,plain,
% 1.97/2.19 (b(elem!1, s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1087, 7892, 7675])).
% 1.97/2.19 tff(7894,plain,
% 1.97/2.19 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7895,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7894])).
% 1.97/2.19 tff(7896,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7895, 5550])).
% 1.97/2.19 tff(7897,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(7898,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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7897, 7896])).
% 1.97/2.19 tff(7899,plain,
% 1.97/2.19 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7898, 453, 7860, 7893, 7891])).
% 1.97/2.19 tff(7900,plain,
% 1.97/2.19 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[328, 7899])).
% 1.97/2.19 tff(7901,plain,
% 1.97/2.19 (~r(s(s(s(s(s(z))))), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2414, 7900, 1099])).
% 1.97/2.19 tff(7902,plain,
% 1.97/2.19 (b(s(s(s(s(s(z))))), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[297, 7901])).
% 1.97/2.19 tff(7903,plain,
% 1.97/2.19 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[309, 7900, 300])).
% 1.97/2.19 tff(7904,plain,
% 1.97/2.19 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[687, 7903])).
% 1.97/2.19 tff(7905,plain,
% 1.97/2.19 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7906,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(z))), 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(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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)))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7905])).
% 1.97/2.19 tff(7907,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(z))), 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(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7906, 3295])).
% 1.97/2.19 tff(7908,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(z))), 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(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(7909,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7908, 7907])).
% 1.97/2.19 tff(7910,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7909, 453, 7904, 7902, 4540, 7301])).
% 1.97/2.19 tff(7911,plain,(b(s(s(s(s(z)))), s(z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(7912,plain,
% 1.97/2.19 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7911, 4535, 1123])).
% 1.97/2.19 tff(7913,plain,
% 1.97/2.19 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1656, 7912])).
% 1.97/2.19 tff(7914,plain,
% 1.97/2.19 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4119, 4536, 233])).
% 1.97/2.19 tff(7915,plain,
% 1.97/2.19 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[518, 7914])).
% 1.97/2.19 tff(7916,plain,
% 1.97/2.19 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1788, 7915, 1779, 7913])).
% 1.97/2.19 tff(7917,plain,
% 1.97/2.19 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[328, 7916])).
% 1.97/2.19 tff(7918,plain,
% 1.97/2.19 (~r(s(s(s(s(z)))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[5352, 7917, 722, 4536])).
% 1.97/2.19 tff(7919,plain,
% 1.97/2.19 (s(s(s(s(z)))) = elem!1),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[254, 7918, 249])).
% 1.97/2.19 tff(7920,plain,
% 1.97/2.19 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1273, 7919])).
% 1.97/2.19 tff(7921,plain,
% 1.97/2.19 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4108, 7919])).
% 1.97/2.19 tff(7922,plain,
% 1.97/2.19 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7921])).
% 1.97/2.19 tff(7923,plain,
% 1.97/2.19 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.97/2.19 inference(symmetry,[status(thm)],[7922])).
% 1.97/2.19 tff(7924,plain,
% 1.97/2.19 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7923])).
% 1.97/2.19 tff(7925,plain,
% 1.97/2.19 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 1.97/2.19 inference(symmetry,[status(thm)],[7924])).
% 1.97/2.19 tff(7926,plain,
% 1.97/2.19 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7925])).
% 1.97/2.19 tff(7927,plain,
% 1.97/2.19 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.97/2.19 inference(symmetry,[status(thm)],[7926])).
% 1.97/2.19 tff(7928,plain,
% 1.97/2.19 (r(elem!1, s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1130, 1123, 10])).
% 1.97/2.19 tff(7929,plain,
% 1.97/2.19 (~(s(s(s(elem!1))) = elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1215, 7919, 4877])).
% 1.97/2.19 tff(7930,plain,
% 1.97/2.19 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7924])).
% 1.97/2.19 tff(7931,plain,
% 1.97/2.19 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7930, 1307])).
% 1.97/2.19 tff(7932,plain,
% 1.97/2.19 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.97/2.19 inference(symmetry,[status(thm)],[7931])).
% 1.97/2.19 tff(7933,plain,
% 1.97/2.19 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7932])).
% 1.97/2.19 tff(7934,plain,
% 1.97/2.19 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1436, 7920])).
% 1.97/2.19 tff(7935,plain,
% 1.97/2.19 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[7934, 7933])).
% 1.97/2.19 tff(7936,plain,
% 1.97/2.19 (~(elem!1 = s(s(elem!1)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4223, 7935])).
% 1.97/2.19 tff(7937,plain,
% 1.97/2.19 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(elem!1), s(z))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7921])).
% 1.97/2.19 tff(7938,plain,
% 1.97/2.19 (b(s(elem!1), s(z))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[374, 7937])).
% 1.97/2.19 tff(7939,plain,
% 1.97/2.19 (~(s(elem!1) = s(s(elem!1)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1861, 7936])).
% 1.97/2.19 tff(7940,plain,
% 1.97/2.19 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7921])).
% 1.97/2.19 tff(7941,plain,
% 1.97/2.19 (r(s(elem!1), elem!1)),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[722, 7940])).
% 1.97/2.19 tff(7942,plain,
% 1.97/2.19 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7921])).
% 1.97/2.19 tff(7943,plain,
% 1.97/2.19 ((s(z) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(z))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7942, 173])).
% 1.97/2.19 tff(7944,plain,
% 1.97/2.19 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7943, 174])).
% 1.97/2.19 tff(7945,plain,
% 1.97/2.19 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(z) = s(elem!1)))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7944])).
% 1.97/2.19 tff(7946,plain,
% 1.97/2.19 (~(s(z) = s(elem!1))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[289, 7945])).
% 1.97/2.19 tff(7947,plain,
% 1.97/2.19 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(elem!1))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[7921])).
% 1.97/2.19 tff(7948,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(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(7949,plain,
% 1.97/2.19 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.97/2.20 inference(rewrite,[status(thm)],[])).
% 1.97/2.20 tff(7950,plain,
% 1.97/2.20 (((~![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(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 1.97/2.20 inference(monotonicity,[status(thm)],[7949])).
% 1.97/2.20 tff(7951,plain,
% 1.97/2.20 (((~![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(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.97/2.20 inference(transitivity,[status(thm)],[7950, 7948])).
% 1.97/2.20 tff(7952,plain,
% 1.97/2.20 ((~![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(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.97/2.20 inference(quant_inst,[status(thm)],[])).
% 1.97/2.20 tff(7953,plain,
% 1.97/2.20 ((~![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(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.97/2.20 inference(modus_ponens,[status(thm)],[7952, 7951])).
% 1.97/2.20 tff(7954,plain,
% 1.97/2.20 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[7953, 453, 1291, 1779, 1275])).
% 1.97/2.20 tff(7955,plain,
% 1.97/2.20 (r(elem!1, s(s(s(s(s(z))))))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[466, 7954, 2073])).
% 1.97/2.20 tff(7956,plain,
% 1.97/2.20 (r(elem!1, s(elem!1))),
% 1.97/2.20 inference(modus_ponens,[status(thm)],[7955, 7947])).
% 1.97/2.20 tff(7957,plain,
% 1.97/2.20 (~r(s(z), s(elem!1))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[1496, 7956, 7928])).
% 1.97/2.20 tff(7958,plain,
% 1.97/2.20 (b(s(z), s(elem!1))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[397, 7957, 7946])).
% 1.97/2.20 tff(7959,plain,
% 1.97/2.20 (~r(elem!1, s(s(elem!1)))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[2017, 7958, 7928, 7941, 7939, 7938])).
% 1.97/2.20 tff(7960,plain,
% 1.97/2.20 (b(elem!1, s(s(elem!1)))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[1024, 7959, 7936])).
% 1.97/2.20 tff(7961,plain,
% 1.97/2.20 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.97/2.20 inference(monotonicity,[status(thm)],[4146])).
% 1.97/2.20 tff(7962,plain,
% 1.97/2.20 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.97/2.20 inference(symmetry,[status(thm)],[7961])).
% 1.97/2.20 tff(7963,plain,
% 1.97/2.20 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 1.97/2.20 inference(monotonicity,[status(thm)],[7962])).
% 1.97/2.20 tff(7964,plain,
% 1.97/2.20 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.97/2.20 inference(monotonicity,[status(thm)],[7963])).
% 1.97/2.20 tff(7965,plain,
% 1.97/2.20 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.97/2.20 inference(modus_ponens,[status(thm)],[834, 7964])).
% 1.97/2.20 tff(7966,plain,
% 1.97/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7967,plain,
% 2.04/2.20 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7968,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7967])).
% 2.04/2.20 tff(7969,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[7968, 7966])).
% 2.04/2.20 tff(7970,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7971,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7970, 7969])).
% 2.04/2.20 tff(7972,plain,
% 2.04/2.20 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7971, 268, 233, 7965])).
% 2.04/2.20 tff(7973,plain,
% 2.04/2.20 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7963])).
% 2.04/2.20 tff(7974,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 2.04/2.20 tff(7975,plain,
% 2.04/2.20 (~r(s(s(s(elem!1))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[842, 834, 238])).
% 2.04/2.20 tff(7976,plain,
% 2.04/2.20 (b(s(s(s(elem!1))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[567, 7975, 7974])).
% 2.04/2.20 tff(7977,plain,
% 2.04/2.20 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7976, 7973])).
% 2.04/2.20 tff(7978,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(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7979,plain,
% 2.04/2.20 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7980,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(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(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7979])).
% 2.04/2.20 tff(7981,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(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(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.04/2.20 inference(transitivity,[status(thm)],[7980, 7978])).
% 2.04/2.20 tff(7982,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7983,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7982, 7981])).
% 2.04/2.20 tff(7984,plain,
% 2.04/2.20 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7983, 453, 907, 1291, 7977])).
% 2.04/2.20 tff(7985,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7740, 7984, 7972, 3475])).
% 2.04/2.20 tff(7986,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~(s(s(s(s(s(z))))) = s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(7987,plain,
% 2.04/2.20 (~r(s(s(s(elem!1))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7986, 7960, 1291, 233, 7921, 7929, 7928])).
% 2.04/2.20 tff(7988,plain,
% 2.04/2.20 (b(s(s(s(elem!1))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[856, 7987])).
% 2.04/2.20 tff(7989,plain,
% 2.04/2.20 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7988, 7927])).
% 2.04/2.20 tff(7990,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(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(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7991,plain,
% 2.04/2.20 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7992,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7991])).
% 2.04/2.20 tff(7993,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[7992, 7990])).
% 2.04/2.20 tff(7994,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(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7995,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(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7994, 7993])).
% 2.04/2.20 tff(7996,plain,
% 2.04/2.20 ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7995, 453, 7938, 7958])).
% 2.04/2.20 tff(7997,plain,
% 2.04/2.20 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7996, 7989])).
% 2.04/2.20 tff(7998,plain,
% 2.04/2.20 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3999, 7997, 7920])).
% 2.04/2.20 tff(7999,plain,
% 2.04/2.20 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7911, 1057, 1123])).
% 2.04/2.20 tff(8000,plain,
% 2.04/2.20 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1656, 7999])).
% 2.04/2.20 tff(8001,plain,
% 2.04/2.20 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4119, 1099, 233])).
% 2.04/2.20 tff(8002,plain,
% 2.04/2.20 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[518, 8001])).
% 2.04/2.20 tff(8003,plain,
% 2.04/2.20 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1788, 8002, 1779, 8000])).
% 2.04/2.20 tff(8004,plain,
% 2.04/2.20 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[328, 8003])).
% 2.04/2.20 tff(8005,plain,
% 2.04/2.20 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[5352, 8004, 722, 1099])).
% 2.04/2.20 tff(8006,plain,
% 2.04/2.20 (s(s(s(s(z)))) = elem!1),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[254, 8005, 249])).
% 2.04/2.20 tff(8007,plain,
% 2.04/2.20 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4108, 8006])).
% 2.04/2.20 tff(8008,plain,
% 2.04/2.20 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[8007])).
% 2.04/2.20 tff(8009,plain,
% 2.04/2.20 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 2.04/2.20 inference(symmetry,[status(thm)],[8008])).
% 2.04/2.20 tff(8010,plain,
% 2.04/2.20 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[8009])).
% 2.04/2.20 tff(8011,plain,
% 2.04/2.20 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[8010])).
% 2.04/2.20 tff(8012,plain,
% 2.04/2.20 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.04/2.20 inference(symmetry,[status(thm)],[8011])).
% 2.04/2.20 tff(8013,plain,
% 2.04/2.20 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1273, 8006])).
% 2.04/2.20 tff(8014,plain,
% 2.04/2.20 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[8010])).
% 2.04/2.20 tff(8015,plain,
% 2.04/2.20 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[1712, 8014])).
% 2.04/2.20 tff(8016,plain,
% 2.04/2.20 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[8007])).
% 2.04/2.20 tff(8017,plain,
% 2.04/2.20 (r(s(elem!1), elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[722, 8016])).
% 2.04/2.20 tff(8018,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(8019,plain,
% 2.04/2.20 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(8020,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[8019])).
% 2.04/2.20 tff(8021,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[8020, 8018])).
% 2.04/2.20 tff(8022,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(8023,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[8022, 8021])).
% 2.04/2.20 tff(8024,plain,
% 2.04/2.20 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[8023, 268, 8017, 8015])).
% 2.04/2.20 tff(8025,plain,
% 2.04/2.20 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3999, 8024, 8013])).
% 2.04/2.20 tff(8026,plain,
% 2.04/2.20 (b(s(s(s(elem!1))), s(elem!1))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[8025, 8012])).
% 2.04/2.20 tff(8027,plain,
% 2.04/2.20 (~r(s(s(s(elem!1))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[842, 1712, 7928])).
% 2.04/2.20 tff(8028,plain,
% 2.04/2.20 (b(s(s(s(elem!1))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[856, 8027])).
% 2.04/2.20 tff(8029,plain,
% 2.04/2.20 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(elem!1), s(z))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[8007])).
% 2.04/2.20 tff(8030,plain,
% 2.04/2.20 (b(s(elem!1), s(z))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[374, 8029])).
% 2.04/2.20 tff(8031,plain,
% 2.04/2.20 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[8007])).
% 2.04/2.20 tff(8032,plain,
% 2.04/2.20 ((s(z) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(z))),
% 2.04/2.20 inference(transitivity,[status(thm)],[8031, 173])).
% 2.04/2.20 tff(8033,plain,
% 2.04/2.20 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 2.04/2.20 inference(transitivity,[status(thm)],[8032, 174])).
% 2.04/2.20 tff(8034,plain,
% 2.04/2.20 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(z) = s(elem!1)))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[8033])).
% 2.04/2.20 tff(8035,plain,
% 2.04/2.20 (~(s(z) = s(elem!1))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[289, 8034])).
% 2.04/2.20 tff(8036,plain,
% 2.04/2.20 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[8007])).
% 2.04/2.20 tff(8037,plain,
% 2.04/2.20 (r(elem!1, s(elem!1))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[412, 8036])).
% 2.04/2.20 tff(8038,plain,
% 2.04/2.20 (~r(s(z), s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1496, 8037, 7928])).
% 2.04/2.20 tff(8039,plain,
% 2.04/2.20 (b(s(z), s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[397, 8038, 8035])).
% 2.04/2.20 tff(8040,plain,
% 2.04/2.20 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7215, 8039, 8030, 8028])).
% 2.04/2.20 tff(8041,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[8040, 8026])).
% 2.04/2.20 tff(8042,plain,(b(s(s(s(s(z)))), s(z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), elem!1) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | b(s(z), s(s(s(z)))) | b(elem!1, s(z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(8043,plain,
% 2.04/2.20 (b(s(z), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[8042, 4535, 722, 7955, 249, 1779, 233, 374, 10, 1123])).
% 2.04/2.20 tff(8044,plain,
% 2.04/2.20 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7919])).
% 2.04/2.20 tff(8045,plain,
% 2.04/2.20 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.20 inference(symmetry,[status(thm)],[8044])).
% 2.04/2.20 tff(8046,plain,
% 2.04/2.20 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7955, 8045])).
% 2.04/2.20 tff(8047,plain,
% 2.04/2.20 (~r(s(z), s(s(s(s(s(z))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2254, 8046, 4536])).
% 2.04/2.20 tff(8048,plain,
% 2.04/2.20 (b(s(z), s(s(s(s(s(z))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[372, 8047])).
% 2.04/2.20 tff(8049,plain,
% 2.04/2.20 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(8050,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[8049])).
% 2.04/2.20 tff(8051,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[8050, 4388])).
% 2.04/2.20 tff(8052,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(8053,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8052, 8051])).
% 2.04/2.21 tff(8054,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8053, 453, 443, 1779, 2611, 2090])).
% 2.04/2.21 tff(8055,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(8056,plain,
% 2.04/2.21 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8055, 8048, 1779, 8043])).
% 2.04/2.21 tff(8057,plain,
% 2.04/2.21 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2570, 8056])).
% 2.04/2.21 tff(8058,plain,
% 2.04/2.21 (r(s(s(s(z))), s(elem!1))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7024, 8057, 7919])).
% 2.04/2.21 tff(8059,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8060,plain,
% 2.04/2.21 (((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8061,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8060])).
% 2.04/2.21 tff(8062,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[8061, 8059])).
% 2.04/2.21 tff(8063,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(8064,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8063, 8062])).
% 2.04/2.21 tff(8065,plain,
% 2.04/2.21 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8064, 268, 8058, 7998])).
% 2.04/2.21 tff(8066,plain,
% 2.04/2.21 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7924])).
% 2.04/2.21 tff(8067,plain,
% 2.04/2.21 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7921])).
% 2.04/2.21 tff(8068,plain,
% 2.04/2.21 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[8067])).
% 2.04/2.21 tff(8069,plain,
% 2.04/2.21 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7925])).
% 2.04/2.21 tff(8070,plain,
% 2.04/2.21 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[8069, 8068])).
% 2.04/2.21 tff(8071,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(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(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(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8072,plain,
% 2.04/2.21 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8073,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(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(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(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8072])).
% 2.04/2.21 tff(8074,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(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(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(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[8073, 8071])).
% 2.04/2.21 tff(8075,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(8076,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(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8075, 8074])).
% 2.04/2.21 tff(8077,plain,
% 2.04/2.21 ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8076, 453, 7938, 7958])).
% 2.04/2.21 tff(8078,plain,
% 2.04/2.21 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8077, 7989])).
% 2.04/2.21 tff(8079,plain,
% 2.04/2.21 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1320, 8078, 7934])).
% 2.04/2.21 tff(8080,plain,
% 2.04/2.21 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8079, 8070])).
% 2.04/2.21 tff(8081,assumption,(r(s(s(s(s(s(z))))), s(s(s(elem!1))))), introduced(assumption)).
% 2.04/2.21 tff(8082,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8083,plain,
% 2.04/2.21 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8084,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8083])).
% 2.04/2.21 tff(8085,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[8084, 8082])).
% 2.04/2.21 tff(8086,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(8087,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8086, 8085])).
% 2.04/2.21 tff(8088,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8087, 268, 833, 722, 8081])).
% 2.04/2.21 tff(8089,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(8090,plain,
% 2.04/2.21 (~r(s(s(s(elem!1))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8089, 8080, 722])).
% 2.04/2.21 tff(8091,plain,
% 2.04/2.21 (b(s(s(s(elem!1))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[567, 8090, 7929])).
% 2.04/2.21 tff(8092,plain,
% 2.04/2.21 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8091, 8066])).
% 2.04/2.21 tff(8093,plain,
% 2.04/2.21 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7983, 453, 7960, 1291, 8092])).
% 2.04/2.21 tff(8094,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7740, 8093, 8065, 3475])).
% 2.04/2.21 tff(8095,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | b(s(s(s(s(z)))), elem!1) | b(elem!1, s(z)) | (elem!1 = s(z)) | (elem!1 = s(s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(8096,plain,
% 2.04/2.21 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8095, 4494, 3457, 3448, 4452, 249, 10, 3446, 2925, 4493])).
% 2.04/2.21 tff(8097,plain,
% 2.04/2.21 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[687, 8096])).
% 2.04/2.21 tff(8098,plain,
% 2.04/2.21 (~r(s(z), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[3160, 2246, 256])).
% 2.04/2.21 tff(8099,plain,
% 2.04/2.21 (b(s(z), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[227, 8098])).
% 2.04/2.21 tff(8100,plain,
% 2.04/2.21 (~r(s(z), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4530, 2246, 722])).
% 2.04/2.21 tff(8101,plain,
% 2.04/2.21 (b(s(z), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[506, 8100, 492])).
% 2.04/2.21 tff(8102,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(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), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8103,plain,
% 2.04/2.21 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8104,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8103])).
% 2.04/2.21 tff(8105,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[8104, 8102])).
% 2.04/2.21 tff(8106,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(8107,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8106, 8105])).
% 2.04/2.21 tff(8108,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8107, 453, 8101, 1291, 8099, 1275])).
% 2.04/2.21 tff(8109,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (s(z) = elem!1) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(8110,plain,
% 2.04/2.21 (~r(s(z), s(s(s(s(s(z))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8109, 4494, 4493, 3447, 8097, 3457])).
% 2.04/2.21 tff(8111,plain,
% 2.04/2.21 (b(s(z), s(s(s(s(s(z))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[372, 8110])).
% 2.04/2.21 tff(8112,plain,
% 2.04/2.21 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4108, 1170])).
% 2.04/2.21 tff(8113,plain,
% 2.04/2.21 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8112])).
% 2.04/2.21 tff(8114,plain,
% 2.04/2.21 (r(s(elem!1), s(s(s(z))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[256, 8113])).
% 2.04/2.21 tff(8115,plain,
% 2.04/2.21 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8112])).
% 2.04/2.21 tff(8116,plain,
% 2.04/2.21 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[8115])).
% 2.04/2.21 tff(8117,plain,
% 2.04/2.21 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8116])).
% 2.04/2.21 tff(8118,plain,
% 2.04/2.21 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 2.04/2.21 inference(symmetry,[status(thm)],[8117])).
% 2.04/2.21 tff(8119,plain,
% 2.04/2.21 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8118])).
% 2.04/2.21 tff(8120,plain,
% 2.04/2.21 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.04/2.21 inference(symmetry,[status(thm)],[8119])).
% 2.04/2.21 tff(8121,plain,
% 2.04/2.21 (~(s(s(s(elem!1))) = elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1215, 1170, 555])).
% 2.04/2.21 tff(8122,plain,
% 2.04/2.21 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8117])).
% 2.04/2.21 tff(8123,plain,
% 2.04/2.21 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[8122, 1307])).
% 2.04/2.21 tff(8124,plain,
% 2.04/2.21 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.21 inference(symmetry,[status(thm)],[8123])).
% 2.04/2.21 tff(8125,plain,
% 2.04/2.21 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8124])).
% 2.04/2.21 tff(8126,plain,
% 2.04/2.21 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[6679, 8125])).
% 2.04/2.21 tff(8127,plain,
% 2.04/2.21 (~(elem!1 = s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4223, 8126])).
% 2.04/2.21 tff(8128,plain,
% 2.04/2.21 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(elem!1), s(z))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8112])).
% 2.04/2.21 tff(8129,plain,
% 2.04/2.21 (b(s(elem!1), s(z))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[374, 8128])).
% 2.04/2.21 tff(8130,plain,
% 2.04/2.21 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(elem!1))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8112])).
% 2.04/2.21 tff(8131,plain,
% 2.04/2.21 (b(s(z), s(elem!1))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[443, 8130])).
% 2.04/2.21 tff(8132,plain,
% 2.04/2.21 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8112])).
% 2.04/2.21 tff(8133,plain,
% 2.04/2.21 (r(s(elem!1), elem!1)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[722, 8132])).
% 2.04/2.21 tff(8134,plain,
% 2.04/2.21 (~(s(elem!1) = s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1861, 8127])).
% 2.04/2.21 tff(8135,plain,
% 2.04/2.21 (~r(elem!1, s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2017, 8134, 238, 8133, 8131, 8129])).
% 2.04/2.21 tff(8136,plain,
% 2.04/2.21 (b(elem!1, s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1024, 8135, 8127])).
% 2.04/2.21 tff(8137,plain,
% 2.04/2.21 (~r(s(s(s(elem!1))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7986, 8136, 1291, 233, 8112, 8121, 238])).
% 2.04/2.21 tff(8138,plain,
% 2.04/2.21 (b(s(s(s(elem!1))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[856, 8137])).
% 2.04/2.21 tff(8139,plain,
% 2.04/2.21 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8138, 8120])).
% 2.04/2.21 tff(8140,plain,
% 2.04/2.21 ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8076, 453, 8129, 8131])).
% 2.04/2.21 tff(8141,plain,
% 2.04/2.21 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8140, 8139])).
% 2.04/2.21 tff(8142,plain,
% 2.04/2.21 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1320, 8141, 6679])).
% 2.04/2.21 tff(8143,plain,
% 2.04/2.21 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8117])).
% 2.04/2.21 tff(8144,plain,
% 2.04/2.21 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8112])).
% 2.04/2.21 tff(8145,plain,
% 2.04/2.21 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[8144])).
% 2.04/2.21 tff(8146,plain,
% 2.04/2.21 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8118])).
% 2.04/2.21 tff(8147,plain,
% 2.04/2.21 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[8146, 8145])).
% 2.04/2.21 tff(8148,plain,
% 2.04/2.21 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8142, 8147])).
% 2.04/2.21 tff(8149,plain,
% 2.04/2.21 (~r(s(s(s(elem!1))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8089, 8148, 722])).
% 2.04/2.21 tff(8150,plain,
% 2.04/2.21 (b(s(s(s(elem!1))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[567, 8149, 8121])).
% 2.04/2.21 tff(8151,plain,
% 2.04/2.21 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8150, 8143])).
% 2.04/2.21 tff(8152,plain,
% 2.04/2.21 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7983, 453, 8136, 1291, 8151])).
% 2.04/2.21 tff(8153,plain,
% 2.04/2.21 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7740, 8152, 3475])).
% 2.04/2.21 tff(8154,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8155,plain,
% 2.04/2.21 (((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(8156,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[8155])).
% 2.04/2.21 tff(8157,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[8156, 8154])).
% 2.04/2.21 tff(8158,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(8159,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8158, 8157])).
% 2.04/2.21 tff(8160,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8159, 268, 8153, 8142, 8114])).
% 2.04/2.21 tff(8161,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(8162,plain,
% 2.04/2.21 (~(s(s(s(s(z)))) = elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8161, 4494, 3457, 3448, 3449, 4452, 8111, 8097, 4431])).
% 2.04/2.21 tff(8163,plain,
% 2.04/2.21 (~(elem!1 = s(s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8, 8162])).
% 2.04/2.21 tff(8164,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(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8165,plain,
% 2.04/2.22 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8166,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(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z)))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8165])).
% 2.04/2.22 tff(8167,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(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[8166, 8164])).
% 2.04/2.22 tff(8168,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(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(8169,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z)))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8168, 8167])).
% 2.04/2.22 tff(8170,plain,
% 2.04/2.22 (~b(elem!1, s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8169, 453, 4121, 1291, 1275])).
% 2.04/2.22 tff(8171,plain,
% 2.04/2.22 (r(elem!1, s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1087, 8170, 1055])).
% 2.04/2.22 tff(8172,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1596, 268, 238, 1132, 8171])).
% 2.04/2.22 tff(8173,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(8174,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8173, 8163, 3449, 4494, 4493, 3448])).
% 2.04/2.22 tff(8175,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1098, 8174])).
% 2.04/2.22 tff(8176,plain,
% 2.04/2.22 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[254, 8162, 249])).
% 2.04/2.22 tff(8177,plain,
% 2.04/2.22 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4508, 268, 3457, 8176])).
% 2.04/2.22 tff(8178,plain,
% 2.04/2.22 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[328, 8177])).
% 2.04/2.22 tff(8179,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(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(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(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8180,plain,
% 2.04/2.22 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8181,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8180])).
% 2.04/2.22 tff(8182,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[8181, 8179])).
% 2.04/2.22 tff(8183,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(8184,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8183, 8182])).
% 2.04/2.22 tff(8185,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8184, 453, 443, 1764, 1780, 2497])).
% 2.04/2.22 tff(8186,plain,((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(8187,plain,
% 2.04/2.22 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8186, 8178, 8111, 8175])).
% 2.04/2.22 tff(8188,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4516, 268, 3457, 8176])).
% 2.04/2.22 tff(8189,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2463, 69, 8188, 8187, 2453])).
% 2.04/2.22 tff(8190,plain,(b(s(s(s(s(s(z))))), elem!1) | b(s(s(s(s(z)))), elem!1) | b(elem!1, s(z)) | r(s(s(s(z))), elem!1) | b(s(s(s(z))), s(z)) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(8191,plain,
% 2.04/2.22 (b(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8190, 128, 10, 2, 249, 637])).
% 2.04/2.22 tff(8192,plain,
% 2.04/2.22 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[76])).
% 2.04/2.22 tff(8193,plain,
% 2.04/2.22 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4309, 4463, 10])).
% 2.04/2.22 tff(8194,plain,
% 2.04/2.22 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4499, 8193])).
% 2.04/2.22 tff(8195,plain,
% 2.04/2.22 (~(s(s(s(s(z)))) = elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4108, 8194])).
% 2.04/2.22 tff(8196,plain,
% 2.04/2.22 (b(s(z), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2070, 8195, 76, 10, 3448])).
% 2.04/2.22 tff(8197,plain,
% 2.04/2.22 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[201])).
% 2.04/2.22 tff(8198,plain,
% 2.04/2.22 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[414])).
% 2.04/2.22 tff(8199,plain,
% 2.04/2.22 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[8198, 8197])).
% 2.04/2.22 tff(8200,plain,
% 2.04/2.22 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[4726])).
% 2.04/2.22 tff(8201,plain,
% 2.04/2.22 (~(elem!1 = s(s(elem!1)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4877, 8200])).
% 2.04/2.22 tff(8202,plain,
% 2.04/2.22 (r(elem!1, s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1130, 2081, 1123])).
% 2.04/2.22 tff(8203,plain,
% 2.04/2.22 (~r(s(z), s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1496, 8202, 7583])).
% 2.04/2.22 tff(8204,plain,
% 2.04/2.22 (b(s(z), s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[397, 8203, 172])).
% 2.04/2.22 tff(8205,plain,
% 2.04/2.22 (b(s(elem!1), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1795, 162, 1764])).
% 2.04/2.22 tff(8206,plain,
% 2.04/2.22 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[512, 162, 11])).
% 2.04/2.22 tff(8207,plain,
% 2.04/2.22 (r(s(elem!1), elem!1)),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8206, 231])).
% 2.04/2.22 tff(8208,plain,
% 2.04/2.22 (~r(elem!1, s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2017, 8207, 8202, 411, 8205, 8204])).
% 2.04/2.22 tff(8209,plain,
% 2.04/2.22 (b(elem!1, s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1024, 8208, 8201])).
% 2.04/2.22 tff(8210,plain,
% 2.04/2.22 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8209, 8199])).
% 2.04/2.22 tff(8211,plain,
% 2.04/2.22 (~(s(elem!1) = elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4342, 8205, 2081])).
% 2.04/2.22 tff(8212,plain,
% 2.04/2.22 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[607, 8211])).
% 2.04/2.22 tff(8213,plain,
% 2.04/2.22 (b(s(z), s(s(s(s(z)))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8204, 375])).
% 2.04/2.22 tff(8214,plain,
% 2.04/2.22 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1992, 8213, 1764, 162, 8202, 11])).
% 2.04/2.22 tff(8215,plain,
% 2.04/2.22 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[687, 8214])).
% 2.04/2.22 tff(8216,plain,
% 2.04/2.22 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4403, 8215, 8212, 8210, 2090, 162])).
% 2.04/2.22 tff(8217,plain,
% 2.04/2.22 (~b(s(s(s(elem!1))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4409, 8216, 162])).
% 2.04/2.22 tff(8218,plain,
% 2.04/2.22 (r(s(s(s(elem!1))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[567, 8217, 200])).
% 2.04/2.22 tff(8219,plain,
% 2.04/2.22 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8218, 4566])).
% 2.04/2.22 tff(8220,plain,
% 2.04/2.22 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8219, 4565])).
% 2.04/2.22 tff(8221,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8222,plain,
% 2.04/2.22 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8223,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8222])).
% 2.04/2.22 tff(8224,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[8223, 8221])).
% 2.04/2.22 tff(8225,plain,
% 2.04/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(8226,plain,
% 2.04/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8225, 8224])).
% 2.04/2.22 tff(8227,plain,
% 2.04/2.22 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8226, 268, 11])).
% 2.04/2.22 tff(8228,plain,
% 2.04/2.22 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8227, 8220])).
% 2.04/2.22 tff(8229,plain,
% 2.04/2.22 (~r(s(s(s(elem!1))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[842, 8218, 8202])).
% 2.04/2.22 tff(8230,plain,
% 2.04/2.22 (b(s(s(s(elem!1))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[856, 8229])).
% 2.04/2.22 tff(8231,plain,
% 2.04/2.22 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8230, 243])).
% 2.04/2.22 tff(8232,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8233,plain,
% 2.04/2.22 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8234,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(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8233])).
% 2.04/2.22 tff(8235,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(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[8234, 8232])).
% 2.04/2.22 tff(8236,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(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(8237,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8236, 8235])).
% 2.04/2.22 tff(8238,plain,
% 2.04/2.22 ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8237, 453, 1764, 8213])).
% 2.04/2.22 tff(8239,plain,
% 2.04/2.22 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8238, 8231])).
% 2.04/2.22 tff(8240,plain,
% 2.04/2.22 (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2210, 69, 8239, 8228])).
% 2.04/2.22 tff(8241,plain,
% 2.04/2.22 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 2.04/2.22 inference(transitivity,[status(thm)],[8240, 531])).
% 2.04/2.22 tff(8242,plain,
% 2.04/2.22 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[6514, 540])).
% 2.04/2.22 tff(8243,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8242, 8241])).
% 2.04/2.22 tff(8244,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (elem!1 = s(z)) | b(s(s(s(z))), s(z)) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(8245,plain,
% 2.04/2.22 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8244, 8196, 76, 128, 1123, 4463, 4454])).
% 2.04/2.22 tff(8246,plain,
% 2.04/2.22 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1656, 8245])).
% 2.04/2.22 tff(8247,plain,
% 2.04/2.22 (b(elem!1, s(s(s(s(z)))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8246, 8192])).
% 2.04/2.22 tff(8248,plain,
% 2.04/2.22 (b(s(z), elem!1)),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8196, 115])).
% 2.04/2.22 tff(8249,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3620, 8248, 8247, 374, 646])).
% 2.04/2.22 tff(8250,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | b(s(s(s(z))), s(z)) | (elem!1 = s(z)) | b(elem!1, s(z)) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(8251,plain,
% 2.04/2.22 (~(s(s(s(z))) = elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8250, 4452, 8191, 128, 3446, 10, 249])).
% 2.04/2.22 tff(8252,plain,
% 2.04/2.22 (~(elem!1 = s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4487, 8251])).
% 2.04/2.22 tff(8253,plain,
% 2.04/2.22 (b(elem!1, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4492, 8252, 3456])).
% 2.04/2.22 tff(8254,plain,
% 2.04/2.22 (~r(elem!1, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3455, 268, 238, 233])).
% 2.04/2.22 tff(8255,plain,
% 2.04/2.22 (b(elem!1, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4492, 5525, 8254])).
% 2.04/2.22 tff(8256,plain,
% 2.04/2.22 (~(s(s(s(elem!1))) = elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1215, 1170, 548])).
% 2.04/2.22 tff(8257,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(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8258,plain,
% 2.04/2.22 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8259,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8258])).
% 2.04/2.22 tff(8260,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[8259, 8257])).
% 2.04/2.22 tff(8261,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(8262,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8261, 8260])).
% 2.04/2.22 tff(8263,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8262, 453, 1059, 499, 629, 1275])).
% 2.04/2.22 tff(8264,plain,((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(8265,plain,
% 2.04/2.22 (~b(s(z), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8264, 8129, 6699, 8255])).
% 2.04/2.22 tff(8266,plain,
% 2.04/2.22 (r(s(z), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[506, 8265, 492])).
% 2.04/2.22 tff(8267,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(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8268,plain,
% 2.04/2.22 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8269,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8268])).
% 2.04/2.23 tff(8270,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.23 inference(transitivity,[status(thm)],[8269, 8267])).
% 2.04/2.23 tff(8271,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8272,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(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8271, 8270])).
% 2.04/2.23 tff(8273,plain,
% 2.04/2.23 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8272, 453, 4165, 646, 8255])).
% 2.04/2.23 tff(8274,plain,
% 2.04/2.23 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2570, 8273])).
% 2.04/2.23 tff(8275,plain,
% 2.04/2.23 (r(s(s(s(z))), s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7024, 1170, 8274])).
% 2.04/2.23 tff(8276,plain,
% 2.04/2.23 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[1170])).
% 2.04/2.23 tff(8277,plain,
% 2.04/2.23 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8276])).
% 2.04/2.23 tff(8278,plain,
% 2.04/2.23 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[2690, 8277])).
% 2.04/2.23 tff(8279,plain,
% 2.04/2.23 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[7963])).
% 2.04/2.23 tff(8280,plain,
% 2.04/2.23 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[833, 8279])).
% 2.04/2.23 tff(8281,plain,
% 2.04/2.23 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.23 inference(symmetry,[status(thm)],[4152])).
% 2.04/2.23 tff(8282,plain,
% 2.04/2.23 ((~r(elem!1, s(elem!1))) <=> (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8281])).
% 2.04/2.23 tff(8283,plain,
% 2.04/2.23 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1436, 1284])).
% 2.04/2.23 tff(8284,plain,
% 2.04/2.23 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 2.04/2.23 inference(symmetry,[status(thm)],[7963])).
% 2.04/2.23 tff(8285,plain,
% 2.04/2.23 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8284])).
% 2.04/2.23 tff(8286,plain,
% 2.04/2.23 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.04/2.23 inference(symmetry,[status(thm)],[8285])).
% 2.04/2.23 tff(8287,plain,
% 2.04/2.23 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[1110, 8286])).
% 2.04/2.23 tff(8288,plain,
% 2.04/2.23 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(z))),
% 2.04/2.23 inference(commutativity,[status(thm)],[])).
% 2.04/2.23 tff(8289,plain,
% 2.04/2.23 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(z) = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(symmetry,[status(thm)],[8288])).
% 2.04/2.23 tff(8290,plain,
% 2.04/2.23 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(s(s(z)))))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8289])).
% 2.04/2.23 tff(8291,plain,
% 2.04/2.23 (~(s(z) = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[2636, 8290])).
% 2.04/2.23 tff(8292,assumption,(r(s(s(s(s(s(s(s(z))))))), elem!1)), introduced(assumption)).
% 2.04/2.23 tff(8293,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8294,plain,
% 2.04/2.23 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8295,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8294])).
% 2.04/2.23 tff(8296,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.04/2.23 inference(transitivity,[status(thm)],[8295, 8293])).
% 2.04/2.23 tff(8297,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8298,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8297, 8296])).
% 2.04/2.23 tff(8299,plain,
% 2.04/2.23 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8298, 268, 701, 8292])).
% 2.04/2.23 tff(8300,plain,
% 2.04/2.23 ((s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1485, 69, 8299])).
% 2.04/2.23 tff(8301,plain,
% 2.04/2.23 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8300, 8291])).
% 2.04/2.23 tff(8302,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(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(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8303,plain,
% 2.04/2.23 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8304,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(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(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8303])).
% 2.04/2.23 tff(8305,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(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(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[8304, 8302])).
% 2.04/2.23 tff(8306,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(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8307,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(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8306, 8305])).
% 2.04/2.23 tff(8308,plain,
% 2.04/2.23 ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8307, 453, 1059, 8301])).
% 2.04/2.23 tff(8309,plain,
% 2.04/2.23 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8308, 8287])).
% 2.04/2.23 tff(8310,plain,
% 2.04/2.23 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1320, 8309, 8283])).
% 2.04/2.23 tff(8311,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(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(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8312,plain,
% 2.04/2.23 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8313,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8312])).
% 2.04/2.23 tff(8314,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[8313, 8311])).
% 2.04/2.23 tff(8315,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8316,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8315, 8314])).
% 2.04/2.23 tff(8317,plain,
% 2.04/2.23 ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8316, 453, 1059, 8301])).
% 2.04/2.23 tff(8318,plain,
% 2.04/2.23 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8317, 8287])).
% 2.04/2.23 tff(8319,plain,
% 2.04/2.23 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[3999, 8318, 1284])).
% 2.04/2.23 tff(8320,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8321,plain,
% 2.04/2.23 (((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8322,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8321])).
% 2.04/2.23 tff(8323,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[8322, 8320])).
% 2.04/2.23 tff(8324,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8325,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8324, 8323])).
% 2.04/2.23 tff(8326,plain,
% 2.04/2.23 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8325, 268, 233, 7009, 8319])).
% 2.04/2.23 tff(8327,plain,
% 2.04/2.23 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1238, 69, 2663, 8326])).
% 2.04/2.23 tff(8328,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8329,plain,
% 2.04/2.23 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8330,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(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(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(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8329])).
% 2.04/2.23 tff(8331,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(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(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(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[8330, 8328])).
% 2.04/2.23 tff(8332,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(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8333,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(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8332, 8331])).
% 2.04/2.23 tff(8334,plain,
% 2.04/2.23 (~b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8333, 453, 4165, 8255, 8327])).
% 2.04/2.23 tff(8335,plain,
% 2.04/2.23 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[3856, 8334, 3844])).
% 2.04/2.23 tff(8336,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8337,plain,
% 2.04/2.23 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8338,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8337])).
% 2.04/2.23 tff(8339,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[8338, 8336])).
% 2.04/2.23 tff(8340,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(elem!1))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8341,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8340, 8339])).
% 2.04/2.23 tff(8342,plain,
% 2.04/2.23 (~r(elem!1, s(elem!1))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8341, 268, 8335, 8310])).
% 2.04/2.23 tff(8343,plain,
% 2.04/2.23 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8342, 8282])).
% 2.04/2.23 tff(8344,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(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8345,plain,
% 2.04/2.23 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8346,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8345])).
% 2.04/2.24 tff(8347,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.24 inference(transitivity,[status(thm)],[8346, 8344])).
% 2.04/2.24 tff(8348,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(8349,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))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8348, 8347])).
% 2.04/2.24 tff(8350,plain,
% 2.04/2.24 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8349, 453, 4165, 646, 8255])).
% 2.04/2.24 tff(8351,plain,
% 2.04/2.24 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[687, 8350])).
% 2.04/2.24 tff(8352,plain,
% 2.04/2.24 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[7963])).
% 2.04/2.24 tff(8353,plain,
% 2.04/2.24 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[8352, 1307])).
% 2.04/2.24 tff(8354,plain,
% 2.04/2.24 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.24 inference(symmetry,[status(thm)],[8353])).
% 2.04/2.24 tff(8355,plain,
% 2.04/2.24 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8354])).
% 2.04/2.24 tff(8356,plain,
% 2.04/2.24 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8283, 8355])).
% 2.04/2.24 tff(8357,plain,
% 2.04/2.24 (~(elem!1 = s(s(elem!1)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4223, 8356])).
% 2.04/2.24 tff(8358,plain,
% 2.04/2.24 (~(s(s(elem!1)) = elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3359, 8357])).
% 2.04/2.24 tff(8359,plain,
% 2.04/2.24 ((elem!1 = s(s(s(s(s(z)))))) <=> (elem!1 = s(elem!1))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[4146])).
% 2.04/2.24 tff(8360,plain,
% 2.04/2.24 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(elem!1) = elem!1)),
% 2.04/2.24 inference(transitivity,[status(thm)],[8359, 1027])).
% 2.04/2.24 tff(8361,plain,
% 2.04/2.24 ((elem!1 = s(s(s(s(s(z)))))) <=> (elem!1 = s(elem!1))),
% 2.04/2.24 inference(transitivity,[status(thm)],[8360, 1028])).
% 2.04/2.24 tff(8362,plain,
% 2.04/2.24 ((~(elem!1 = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(elem!1)))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8361])).
% 2.04/2.24 tff(8363,plain,
% 2.04/2.24 (~(elem!1 = s(elem!1))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[2073, 8362])).
% 2.04/2.24 tff(8364,plain,
% 2.04/2.24 (b(elem!1, s(elem!1))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1069, 8342, 8363])).
% 2.04/2.24 tff(8365,plain,
% 2.04/2.24 (~b(s(s(elem!1)), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4210, 8364, 2, 555, 59, 646])).
% 2.04/2.24 tff(8366,plain,
% 2.04/2.24 (r(s(s(elem!1)), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2240, 8365, 8358])).
% 2.04/2.24 tff(8367,plain,
% 2.04/2.24 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[7961])).
% 2.04/2.24 tff(8368,plain,
% 2.04/2.24 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8367])).
% 2.04/2.24 tff(8369,plain,
% 2.04/2.24 (~(s(s(z)) = s(s(elem!1)))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[2661, 8368])).
% 2.04/2.24 tff(8370,plain,
% 2.04/2.24 (~r(s(s(elem!1)), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1970, 8366, 238])).
% 2.04/2.24 tff(8371,plain,
% 2.04/2.24 (b(s(s(elem!1)), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1047, 8370])).
% 2.04/2.24 tff(8372,plain,
% 2.04/2.24 (~r(s(s(z)), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4248, 8371, 8369, 701, 8366])).
% 2.04/2.24 tff(8373,plain,
% 2.04/2.24 (b(s(s(z)), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[782, 8372, 4060])).
% 2.04/2.24 tff(8374,plain,
% 2.04/2.24 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4084, 8373, 646, 4165, 8351])).
% 2.04/2.24 tff(8375,plain,
% 2.04/2.24 (r(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[466, 8374, 2073])).
% 2.04/2.24 tff(8376,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8375, 8343])).
% 2.04/2.24 tff(8377,plain,((~r(s(z), elem!1)) | (~(s(s(s(s(s(z))))) = s(elem!1))) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (s(s(z)) = elem!1) | (~r(elem!1, s(z))) | r(s(s(s(z))), elem!1) | (s(s(s(z))) = s(s(elem!1))) | (s(s(s(z))) = elem!1) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(8378,plain,
% 2.04/2.24 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8377, 2220, 2073, 646, 4060, 238, 2, 555, 59, 3844, 233, 7009, 1284, 1059, 4146, 701])).
% 2.04/2.24 tff(8379,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8378, 8280])).
% 2.04/2.24 tff(8380,plain,((~r(s(s(s(elem!1))), elem!1)) | (~(s(s(s(s(s(z))))) = s(elem!1))) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (s(s(z)) = elem!1) | (~r(elem!1, s(z))) | r(s(s(s(z))), elem!1) | (s(s(s(z))) = s(s(elem!1))) | (s(s(s(z))) = elem!1) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~b(s(elem!1), s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(8381,plain,
% 2.04/2.24 (~r(s(s(s(elem!1))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8380, 8112, 2073, 646, 4060, 238, 2, 548, 59, 8278, 233, 8275, 6678, 8129, 8266])).
% 2.04/2.24 tff(8382,plain,
% 2.04/2.24 (b(s(s(s(elem!1))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[567, 8381, 8256])).
% 2.04/2.24 tff(8383,plain,
% 2.04/2.24 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8382, 8143])).
% 2.04/2.24 tff(8384,plain,
% 2.04/2.24 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1234, 453, 4165, 8383, 8255])).
% 2.04/2.24 tff(8385,plain,
% 2.04/2.24 (s(elem!1) = s(s(s(s(s(z)))))),
% 2.04/2.24 inference(symmetry,[status(thm)],[8112])).
% 2.04/2.24 tff(8386,plain,
% 2.04/2.24 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8385])).
% 2.04/2.24 tff(8387,plain,
% 2.04/2.24 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.04/2.24 inference(symmetry,[status(thm)],[8386])).
% 2.04/2.24 tff(8388,plain,
% 2.04/2.24 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8387])).
% 2.04/2.24 tff(8389,plain,
% 2.04/2.24 (~(s(elem!1) = s(s(s(z))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[111, 8388])).
% 2.04/2.24 tff(8390,plain,
% 2.04/2.24 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1329, 8383, 6699, 4165, 6678, 8255, 8389])).
% 2.04/2.24 tff(8391,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1238, 69, 2663, 8390, 8384])).
% 2.04/2.24 tff(8392,plain,((~(s(s(s(s(z)))) = elem!1)) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (s(s(z)) = elem!1) | (~r(elem!1, s(z))) | r(s(s(s(z))), elem!1) | (s(s(s(z))) = elem!1) | (~r(s(s(s(z))), s(z))) | (s(z) = elem!1) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(8393,plain,
% 2.04/2.24 (~(s(s(s(s(z)))) = elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8392, 8191, 2925, 4051, 3449, 2, 8251, 3448, 3447, 4452])).
% 2.04/2.24 tff(8394,plain,
% 2.04/2.24 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[254, 8393, 249])).
% 2.04/2.24 tff(8395,plain,
% 2.04/2.24 (b(s(s(s(z))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[74, 8251, 2])).
% 2.04/2.24 tff(8396,plain,
% 2.04/2.24 (~(elem!1 = s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8, 8393])).
% 2.04/2.24 tff(8397,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8173, 8396, 3449, 8395, 8253, 3448])).
% 2.04/2.24 tff(8398,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1098, 8397])).
% 2.04/2.24 tff(8399,plain,
% 2.04/2.24 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8349, 453, 1291, 646, 1275])).
% 2.04/2.24 tff(8400,plain,
% 2.04/2.24 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[687, 8399])).
% 2.04/2.24 tff(8401,plain,
% 2.04/2.24 (~r(s(z), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7287, 268, 701, 1159])).
% 2.04/2.24 tff(8402,plain,
% 2.04/2.24 (b(s(z), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1677, 69, 8401, 50])).
% 2.04/2.24 tff(8403,plain,
% 2.04/2.24 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1990, 453, 1764, 8402, 374])).
% 2.04/2.24 tff(8404,plain,
% 2.04/2.24 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[328, 8403])).
% 2.04/2.24 tff(8405,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1982, 8404, 8400])).
% 2.04/2.24 tff(8406,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[518, 8405])).
% 2.04/2.24 tff(8407,plain,
% 2.04/2.24 (~b(elem!1, s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8169, 453, 8406, 1291, 1275])).
% 2.04/2.24 tff(8408,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8409,plain,
% 2.04/2.24 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8410,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8409])).
% 2.04/2.24 tff(8411,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.04/2.24 inference(transitivity,[status(thm)],[8410, 8408])).
% 2.04/2.24 tff(8412,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(8413,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8412, 8411])).
% 2.04/2.24 tff(8414,plain,
% 2.04/2.24 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8413, 268, 700, 1159])).
% 2.04/2.24 tff(8415,plain,
% 2.04/2.24 (b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2370, 69, 8414, 2359])).
% 2.04/2.24 tff(8416,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4297, 700, 1159])).
% 2.04/2.24 tff(8417,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4293, 8416])).
% 2.04/2.24 tff(8418,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1167, 1159, 701])).
% 2.04/2.24 tff(8419,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1098, 8418])).
% 2.04/2.24 tff(8420,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(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8421,plain,
% 2.04/2.24 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(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(z))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8422,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(s(s(s(z)))))) | (~b(s(z), s(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(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(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8421])).
% 2.04/2.24 tff(8423,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(s(s(s(z)))))) | (~b(s(z), s(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(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(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[8422, 8420])).
% 2.04/2.24 tff(8424,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(s(s(s(z)))))) | (~b(s(z), s(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(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(8425,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8424, 8423])).
% 2.04/2.24 tff(8426,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8425, 453, 8419, 1974, 758, 8417, 8415])).
% 2.04/2.24 tff(8427,plain,((~r(s(s(z)), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(8428,plain,
% 2.04/2.24 (~r(s(s(z)), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8427, 8402, 1159, 701])).
% 2.04/2.24 tff(8429,plain,
% 2.04/2.24 (b(s(s(z)), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[782, 8428, 4060])).
% 2.04/2.24 tff(8430,plain,
% 2.04/2.24 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4084, 8429, 646, 1291, 8400])).
% 2.04/2.24 tff(8431,plain,
% 2.04/2.24 (r(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[466, 8430, 2073])).
% 2.04/2.24 tff(8432,plain,
% 2.04/2.24 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1770, 453, 1764, 8402, 374])).
% 2.04/2.24 tff(8433,plain,
% 2.04/2.24 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2463, 69, 8432, 2453])).
% 2.04/2.24 tff(8434,plain,
% 2.04/2.24 (~r(elem!1, s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[427, 8433, 8431])).
% 2.04/2.24 tff(8435,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1087, 8434, 8407, 1055])).
% 2.04/2.24 tff(8436,plain,((~r(s(z), elem!1)) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (s(s(z)) = elem!1) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(8437,plain,
% 2.04/2.24 (~r(s(z), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8436, 8396, 8395, 8253, 8398, 4452, 2925, 8191, 4051, 8394])).
% 2.04/2.24 tff(8438,plain,
% 2.04/2.24 (b(s(z), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[506, 8437, 3447])).
% 2.04/2.24 tff(8439,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), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8440,plain,
% 2.04/2.24 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8441,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8440])).
% 2.04/2.24 tff(8442,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.24 inference(transitivity,[status(thm)],[8441, 8439])).
% 2.04/2.24 tff(8443,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(8444,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8443, 8442])).
% 2.04/2.24 tff(8445,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8444, 453, 8438, 8191, 4452, 8253])).
% 2.04/2.24 tff(8446,plain,(b(s(s(s(z))), s(z)) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(z))), elem!1) | b(elem!1, s(z)) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(8447,plain,
% 2.04/2.24 (b(s(s(s(z))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8446, 249, 2, 10, 637])).
% 2.04/2.24 tff(8448,plain,
% 2.04/2.24 (~(s(s(s(z))) = elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[122, 8447, 10])).
% 2.04/2.24 tff(8449,plain,
% 2.04/2.24 (b(s(s(s(z))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[74, 8448, 2])).
% 2.04/2.24 tff(8450,plain,
% 2.04/2.24 (~(elem!1 = s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4487, 8448])).
% 2.04/2.24 tff(8451,plain,
% 2.04/2.24 (~(s(s(s(z))) = elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[122, 120, 10])).
% 2.04/2.24 tff(8452,plain,
% 2.04/2.24 (~(elem!1 = s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4487, 8451])).
% 2.04/2.24 tff(8453,plain,
% 2.04/2.24 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[254, 3, 249])).
% 2.04/2.24 tff(8454,plain,
% 2.04/2.24 (~r(s(z), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1167, 1132, 1159])).
% 2.04/2.24 tff(8455,plain,
% 2.04/2.24 (b(s(z), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[506, 8454, 492])).
% 2.04/2.24 tff(8456,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8457,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(8458,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8457, 8456])).
% 2.04/2.24 tff(8459,plain,
% 2.04/2.24 ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8458, 268])).
% 2.04/2.24 tff(8460,plain,
% 2.04/2.24 (~r(elem!1, s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8459, 1132, 238, 1159])).
% 2.04/2.24 tff(8461,plain,
% 2.04/2.24 (b(elem!1, s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4492, 8460, 4489])).
% 2.04/2.24 tff(8462,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5465, 8461, 8455, 120, 1291])).
% 2.04/2.24 tff(8463,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (elem!1 = s(s(s(z)))) | (s(z) = elem!1) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(8464,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8463, 8453, 1291, 8452, 492, 238, 120])).
% 2.04/2.24 tff(8465,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1098, 8464])).
% 2.04/2.24 tff(8466,plain,
% 2.04/2.24 (~r(s(z), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1157, 1149, 238])).
% 2.04/2.24 tff(8467,plain,
% 2.04/2.24 (b(s(z), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[227, 8466])).
% 2.04/2.24 tff(8468,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8469,plain,
% 2.04/2.25 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8470,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8469])).
% 2.04/2.25 tff(8471,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8470, 8468])).
% 2.04/2.25 tff(8472,plain,
% 2.04/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(8473,plain,
% 2.04/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8472, 8471])).
% 2.04/2.25 tff(8474,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8473, 268, 11, 1159, 1149])).
% 2.04/2.25 tff(8475,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(8476,plain,
% 2.04/2.25 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8475, 1149, 1159])).
% 2.04/2.25 tff(8477,plain,
% 2.04/2.25 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[518, 8476])).
% 2.04/2.25 tff(8478,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3782, 8477, 8467, 120, 1764])).
% 2.04/2.25 tff(8479,plain,((~r(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(8480,plain,
% 2.04/2.25 (~r(elem!1, s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8479, 8465, 120, 8453, 238])).
% 2.04/2.25 tff(8481,plain,
% 2.04/2.25 (b(elem!1, s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4492, 8480, 8452])).
% 2.04/2.25 tff(8482,plain,
% 2.04/2.25 (~b(s(z), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5465, 8481, 120, 1291])).
% 2.04/2.25 tff(8483,plain,
% 2.04/2.25 (r(s(z), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[506, 8482, 492])).
% 2.04/2.25 tff(8484,plain,
% 2.04/2.25 (~r(s(z), s(s(s(s(s(z))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4530, 8483, 722])).
% 2.04/2.25 tff(8485,plain,
% 2.04/2.25 (b(s(z), s(s(s(s(s(z))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[372, 8484])).
% 2.04/2.25 tff(8486,plain,
% 2.04/2.25 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7293, 8483, 120, 1291, 3, 8481])).
% 2.04/2.25 tff(8487,plain,
% 2.04/2.25 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[518, 8486])).
% 2.04/2.25 tff(8488,plain,
% 2.04/2.25 (~r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[730, 8483, 722])).
% 2.04/2.25 tff(8489,plain,
% 2.04/2.25 (b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[297, 8488])).
% 2.04/2.25 tff(8490,plain,
% 2.04/2.25 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4534, 8489, 492, 722, 8465, 249, 10])).
% 2.04/2.25 tff(8491,plain,
% 2.04/2.25 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[687, 8490])).
% 2.04/2.25 tff(8492,plain,
% 2.04/2.25 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1982, 8491, 8487])).
% 2.04/2.25 tff(8493,plain,
% 2.04/2.25 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[328, 8492])).
% 2.04/2.25 tff(8494,plain,
% 2.04/2.25 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8186, 8493, 8465, 8485])).
% 2.04/2.25 tff(8495,plain,
% 2.04/2.25 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3216, 268, 8487, 8491])).
% 2.04/2.25 tff(8496,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2463, 69, 8495, 8494, 2453])).
% 2.04/2.25 tff(8497,plain,((s(s(s(s(z)))) = elem!1) | (s(z) = elem!1) | (~r(s(s(s(s(s(z))))), elem!1)) | b(s(s(s(s(z)))), elem!1) | b(elem!1, s(z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(8498,plain,
% 2.04/2.25 (s(s(s(s(z)))) = elem!1),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8497, 722, 4495, 249, 10, 120, 1291, 7928])).
% 2.04/2.25 tff(8499,plain,
% 2.04/2.25 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4108, 8498])).
% 2.04/2.25 tff(8500,plain,
% 2.04/2.25 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8499])).
% 2.04/2.25 tff(8501,plain,
% 2.04/2.25 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 2.04/2.25 inference(symmetry,[status(thm)],[8500])).
% 2.04/2.25 tff(8502,plain,
% 2.04/2.25 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8501])).
% 2.04/2.25 tff(8503,plain,
% 2.04/2.25 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8502])).
% 2.04/2.25 tff(8504,plain,
% 2.04/2.25 (b(s(s(s(s(s(s(s(z))))))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.04/2.25 inference(symmetry,[status(thm)],[8503])).
% 2.04/2.25 tff(8505,plain,
% 2.04/2.25 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1273, 8498])).
% 2.04/2.25 tff(8506,plain,
% 2.04/2.25 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.04/2.25 inference(symmetry,[status(thm)],[3858])).
% 2.04/2.25 tff(8507,plain,
% 2.04/2.25 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8498])).
% 2.04/2.25 tff(8508,plain,
% 2.04/2.25 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.04/2.25 inference(transitivity,[status(thm)],[8507, 8506])).
% 2.04/2.25 tff(8509,plain,
% 2.04/2.25 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8508])).
% 2.04/2.25 tff(8510,plain,
% 2.04/2.25 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[2690, 8509])).
% 2.04/2.25 tff(8511,plain,
% 2.04/2.25 (s(elem!1) = s(s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4499, 8499])).
% 2.04/2.25 tff(8512,plain,
% 2.04/2.25 (~b(s(s(s(s(z)))), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4309, 8511, 10])).
% 2.04/2.25 tff(8513,plain,
% 2.04/2.25 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8502])).
% 2.04/2.25 tff(8514,plain,
% 2.04/2.25 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8513, 1307])).
% 2.04/2.25 tff(8515,plain,
% 2.04/2.25 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.25 inference(symmetry,[status(thm)],[8514])).
% 2.04/2.25 tff(8516,plain,
% 2.04/2.25 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8515])).
% 2.04/2.25 tff(8517,plain,
% 2.04/2.25 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1436, 8505])).
% 2.04/2.25 tff(8518,plain,
% 2.04/2.25 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8517, 8516])).
% 2.04/2.25 tff(8519,plain,
% 2.04/2.25 (~(elem!1 = s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4223, 8518])).
% 2.04/2.25 tff(8520,plain,
% 2.04/2.25 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(elem!1), s(z))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8499])).
% 2.04/2.25 tff(8521,plain,
% 2.04/2.25 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4469, 8498, 722])).
% 2.04/2.25 tff(8522,plain,
% 2.04/2.25 (r(s(s(s(s(z)))), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1098, 8512])).
% 2.04/2.25 tff(8523,plain,
% 2.04/2.25 (~r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2414, 8522, 8521])).
% 2.04/2.25 tff(8524,plain,
% 2.04/2.25 (b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[297, 8523])).
% 2.04/2.25 tff(8525,plain,
% 2.04/2.25 (b(s(elem!1), s(z))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8524, 8520])).
% 2.04/2.25 tff(8526,plain,
% 2.04/2.25 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8499])).
% 2.04/2.25 tff(8527,plain,
% 2.04/2.25 (r(s(elem!1), elem!1)),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[722, 8526])).
% 2.04/2.25 tff(8528,plain,
% 2.04/2.25 (b(s(z), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5502, 499, 120, 1057, 1123])).
% 2.04/2.25 tff(8529,plain,
% 2.04/2.25 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4096, 8528, 1291, 499])).
% 2.04/2.25 tff(8530,plain,
% 2.04/2.25 (r(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[466, 8529, 2073])).
% 2.04/2.25 tff(8531,plain,
% 2.04/2.25 (r(elem!1, s(elem!1))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8530, 4152])).
% 2.04/2.25 tff(8532,plain,
% 2.04/2.25 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[4146])).
% 2.04/2.25 tff(8533,plain,
% 2.04/2.25 ((s(z) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(z))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8532, 173])).
% 2.04/2.25 tff(8534,plain,
% 2.04/2.25 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8533, 174])).
% 2.04/2.25 tff(8535,plain,
% 2.04/2.25 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(z) = s(elem!1)))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8534])).
% 2.04/2.25 tff(8536,plain,
% 2.04/2.25 (~(s(z) = s(elem!1))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[289, 8535])).
% 2.04/2.25 tff(8537,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8538,plain,
% 2.04/2.25 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8539,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8538])).
% 2.04/2.25 tff(8540,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8539, 8537])).
% 2.04/2.25 tff(8541,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(8542,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8541, 8540])).
% 2.04/2.25 tff(8543,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8542, 453, 499, 907, 1291, 2090])).
% 2.04/2.25 tff(8544,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(8545,plain,
% 2.04/2.25 (~b(elem!1, s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8544, 8528, 1291, 499])).
% 2.04/2.25 tff(8546,plain,
% 2.04/2.25 (r(elem!1, s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1024, 8545, 216])).
% 2.04/2.25 tff(8547,plain,
% 2.04/2.25 (~b(s(z), s(elem!1))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2017, 8546, 238, 1892, 7118, 1059])).
% 2.04/2.25 tff(8548,plain,
% 2.04/2.25 (r(s(z), s(elem!1))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[397, 8547, 8536])).
% 2.04/2.25 tff(8549,plain,
% 2.04/2.25 (~r(elem!1, s(elem!1))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1496, 8548, 238])).
% 2.04/2.25 tff(8550,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8549, 8531])).
% 2.04/2.25 tff(8551,plain,((~b(s(z), elem!1)) | (~(s(s(s(s(s(z))))) = s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (elem!1 = s(s(s(s(s(z)))))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | b(s(s(s(s(z)))), s(z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(8552,plain,
% 2.04/2.25 (~b(s(z), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8551, 8499, 7928, 8527, 8525, 2073, 8519, 1291, 120, 8512, 1123])).
% 2.04/2.25 tff(8553,plain,
% 2.04/2.25 (r(s(z), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[506, 8552, 4495])).
% 2.04/2.25 tff(8554,plain,
% 2.04/2.25 (~r(s(s(z)), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[777, 8553, 722])).
% 2.04/2.25 tff(8555,plain,
% 2.04/2.25 (b(s(s(z)), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[782, 8554, 4060])).
% 2.04/2.25 tff(8556,plain,
% 2.04/2.25 (~(s(elem!1) = s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1861, 8519])).
% 2.04/2.25 tff(8557,plain,
% 2.04/2.25 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8499])).
% 2.04/2.25 tff(8558,plain,
% 2.04/2.25 ((s(z) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(z))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8557, 173])).
% 2.04/2.25 tff(8559,plain,
% 2.04/2.25 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8558, 174])).
% 2.04/2.25 tff(8560,plain,
% 2.04/2.25 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(z) = s(elem!1)))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8559])).
% 2.04/2.25 tff(8561,plain,
% 2.04/2.25 (~(s(z) = s(elem!1))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[289, 8560])).
% 2.04/2.25 tff(8562,plain,
% 2.04/2.25 (~r(s(z), s(elem!1))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1912, 8553, 8527])).
% 2.04/2.25 tff(8563,plain,
% 2.04/2.25 (b(s(z), s(elem!1))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[397, 8562, 8561])).
% 2.04/2.25 tff(8564,plain,
% 2.04/2.25 (~r(elem!1, s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2017, 8563, 7928, 8527, 8556, 8525])).
% 2.04/2.25 tff(8565,plain,
% 2.04/2.25 (b(elem!1, s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1024, 8564, 8519])).
% 2.04/2.25 tff(8566,assumption,(s(s(z)) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.04/2.25 tff(8567,plain,
% 2.04/2.25 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8566])).
% 2.04/2.25 tff(8568,plain,
% 2.04/2.25 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(z)))),
% 2.04/2.25 inference(symmetry,[status(thm)],[8567])).
% 2.04/2.25 tff(8569,plain,
% 2.04/2.25 (s(s(elem!1)) = s(z)),
% 2.04/2.25 inference(transitivity,[status(thm)],[7962, 1375, 8568, 28])).
% 2.04/2.25 tff(8570,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[816, 8569])).
% 2.04/2.25 tff(8571,plain,((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) | (~(s(s(s(s(s(z))))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(8572,plain,
% 2.04/2.25 (~(s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8571, 8499])).
% 2.04/2.25 tff(8573,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(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(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(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8574,plain,
% 2.04/2.25 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8575,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(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(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8574])).
% 2.04/2.25 tff(8576,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(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(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8575, 8573])).
% 2.04/2.25 tff(8577,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(8578,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(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8577, 8576])).
% 2.04/2.25 tff(8579,plain,
% 2.04/2.25 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8578, 453, 907, 922, 1276])).
% 2.04/2.25 tff(8580,assumption,(~(s(s(z)) = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.04/2.25 tff(8581,plain,
% 2.04/2.25 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8582,plain,
% 2.04/2.25 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(8583,plain,
% 2.04/2.25 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8582, 8581])).
% 2.04/2.25 tff(8584,plain,
% 2.04/2.25 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8583, 69, 8580, 8579])).
% 2.04/2.25 tff(8585,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8586,plain,
% 2.04/2.25 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8587,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8586])).
% 2.04/2.25 tff(8588,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8587, 8585])).
% 2.04/2.25 tff(8589,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(8590,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(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8589, 8588])).
% 2.04/2.25 tff(8591,plain,
% 2.04/2.25 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8590, 453, 907, 1291, 1276])).
% 2.04/2.25 tff(8592,plain,
% 2.04/2.25 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1238, 69, 2663, 8591])).
% 2.04/2.25 tff(8593,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(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8594,plain,
% 2.04/2.25 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8595,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8594])).
% 2.04/2.25 tff(8596,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8595, 8593])).
% 2.04/2.25 tff(8597,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(8598,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(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8597, 8596])).
% 2.04/2.25 tff(8599,plain,
% 2.04/2.25 (~b(s(s(z)), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8598, 453, 907, 1291, 922])).
% 2.04/2.25 tff(8600,plain,
% 2.04/2.25 ((s(s(z)) = s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1350, 69, 8599])).
% 2.04/2.25 tff(8601,plain,
% 2.04/2.25 (r(s(s(z)), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8600, 1243])).
% 2.04/2.25 tff(8602,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8603,plain,
% 2.04/2.25 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8604,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8603])).
% 2.04/2.26 tff(8605,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8604, 8602])).
% 2.04/2.26 tff(8606,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(8607,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8606, 8605])).
% 2.04/2.26 tff(8608,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8607, 268, 8601, 8592, 8584])).
% 2.04/2.26 tff(8609,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(z)) = s(s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(8610,plain,
% 2.04/2.26 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8609, 8572, 8565, 8555, 1291])).
% 2.04/2.26 tff(8611,plain,
% 2.04/2.26 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[3875, 8610, 8510])).
% 2.04/2.26 tff(8612,plain,
% 2.04/2.26 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8023, 268, 8527, 8611])).
% 2.04/2.26 tff(8613,plain,
% 2.04/2.26 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[3999, 8612, 8505])).
% 2.04/2.26 tff(8614,plain,
% 2.04/2.26 (b(s(s(s(elem!1))), s(elem!1))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8613, 8504])).
% 2.04/2.26 tff(8615,plain,
% 2.04/2.26 (r(s(z), s(s(s(s(z))))) <=> r(s(z), elem!1)),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8498])).
% 2.04/2.26 tff(8616,plain,
% 2.04/2.26 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(z)))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[8615])).
% 2.04/2.26 tff(8617,plain,
% 2.04/2.26 (r(s(z), s(s(s(s(z)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8553, 8616])).
% 2.04/2.26 tff(8618,plain,
% 2.04/2.26 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8498])).
% 2.04/2.26 tff(8619,plain,
% 2.04/2.26 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[8618])).
% 2.04/2.26 tff(8620,plain,
% 2.04/2.26 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8502])).
% 2.04/2.26 tff(8621,plain,
% 2.04/2.26 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.04/2.26 inference(symmetry,[status(thm)],[8620])).
% 2.04/2.26 tff(8622,plain,
% 2.04/2.26 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8621, 8619])).
% 2.04/2.26 tff(8623,plain,
% 2.04/2.26 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8611, 8622])).
% 2.04/2.26 tff(8624,plain,
% 2.04/2.26 (~r(s(s(s(elem!1))), s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6002, 8623, 8617])).
% 2.04/2.26 tff(8625,plain,
% 2.04/2.26 (b(s(s(s(elem!1))), s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[856, 8624])).
% 2.04/2.26 tff(8626,plain,
% 2.04/2.26 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7215, 8625, 8525, 8563])).
% 2.04/2.26 tff(8627,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8626, 8614])).
% 2.04/2.26 tff(8628,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (s(s(z)) = elem!1) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (elem!1 = s(z)) | b(elem!1, s(z)) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(8629,plain,
% 2.04/2.26 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8628, 8449, 4051, 2925, 8447, 3446, 10, 249])).
% 2.04/2.26 tff(8630,plain,
% 2.04/2.26 (b(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[643, 8629, 637])).
% 2.04/2.26 tff(8631,plain,
% 2.04/2.26 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8463, 1099, 4165, 5525, 3447, 238, 120])).
% 2.04/2.26 tff(8632,plain,
% 2.04/2.26 (s(s(s(s(z)))) = elem!1),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[254, 8631, 249])).
% 2.04/2.26 tff(8633,plain,
% 2.04/2.26 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4108, 8632])).
% 2.04/2.26 tff(8634,plain,
% 2.04/2.26 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8633])).
% 2.04/2.26 tff(8635,plain,
% 2.04/2.26 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7911, 1057, 3446])).
% 2.04/2.26 tff(8636,plain,
% 2.04/2.26 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1656, 8635])).
% 2.04/2.26 tff(8637,plain,
% 2.04/2.26 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8112])).
% 2.04/2.26 tff(8638,plain,
% 2.04/2.26 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[8637])).
% 2.04/2.26 tff(8639,plain,
% 2.04/2.26 ((~r(elem!1, s(elem!1))) <=> (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8638])).
% 2.04/2.26 tff(8640,plain,
% 2.04/2.26 ((elem!1 = s(s(s(s(s(z)))))) <=> (elem!1 = s(elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8112])).
% 2.04/2.26 tff(8641,plain,
% 2.04/2.26 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(elem!1) = elem!1)),
% 2.04/2.26 inference(transitivity,[status(thm)],[8640, 1027])).
% 2.04/2.26 tff(8642,plain,
% 2.04/2.26 ((elem!1 = s(s(s(s(s(z)))))) <=> (elem!1 = s(elem!1))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8641, 1028])).
% 2.04/2.26 tff(8643,plain,
% 2.04/2.26 ((~(elem!1 = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(elem!1)))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8642])).
% 2.04/2.26 tff(8644,plain,
% 2.04/2.26 (~(elem!1 = s(elem!1))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[2073, 8643])).
% 2.04/2.26 tff(8645,plain,
% 2.04/2.26 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8112])).
% 2.04/2.26 tff(8646,plain,
% 2.04/2.26 (b(s(elem!1), s(s(s(z))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[1779, 8645])).
% 2.04/2.26 tff(8647,plain,
% 2.04/2.26 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[1170])).
% 2.04/2.26 tff(8648,plain,
% 2.04/2.26 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(elem!1, s(elem!1))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8647, 8637])).
% 2.04/2.26 tff(8649,plain,
% 2.04/2.26 ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~r(elem!1, s(elem!1)))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8648])).
% 2.04/2.26 tff(8650,plain,
% 2.04/2.26 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[1332, 7309])).
% 2.04/2.26 tff(8651,plain,
% 2.04/2.26 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[629, 8650])).
% 2.04/2.26 tff(8652,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[320, 8651])).
% 2.04/2.26 tff(8653,plain,((~b(s(elem!1), elem!1)) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(8654,plain,
% 2.04/2.26 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8653, 629, 1170])).
% 2.04/2.26 tff(8655,plain,
% 2.04/2.26 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1788, 1779, 8654, 1633])).
% 2.04/2.26 tff(8656,plain,
% 2.04/2.26 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[518, 8655])).
% 2.04/2.26 tff(8657,plain,
% 2.04/2.26 (~r(s(z), s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2254, 418, 1132])).
% 2.04/2.26 tff(8658,plain,
% 2.04/2.26 (b(s(z), s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[372, 8657])).
% 2.04/2.26 tff(8659,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8660,plain,
% 2.04/2.26 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(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(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8661,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8660])).
% 2.04/2.26 tff(8662,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8661, 8659])).
% 2.04/2.26 tff(8663,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(8664,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8663, 8662])).
% 2.04/2.26 tff(8665,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8664, 268, 11, 4621, 418])).
% 2.04/2.26 tff(8666,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(8667,plain,
% 2.04/2.26 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8666, 418, 11])).
% 2.04/2.26 tff(8668,plain,
% 2.04/2.26 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2570, 8667])).
% 2.04/2.26 tff(8669,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8055, 8668, 8658, 1779, 2090])).
% 2.04/2.26 tff(8670,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(8671,plain,
% 2.04/2.26 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8670, 1779, 2090, 8656, 1132])).
% 2.04/2.26 tff(8672,plain,
% 2.04/2.26 (~r(elem!1, s(elem!1))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8671, 8649])).
% 2.04/2.26 tff(8673,plain,
% 2.04/2.26 (b(elem!1, s(elem!1))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1069, 8672, 1056])).
% 2.04/2.26 tff(8674,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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8675,plain,
% 2.04/2.26 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8676,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8675])).
% 2.04/2.26 tff(8677,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8676, 8674])).
% 2.04/2.26 tff(8678,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(8679,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8678, 8677])).
% 2.04/2.26 tff(8680,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8679, 453, 629, 8673, 1291, 8646])).
% 2.04/2.26 tff(8681,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (elem!1 = s(elem!1)) | (~(s(s(s(s(z)))) = elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(8682,plain,
% 2.04/2.26 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8681, 8467, 4165, 8644, 1170, 6699, 1132, 1633])).
% 2.04/2.26 tff(8683,plain,
% 2.04/2.26 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[687, 8682])).
% 2.04/2.26 tff(8684,plain,
% 2.04/2.26 (r(s(elem!1), s(s(s(z))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8683, 8113])).
% 2.04/2.26 tff(8685,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8686,plain,
% 2.04/2.26 (((~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8687,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8686])).
% 2.04/2.26 tff(8688,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8687, 8685])).
% 2.04/2.26 tff(8689,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(elem!1, s(elem!1))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(8690,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8689, 8688])).
% 2.04/2.26 tff(8691,plain,
% 2.04/2.26 (~r(elem!1, s(elem!1))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8690, 268, 1149, 8684])).
% 2.04/2.26 tff(8692,plain,
% 2.04/2.26 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8691, 8639])).
% 2.04/2.26 tff(8693,plain,
% 2.04/2.26 (~(s(s(elem!1)) = elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[3359, 8127])).
% 2.04/2.26 tff(8694,plain,
% 2.04/2.26 (b(elem!1, s(elem!1))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1069, 8691, 8644])).
% 2.04/2.26 tff(8695,plain,
% 2.04/2.26 (~b(s(s(elem!1)), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4210, 8694, 2, 555, 59, 646])).
% 2.04/2.26 tff(8696,plain,
% 2.04/2.26 (r(s(s(elem!1)), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2240, 8695, 8693])).
% 2.04/2.26 tff(8697,plain,
% 2.04/2.26 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8115])).
% 2.04/2.26 tff(8698,plain,
% 2.04/2.26 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8697])).
% 2.04/2.26 tff(8699,plain,
% 2.04/2.26 (~(s(s(z)) = s(s(elem!1)))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[2661, 8698])).
% 2.04/2.26 tff(8700,plain,
% 2.04/2.26 (~r(s(s(elem!1)), s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1970, 8696, 238])).
% 2.04/2.26 tff(8701,plain,
% 2.04/2.26 (b(s(s(elem!1)), s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1047, 8700])).
% 2.04/2.26 tff(8702,plain,
% 2.04/2.26 (~r(s(s(z)), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4248, 8701, 8699, 701, 8696])).
% 2.04/2.26 tff(8703,plain,
% 2.04/2.26 (b(s(s(z)), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[782, 8702, 4060])).
% 2.04/2.26 tff(8704,plain,
% 2.04/2.26 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4084, 8703, 646, 4165, 8683])).
% 2.04/2.26 tff(8705,plain,
% 2.04/2.26 (r(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[466, 8704, 2073])).
% 2.04/2.26 tff(8706,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8705, 8692])).
% 2.04/2.26 tff(8707,plain,((~r(elem!1, s(s(s(z))))) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (s(s(z)) = elem!1) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | r(s(s(s(z))), elem!1) | (s(s(s(z))) = s(s(elem!1))) | (s(s(s(z))) = elem!1) | (~(s(s(s(s(z)))) = elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(8708,plain,
% 2.04/2.26 (~r(elem!1, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8707, 701, 646, 4060, 2925, 238, 2, 555, 59, 1170, 1132, 1633])).
% 2.04/2.26 tff(8709,plain,
% 2.04/2.26 (b(elem!1, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4492, 8708, 5525])).
% 2.04/2.26 tff(8710,plain,
% 2.04/2.26 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8112])).
% 2.04/2.26 tff(8711,plain,
% 2.04/2.26 ((s(z) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(z))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8710, 173])).
% 2.04/2.26 tff(8712,plain,
% 2.04/2.26 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(elem!1) = s(z)))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8711])).
% 2.04/2.26 tff(8713,plain,
% 2.04/2.26 (~(s(elem!1) = s(z))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[289, 8712])).
% 2.04/2.26 tff(8714,plain,
% 2.04/2.26 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[4146])).
% 2.04/2.26 tff(8715,plain,
% 2.04/2.26 (b(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[466, 4103, 2925])).
% 2.04/2.26 tff(8716,plain,
% 2.04/2.26 (b(elem!1, s(elem!1))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8715, 8714])).
% 2.04/2.26 tff(8717,plain,
% 2.04/2.26 (~b(s(s(elem!1)), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4210, 8716, 2, 555, 59, 646])).
% 2.04/2.26 tff(8718,plain,
% 2.04/2.26 (r(s(s(elem!1)), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2240, 8717, 5181])).
% 2.04/2.26 tff(8719,plain,
% 2.04/2.26 (~r(s(s(elem!1)), s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1970, 8718, 238])).
% 2.04/2.26 tff(8720,plain,
% 2.04/2.26 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4324, 4103, 4165, 637, 238, 258])).
% 2.04/2.26 tff(8721,plain,
% 2.04/2.26 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[687, 8720])).
% 2.04/2.26 tff(8722,plain,
% 2.04/2.26 (~b(s(s(z)), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4084, 8721, 646, 4165, 8715])).
% 2.04/2.26 tff(8723,plain,
% 2.04/2.26 (r(s(s(z)), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[782, 8722, 4060])).
% 2.04/2.26 tff(8724,plain,
% 2.04/2.26 (~b(s(s(elem!1)), s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4248, 8718, 8369, 701, 8723])).
% 2.04/2.26 tff(8725,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1047, 8724, 8719])).
% 2.04/2.26 tff(8726,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (s(s(elem!1)) = elem!1) | r(s(s(s(z))), elem!1) | (s(s(s(z))) = s(s(elem!1))) | (s(s(s(z))) = elem!1) | (~b(s(s(s(s(s(z))))), elem!1)) | (~(s(s(s(s(s(z))))) = s(elem!1))) | (s(s(z)) = elem!1) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(8727,plain,
% 2.04/2.26 (~r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8726, 701, 238, 8693, 2, 555, 59, 646, 8112, 4060, 637])).
% 2.04/2.26 tff(8728,plain,
% 2.04/2.26 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(elem!1), s(z))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[4146])).
% 2.04/2.26 tff(8729,plain,
% 2.04/2.26 (r(s(elem!1), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.26 inference(symmetry,[status(thm)],[8728])).
% 2.04/2.26 tff(8730,plain,
% 2.04/2.26 (r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[340, 8729])).
% 2.04/2.26 tff(8731,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[292, 8730])).
% 2.04/2.26 tff(8732,plain,((~r(s(elem!1), s(z))) | r(s(s(s(s(s(z))))), s(z)) | (~(s(s(s(s(s(z))))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(8733,plain,
% 2.04/2.26 (~r(s(elem!1), s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8732, 8727, 8112])).
% 2.04/2.26 tff(8734,plain,
% 2.04/2.26 (b(s(elem!1), s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[353, 8733, 8713])).
% 2.04/2.26 tff(8735,plain,
% 2.04/2.26 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8112])).
% 2.04/2.26 tff(8736,plain,
% 2.04/2.26 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[8735])).
% 2.04/2.26 tff(8737,plain,
% 2.04/2.26 ((~b(s(s(s(z))), s(elem!1))) <=> (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8736])).
% 2.04/2.26 tff(8738,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(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8739,plain,
% 2.04/2.26 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8740,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8739])).
% 2.04/2.27 tff(8741,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8740, 8738])).
% 2.04/2.27 tff(8742,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(8743,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(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8742, 8741])).
% 2.04/2.27 tff(8744,plain,
% 2.04/2.27 (~b(s(s(s(z))), s(elem!1))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8743, 453, 6699, 4165, 8709])).
% 2.04/2.27 tff(8745,plain,
% 2.04/2.27 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8744, 8737])).
% 2.04/2.27 tff(8746,plain,
% 2.04/2.27 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2570, 8745])).
% 2.04/2.27 tff(8747,plain,
% 2.04/2.27 (r(s(s(s(z))), s(elem!1))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[7024, 8746, 1170])).
% 2.04/2.27 tff(8748,plain,
% 2.04/2.27 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[2220, 8286])).
% 2.04/2.27 tff(8749,plain,
% 2.04/2.27 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8298, 268, 701, 8280])).
% 2.04/2.27 tff(8750,plain,
% 2.04/2.27 ((s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1485, 69, 8749])).
% 2.04/2.27 tff(8751,plain,
% 2.04/2.27 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8750, 8291])).
% 2.04/2.27 tff(8752,plain,
% 2.04/2.27 ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8307, 453, 1059, 8751])).
% 2.04/2.27 tff(8753,plain,
% 2.04/2.27 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8752, 8748])).
% 2.04/2.27 tff(8754,plain,
% 2.04/2.27 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1320, 8753, 1442])).
% 2.04/2.27 tff(8755,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(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(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(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8756,plain,
% 2.04/2.27 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8757,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), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(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(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8756])).
% 2.04/2.27 tff(8758,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), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(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(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8757, 8755])).
% 2.04/2.27 tff(8759,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), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(8760,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(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8759, 8758])).
% 2.04/2.27 tff(8761,plain,
% 2.04/2.27 ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8760, 453, 120, 8751])).
% 2.04/2.27 tff(8762,plain,
% 2.04/2.27 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8761, 8748])).
% 2.04/2.27 tff(8763,plain,
% 2.04/2.27 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[7740, 8762, 3475])).
% 2.04/2.27 tff(8764,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8765,plain,
% 2.04/2.27 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8766,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8765])).
% 2.04/2.27 tff(8767,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8766, 8764])).
% 2.04/2.27 tff(8768,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(elem!1))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(8769,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8768, 8767])).
% 2.04/2.27 tff(8770,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8769, 268, 8763, 8754, 7009])).
% 2.04/2.27 tff(8771,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), s(elem!1))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~(s(s(s(s(s(z))))) = s(elem!1))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(8772,plain,
% 2.04/2.27 (~r(s(s(s(elem!1))), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8771, 8747, 6679, 120, 8734, 8112, 701, 238])).
% 2.04/2.27 tff(8773,plain,
% 2.04/2.27 (b(s(s(s(elem!1))), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[567, 8772, 8121])).
% 2.04/2.27 tff(8774,plain,
% 2.04/2.27 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8773, 8143])).
% 2.04/2.27 tff(8775,plain,
% 2.04/2.27 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1234, 453, 4165, 8774, 8709])).
% 2.04/2.27 tff(8776,plain,
% 2.04/2.27 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1329, 8774, 6699, 4165, 6678, 8709, 8389])).
% 2.04/2.27 tff(8777,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1238, 69, 2663, 8776, 8775])).
% 2.04/2.27 tff(8778,plain,((~r(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~(s(s(s(s(z)))) = elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (s(s(z)) = elem!1) | r(s(s(s(z))), elem!1) | (s(s(s(z))) = s(s(elem!1))) | (s(s(s(z))) = elem!1) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(8779,plain,
% 2.04/2.27 (~r(s(z), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8778, 8632, 238, 120, 646, 4060, 2, 4431, 59, 1099, 8636, 637])).
% 2.04/2.27 tff(8780,plain,
% 2.04/2.27 (b(s(z), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[506, 8779, 3447])).
% 2.04/2.27 tff(8781,plain,
% 2.04/2.27 (b(s(z), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5502, 8780, 120, 1057, 3446])).
% 2.04/2.27 tff(8782,plain,
% 2.04/2.27 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4096, 8780, 4165, 8781])).
% 2.04/2.27 tff(8783,plain,
% 2.04/2.27 (r(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[466, 8782, 2925])).
% 2.04/2.27 tff(8784,plain,
% 2.04/2.27 (r(elem!1, s(elem!1))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8783, 8634])).
% 2.04/2.27 tff(8785,plain,
% 2.04/2.27 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8633])).
% 2.04/2.27 tff(8786,plain,
% 2.04/2.27 ((s(z) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(z))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8785, 173])).
% 2.04/2.27 tff(8787,plain,
% 2.04/2.27 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8786, 174])).
% 2.04/2.27 tff(8788,plain,
% 2.04/2.27 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(z) = s(elem!1)))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8787])).
% 2.04/2.27 tff(8789,plain,
% 2.04/2.27 (~(s(z) = s(elem!1))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[289, 8788])).
% 2.04/2.27 tff(8790,plain,
% 2.04/2.27 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(elem!1) = s(z)))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8786])).
% 2.04/2.27 tff(8791,plain,
% 2.04/2.27 (~(s(elem!1) = s(z))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[289, 8790])).
% 2.04/2.27 tff(8792,plain,
% 2.04/2.27 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8633])).
% 2.04/2.27 tff(8793,plain,
% 2.04/2.27 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 2.04/2.27 inference(symmetry,[status(thm)],[8792])).
% 2.04/2.27 tff(8794,plain,
% 2.04/2.27 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8793])).
% 2.04/2.27 tff(8795,plain,
% 2.04/2.27 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8794])).
% 2.04/2.27 tff(8796,plain,
% 2.04/2.27 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8795, 1307])).
% 2.04/2.27 tff(8797,plain,
% 2.04/2.27 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.27 inference(symmetry,[status(thm)],[8796])).
% 2.04/2.27 tff(8798,plain,
% 2.04/2.27 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8797])).
% 2.04/2.27 tff(8799,plain,
% 2.04/2.27 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1273, 8632])).
% 2.04/2.27 tff(8800,plain,
% 2.04/2.27 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1436, 8799])).
% 2.04/2.27 tff(8801,plain,
% 2.04/2.27 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8800, 8798])).
% 2.04/2.27 tff(8802,plain,
% 2.04/2.27 (~(elem!1 = s(s(elem!1)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4223, 8801])).
% 2.04/2.27 tff(8803,plain,
% 2.04/2.27 (s(elem!1) = s(s(s(s(s(z)))))),
% 2.04/2.27 inference(symmetry,[status(thm)],[8633])).
% 2.04/2.27 tff(8804,plain,
% 2.04/2.27 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8803])).
% 2.04/2.27 tff(8805,plain,
% 2.04/2.27 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.04/2.27 inference(symmetry,[status(thm)],[8804])).
% 2.04/2.27 tff(8806,plain,
% 2.04/2.27 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8805])).
% 2.04/2.27 tff(8807,plain,
% 2.04/2.27 (~(s(elem!1) = s(s(s(z))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[111, 8806])).
% 2.04/2.27 tff(8808,plain,
% 2.04/2.27 (b(s(elem!1), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1336, 8632, 646])).
% 2.04/2.27 tff(8809,plain,
% 2.04/2.27 (~r(elem!1, s(elem!1))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[7132, 8780, 4431, 120, 238, 8808, 8807, 8802, 8791, 8789])).
% 2.04/2.27 tff(8810,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8809, 8784])).
% 2.04/2.27 tff(8811,plain,(b(s(s(s(s(z)))), s(z)) | (~b(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (s(s(z)) = elem!1) | r(s(s(s(z))), elem!1) | (s(s(s(z))) = elem!1) | (s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(8812,plain,
% 2.04/2.27 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8811, 8447, 3449, 8630, 4051, 2, 8448, 637, 249])).
% 2.04/2.27 tff(8813,plain,
% 2.04/2.27 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4309, 8812, 10])).
% 2.04/2.27 tff(8814,plain,
% 2.04/2.27 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4499, 8813])).
% 2.04/2.27 tff(8815,plain,
% 2.04/2.27 (~(s(s(s(s(z)))) = elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4108, 8814])).
% 2.04/2.27 tff(8816,plain,
% 2.04/2.27 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[254, 8815, 249])).
% 2.04/2.27 tff(8817,plain,
% 2.04/2.27 (~r(elem!1, s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8479, 8816, 8447, 8812, 3449])).
% 2.04/2.27 tff(8818,plain,
% 2.04/2.27 (b(elem!1, s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4492, 8817, 8450])).
% 2.04/2.27 tff(8819,plain,
% 2.04/2.27 (~b(s(z), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5465, 8818, 8447, 8449])).
% 2.04/2.27 tff(8820,plain,
% 2.04/2.27 (r(s(z), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[506, 8819, 3447])).
% 2.04/2.27 tff(8821,plain,
% 2.04/2.27 (~(elem!1 = s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8, 8815])).
% 2.04/2.27 tff(8822,plain,
% 2.04/2.27 (~b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8436, 8820, 8449, 8630, 8812, 8821, 2925, 8818, 4051, 8816])).
% 2.04/2.27 tff(8823,plain,
% 2.04/2.27 (r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[297, 8822])).
% 2.04/2.27 tff(8824,plain,
% 2.04/2.27 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3465, 8823, 3449])).
% 2.04/2.27 tff(8825,plain,
% 2.04/2.27 (b(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[466, 8824, 2925])).
% 2.04/2.27 tff(8826,plain,
% 2.04/2.27 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4324, 8824, 8449, 637, 3449, 8823])).
% 2.04/2.27 tff(8827,plain,
% 2.04/2.27 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[687, 8826])).
% 2.04/2.27 tff(8828,plain,
% 2.04/2.27 (~b(s(s(z)), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4084, 8827, 8630, 8449, 8825])).
% 2.04/2.27 tff(8829,plain,
% 2.04/2.27 (r(s(s(z)), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[782, 8828, 4051])).
% 2.04/2.27 tff(8830,plain,
% 2.04/2.27 (~b(s(z), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8427, 8829, 8816, 8820])).
% 2.04/2.27 tff(8831,plain,
% 2.04/2.27 (~r(s(z), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[7287, 268, 8820, 8816])).
% 2.04/2.27 tff(8832,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1677, 69, 8831, 50, 8830])).
% 2.04/2.27 tff(8833,plain,(b(s(s(s(s(z)))), elem!1) | (s(s(s(s(s(z))))) = elem!1) | b(elem!1, s(z)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(8834,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8833, 2268, 112, 10, 2])).
% 2.04/2.27 tff(8835,plain,(r(s(s(s(z))), elem!1) | b(elem!1, s(z)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(8836,plain,
% 2.04/2.27 (b(s(s(s(z))), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8835, 2, 10])).
% 2.04/2.27 tff(8837,plain,
% 2.04/2.27 (b(s(s(s(s(z)))), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8833, 637, 10, 2])).
% 2.04/2.27 tff(8838,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[637, 5931])).
% 2.04/2.27 tff(8839,plain,((~(elem!1 = s(s(s(s(s(z))))))) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(8840,plain,
% 2.04/2.27 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8839, 637])).
% 2.04/2.27 tff(8841,plain,
% 2.04/2.27 (~(s(s(s(z))) = elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2267, 8837, 10, 8840])).
% 2.04/2.27 tff(8842,plain,
% 2.04/2.27 (~(elem!1 = s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4487, 8841])).
% 2.04/2.27 tff(8843,plain,
% 2.04/2.27 (~(s(s(s(z))) = elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2267, 8837, 2925, 10])).
% 2.04/2.27 tff(8844,plain,
% 2.04/2.27 (b(s(s(s(z))), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[74, 8843, 2])).
% 2.04/2.27 tff(8845,plain,
% 2.04/2.27 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4144, 8843])).
% 2.04/2.27 tff(8846,plain,
% 2.04/2.27 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[1100])).
% 2.04/2.27 tff(8847,plain,
% 2.04/2.27 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(z))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[1100])).
% 2.04/2.27 tff(8848,plain,
% 2.04/2.27 ((s(s(z)) = elem!1) <=> (s(z) = s(s(z)))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8847, 745])).
% 2.04/2.27 tff(8849,plain,
% 2.04/2.27 ((s(z) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.04/2.27 inference(symmetry,[status(thm)],[8848])).
% 2.04/2.27 tff(8850,plain,
% 2.04/2.27 ((~(s(z) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8849])).
% 2.04/2.27 tff(8851,plain,
% 2.04/2.27 (~(s(s(z)) = elem!1)),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[752, 8850])).
% 2.04/2.27 tff(8852,assumption,(~(s(s(s(s(z)))) = s(elem!1))), introduced(assumption)).
% 2.04/2.27 tff(8853,plain,
% 2.04/2.27 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(s(z))), elem!1))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4872])).
% 2.04/2.27 tff(8854,plain,
% 2.04/2.27 (~b(s(s(s(z))), elem!1)),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[128, 8853])).
% 2.04/2.27 tff(8855,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1291, 8854])).
% 2.04/2.27 tff(8856,plain,((~(elem!1 = s(z))) | (~b(s(s(s(z))), elem!1)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(8857,plain,
% 2.04/2.27 (b(s(s(s(z))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8856, 1100, 1291])).
% 2.04/2.27 tff(8858,plain,
% 2.04/2.27 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[1100])).
% 2.04/2.27 tff(8859,plain,
% 2.04/2.27 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 2.04/2.27 inference(commutativity,[status(thm)],[])).
% 2.04/2.27 tff(8860,plain,
% 2.04/2.27 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = s(z))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[1100])).
% 2.04/2.27 tff(8861,plain,
% 2.04/2.27 ((s(s(s(s(z)))) = elem!1) <=> (s(z) = s(s(s(s(z)))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8860, 8859])).
% 2.04/2.27 tff(8862,plain,
% 2.04/2.27 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.04/2.27 inference(symmetry,[status(thm)],[8861])).
% 2.04/2.27 tff(8863,plain,
% 2.04/2.27 ((s(z) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8862, 3609])).
% 2.04/2.27 tff(8864,plain,
% 2.04/2.27 ((~(s(z) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8863])).
% 2.04/2.27 tff(8865,plain,
% 2.04/2.27 (~(elem!1 = s(s(s(s(z)))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[50, 8864])).
% 2.04/2.27 tff(8866,plain,
% 2.04/2.27 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[299, 2300])).
% 2.04/2.27 tff(8867,plain,
% 2.04/2.27 (~b(s(z), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3782, 523, 1764, 120])).
% 2.04/2.27 tff(8868,plain,
% 2.04/2.27 (r(s(z), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[227, 8867])).
% 2.04/2.27 tff(8869,plain,
% 2.04/2.27 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 2.04/2.27 inference(symmetry,[status(thm)],[2300])).
% 2.04/2.27 tff(8870,plain,
% 2.04/2.27 (b(s(s(s(s(z)))), elem!1)),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[1764, 8869])).
% 2.04/2.27 tff(8871,plain,
% 2.04/2.27 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[276, 8868, 258])).
% 2.04/2.27 tff(8872,plain,
% 2.04/2.27 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[687, 8871])).
% 2.04/2.27 tff(8873,plain,
% 2.04/2.27 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2596, 8872, 523, 1291])).
% 2.04/2.27 tff(8874,plain,
% 2.04/2.27 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2463, 69, 8873])).
% 2.04/2.27 tff(8875,plain,
% 2.04/2.27 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8874, 5338])).
% 2.04/2.27 tff(8876,plain,
% 2.04/2.27 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(z) = s(s(s(s(s(z))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[1100])).
% 2.04/2.27 tff(8877,plain,
% 2.04/2.27 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.04/2.27 inference(symmetry,[status(thm)],[8876])).
% 2.04/2.27 tff(8878,plain,
% 2.04/2.27 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8877])).
% 2.04/2.27 tff(8879,plain,
% 2.04/2.27 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[289, 8878])).
% 2.04/2.27 tff(8880,plain,
% 2.04/2.27 (b(s(z), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.27 inference(symmetry,[status(thm)],[8858])).
% 2.04/2.27 tff(8881,plain,
% 2.04/2.27 ((~b(s(z), s(s(s(s(s(z))))))) <=> (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8880])).
% 2.04/2.27 tff(8882,plain,
% 2.04/2.27 (~b(s(z), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4039, 523, 1764, 120])).
% 2.04/2.27 tff(8883,plain,
% 2.04/2.27 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8882, 8881])).
% 2.04/2.27 tff(8884,plain,
% 2.04/2.27 (r(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[466, 8883, 8879])).
% 2.04/2.27 tff(8885,plain,
% 2.04/2.27 (~r(elem!1, s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[427, 8884, 8875])).
% 2.04/2.27 tff(8886,plain,
% 2.04/2.27 (b(elem!1, s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1087, 8885, 8865])).
% 2.04/2.27 tff(8887,plain,
% 2.04/2.27 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1641, 8886, 8870, 1291])).
% 2.04/2.27 tff(8888,plain,
% 2.04/2.27 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1656, 8887])).
% 2.04/2.27 tff(8889,plain,
% 2.04/2.27 (~r(s(z), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[384, 8888, 8868])).
% 2.04/2.27 tff(8890,plain,
% 2.04/2.27 (b(s(z), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1677, 69, 8889, 50])).
% 2.04/2.27 tff(8891,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4715, 453, 523, 1764, 8890, 120])).
% 2.04/2.27 tff(8892,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~(elem!1 = s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(8893,plain,
% 2.04/2.27 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8892, 258, 8857, 1291, 1100, 8866])).
% 2.04/2.27 tff(8894,plain,
% 2.04/2.27 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[518, 8893])).
% 2.04/2.27 tff(8895,plain,
% 2.04/2.27 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[1100])).
% 2.04/2.27 tff(8896,plain,
% 2.04/2.27 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 2.04/2.27 inference(symmetry,[status(thm)],[8895])).
% 2.04/2.27 tff(8897,plain,
% 2.04/2.27 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[1103])).
% 2.04/2.27 tff(8898,plain,
% 2.04/2.27 (b(s(elem!1), s(z)) <=> b(s(s(z)), elem!1)),
% 2.04/2.27 inference(transitivity,[status(thm)],[8897, 8896])).
% 2.04/2.27 tff(8899,plain,
% 2.04/2.27 ((~(s(elem!1) = elem!1)) <=> (~(s(elem!1) = s(z)))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[2350])).
% 2.04/2.27 tff(8900,plain,
% 2.04/2.27 ((s(elem!1) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[3345])).
% 2.04/2.27 tff(8901,plain,
% 2.04/2.27 ((elem!1 = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 2.04/2.27 inference(symmetry,[status(thm)],[8900])).
% 2.04/2.27 tff(8902,plain,
% 2.04/2.27 (elem!1 = s(s(elem!1))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3351, 3345])).
% 2.04/2.27 tff(8903,plain,
% 2.04/2.27 (s(elem!1) = s(s(elem!1))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8902, 8901])).
% 2.04/2.27 tff(8904,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1997, 8903])).
% 2.04/2.27 tff(8905,plain,((~(s(elem!1) = elem!1)) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(8906,plain,
% 2.04/2.27 (~(s(elem!1) = elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8905, 2288])).
% 2.04/2.27 tff(8907,plain,
% 2.04/2.27 (~(s(elem!1) = s(z))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8906, 8899])).
% 2.04/2.27 tff(8908,plain,
% 2.04/2.27 (~r(s(z), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3160, 256, 257])).
% 2.04/2.27 tff(8909,plain,
% 2.04/2.27 (b(s(z), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[372, 8908])).
% 2.04/2.27 tff(8910,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), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8911,plain,
% 2.04/2.27 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8912,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), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8911])).
% 2.04/2.27 tff(8913,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), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[8912, 8910])).
% 2.04/2.28 tff(8914,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), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(8915,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8914, 8913])).
% 2.04/2.28 tff(8916,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8915, 453, 4771, 1764, 5914, 298])).
% 2.04/2.28 tff(8917,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8918,plain,
% 2.04/2.28 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8917, 256, 257, 1764])).
% 2.04/2.28 tff(8919,plain,
% 2.04/2.28 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1656, 8918])).
% 2.04/2.28 tff(8920,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(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8921,plain,
% 2.04/2.28 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8922,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), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[8921])).
% 2.04/2.28 tff(8923,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), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[8922, 8920])).
% 2.04/2.28 tff(8924,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), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(8925,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8924, 8923])).
% 2.04/2.28 tff(8926,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8925, 453, 8919, 8909, 1764, 120])).
% 2.04/2.28 tff(8927,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8928,plain,
% 2.04/2.28 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8927, 257, 8857, 8866])).
% 2.04/2.28 tff(8929,plain,
% 2.04/2.28 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[687, 8928])).
% 2.04/2.28 tff(8930,plain,
% 2.04/2.28 (r(s(s(z)), s(z))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[340, 2296])).
% 2.04/2.28 tff(8931,plain,
% 2.04/2.28 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2432, 268, 258, 8930])).
% 2.04/2.28 tff(8932,plain,
% 2.04/2.28 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[3228, 8931, 1100])).
% 2.04/2.28 tff(8933,plain,
% 2.04/2.28 (b(s(elem!1), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[659, 8932, 2275])).
% 2.04/2.28 tff(8934,plain,
% 2.04/2.28 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8933, 2271])).
% 2.04/2.28 tff(8935,plain,
% 2.04/2.28 (~r(s(elem!1), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[3055, 340, 257])).
% 2.04/2.28 tff(8936,plain,
% 2.04/2.28 (b(s(elem!1), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1305, 8935, 3041])).
% 2.04/2.28 tff(8937,assumption,(b(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 2.04/2.28 tff(8938,plain,
% 2.04/2.28 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8937, 3042])).
% 2.04/2.28 tff(8939,assumption,(~b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 2.04/2.28 tff(8940,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8939, 8938])).
% 2.04/2.28 tff(8941,plain,(b(s(s(z)), s(s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8942,plain,
% 2.04/2.28 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8941, 8936, 1100])).
% 2.04/2.28 tff(8943,assumption,(b(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.04/2.28 tff(8944,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[7805, 453, 1779, 120, 2957, 8943])).
% 2.04/2.28 tff(8945,plain,((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8946,plain,
% 2.04/2.28 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8945, 8942, 120, 1779])).
% 2.04/2.28 tff(8947,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8946, 8934])).
% 2.04/2.28 tff(8948,plain,((~r(s(elem!1), s(z))) | (~(elem!1 = s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8949,plain,
% 2.04/2.28 (~r(s(elem!1), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8948, 258, 1100, 8857, 8929, 257])).
% 2.04/2.28 tff(8950,plain,
% 2.04/2.28 (b(s(elem!1), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[353, 8949, 8907])).
% 2.04/2.28 tff(8951,plain,
% 2.04/2.28 (b(s(s(z)), elem!1)),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8950, 8898])).
% 2.04/2.28 tff(8952,plain,
% 2.04/2.28 (~b(elem!1, s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6077, 8951, 299, 1291, 8894])).
% 2.04/2.28 tff(8953,plain,
% 2.04/2.28 (r(elem!1, s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1087, 8952, 8865])).
% 2.04/2.28 tff(8954,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 2.04/2.28 tff(8955,plain,
% 2.04/2.28 (s(elem!1) = elem!1),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8954, 1027])).
% 2.04/2.28 tff(8956,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[605, 8955])).
% 2.04/2.28 tff(8957,plain,((~(elem!1 = s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8958,plain,
% 2.04/2.28 (~(elem!1 = s(elem!1))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8957, 8906])).
% 2.04/2.28 tff(8959,plain,
% 2.04/2.28 (b(s(elem!1), elem!1)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[3034, 8950, 3028])).
% 2.04/2.28 tff(8960,plain,
% 2.04/2.28 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[1100])).
% 2.04/2.28 tff(8961,plain,
% 2.04/2.28 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 2.04/2.28 inference(symmetry,[status(thm)],[8960])).
% 2.04/2.28 tff(8962,plain,
% 2.04/2.28 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[1104])).
% 2.04/2.28 tff(8963,plain,
% 2.04/2.28 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.04/2.28 inference(symmetry,[status(thm)],[8962])).
% 2.04/2.28 tff(8964,plain,
% 2.04/2.28 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 2.04/2.28 inference(transitivity,[status(thm)],[8963, 8961])).
% 2.04/2.28 tff(8965,plain,
% 2.04/2.28 (b(s(s(elem!1)), elem!1)),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8857, 8964])).
% 2.04/2.28 tff(8966,plain,
% 2.04/2.28 (b(s(s(z)), s(z))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8950, 8897])).
% 2.04/2.28 tff(8967,plain,
% 2.04/2.28 (b(s(z), s(s(z))) <=> b(s(z), s(elem!1))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[2269])).
% 2.04/2.28 tff(8968,plain,
% 2.04/2.28 (b(s(z), s(elem!1)) <=> b(s(z), s(s(z)))),
% 2.04/2.28 inference(symmetry,[status(thm)],[8967])).
% 2.04/2.28 tff(8969,plain,
% 2.04/2.28 (b(elem!1, s(elem!1)) <=> b(s(z), s(elem!1))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[1100])).
% 2.04/2.28 tff(8970,plain,
% 2.04/2.28 (b(s(z), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 2.04/2.28 inference(symmetry,[status(thm)],[8969])).
% 2.04/2.28 tff(8971,plain,
% 2.04/2.28 ((~b(s(z), s(elem!1))) <=> (~b(elem!1, s(elem!1)))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[8970])).
% 2.04/2.28 tff(8972,plain,
% 2.04/2.28 (~b(elem!1, s(elem!1))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[3641, 8971])).
% 2.04/2.28 tff(8973,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1071, 8972])).
% 2.04/2.28 tff(8974,plain,((~(elem!1 = s(z))) | (~b(elem!1, s(elem!1))) | b(s(z), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8975,plain,
% 2.04/2.28 (b(s(z), s(elem!1))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8974, 1071, 1100])).
% 2.04/2.28 tff(8976,plain,
% 2.04/2.28 (b(s(z), s(s(z)))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8975, 8968])).
% 2.04/2.28 tff(8977,plain,
% 2.04/2.28 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4290, 453, 1764, 8976, 2495])).
% 2.04/2.28 tff(8978,plain,
% 2.04/2.28 (~b(s(elem!1), s(s(elem!1)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1079, 1071, 909, 629])).
% 2.04/2.28 tff(8979,plain,
% 2.04/2.28 (r(s(elem!1), s(s(elem!1)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[440, 8978, 2288])).
% 2.04/2.28 tff(8980,plain,
% 2.04/2.28 (r(s(s(z)), s(s(s(z))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8979, 2276])).
% 2.04/2.28 tff(8981,plain,
% 2.04/2.28 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2604, 268, 11, 8980])).
% 2.04/2.28 tff(8982,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4293, 8981, 8977])).
% 2.04/2.28 tff(8983,plain,((~b(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~(elem!1 = s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8984,plain,
% 2.04/2.28 (~b(elem!1, s(elem!1))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8983, 8894, 8866, 8966, 1100, 8965, 8959])).
% 2.04/2.28 tff(8985,plain,
% 2.04/2.28 (r(elem!1, s(elem!1))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1069, 8984, 8958])).
% 2.04/2.28 tff(8986,plain,
% 2.04/2.28 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4946, 8985, 8953])).
% 2.04/2.28 tff(8987,plain,
% 2.04/2.28 (b(s(s(s(s(z)))), s(elem!1))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2398, 8986, 8852])).
% 2.04/2.28 tff(8988,plain,
% 2.04/2.28 (b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2405, 8987, 1100])).
% 2.04/2.28 tff(8989,plain,
% 2.04/2.28 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 2.04/2.28 inference(symmetry,[status(thm)],[2447])).
% 2.04/2.28 tff(8990,plain,
% 2.04/2.28 (r(elem!1, s(elem!1)) <=> r(s(z), s(s(z)))),
% 2.04/2.28 inference(transitivity,[status(thm)],[2445, 8989])).
% 2.04/2.28 tff(8991,plain,
% 2.04/2.28 (r(s(z), s(s(z)))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8985, 8990])).
% 2.04/2.28 tff(8992,plain,
% 2.04/2.28 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2476, 8991, 258])).
% 2.04/2.28 tff(8993,plain,
% 2.04/2.28 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4081, 8992])).
% 2.04/2.28 tff(8994,plain,
% 2.04/2.28 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2505, 8993, 8966, 8988])).
% 2.04/2.28 tff(8995,plain,
% 2.04/2.28 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2463, 69, 8994, 2453])).
% 2.04/2.28 tff(8996,plain,
% 2.04/2.28 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[427, 8995, 8953])).
% 2.04/2.28 tff(8997,plain,
% 2.04/2.28 (b(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[466, 8996, 2073])).
% 2.04/2.28 tff(8998,plain,
% 2.04/2.28 (b(s(z), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8997, 8858])).
% 2.04/2.28 tff(8999,plain,
% 2.04/2.28 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8666, 8995, 8894])).
% 2.04/2.28 tff(9000,plain,
% 2.04/2.28 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2570, 8999])).
% 2.04/2.28 tff(9001,plain,
% 2.04/2.28 (~b(s(z), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2619, 9000, 8857, 8929])).
% 2.04/2.28 tff(9002,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[9001, 8998])).
% 2.04/2.28 tff(9003,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~(elem!1 = s(z))) | (elem!1 = s(s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(9004,plain,
% 2.04/2.28 (~r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[9003, 257, 2073, 8852, 299, 1291, 1100])).
% 2.04/2.28 tff(9005,plain,
% 2.04/2.28 (b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[297, 9004])).
% 2.04/2.28 tff(9006,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2943, 453, 443, 1779, 374, 120])).
% 2.04/2.28 tff(9007,plain,((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(9008,plain,
% 2.04/2.28 (~b(s(z), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[9007, 8929, 9005, 8857])).
% 2.04/2.28 tff(9009,plain,
% 2.04/2.28 (r(s(z), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[372, 9008])).
% 2.04/2.28 tff(9010,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(9011,plain,
% 2.04/2.28 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(9012,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[9011])).
% 2.04/2.28 tff(9013,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[9012, 9010])).
% 2.04/2.28 tff(9014,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(9015,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[9014, 9013])).
% 2.04/2.28 tff(9016,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[9015, 268, 2246, 257, 4621])).
% 2.04/2.28 tff(9017,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(9018,plain,
% 2.04/2.28 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[9017, 9009, 257])).
% 2.04/2.28 tff(9019,plain,
% 2.04/2.28 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2570, 9018])).
% 2.04/2.28 tff(9020,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(z))) | (~b(s(z), s(s(z)))) | (~b(s(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(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(9021,plain,
% 2.04/2.28 (((~b(s(z), s(s(z)))) | (~b(s(z), s(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(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(9022,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), s(s(z)))) | (~b(s(z), s(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(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[9021])).
% 2.04/2.28 tff(9023,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), s(s(z)))) | (~b(s(z), s(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(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[9022, 9020])).
% 2.04/2.28 tff(9024,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), s(s(z)))) | (~b(s(z), s(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(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(9025,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[9024, 9023])).
% 2.04/2.28 tff(9026,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[9025, 453, 1008, 374, 2611, 120])).
% 2.04/2.28 tff(9027,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(9028,plain,
% 2.04/2.28 (~b(s(z), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[9027, 9005, 9019, 8857])).
% 2.04/2.28 tff(9029,plain,
% 2.04/2.28 (r(s(z), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[757, 9028])).
% 2.04/2.28 tff(9030,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 2.04/2.28 tff(9031,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(9032,plain,
% 2.04/2.28 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(9033,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[9032])).
% 2.04/2.28 tff(9034,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[9033, 9031])).
% 2.04/2.28 tff(9035,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(9036,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[9035, 9034])).
% 2.04/2.28 tff(9037,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[9036, 268, 257, 733, 9030])).
% 2.04/2.28 tff(9038,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(9039,plain,
% 2.04/2.28 (~r(s(s(s(z))), s(s(z)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[9038, 9029, 257])).
% 2.04/2.28 tff(9040,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(9041,plain,
% 2.04/2.28 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(9042,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[9041])).
% 2.04/2.28 tff(9043,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[9042, 9040])).
% 2.04/2.28 tff(9044,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(9045,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[9044, 9043])).
% 2.04/2.28 tff(9046,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[9045, 268, 2246, 733, 2787])).
% 2.04/2.28 tff(9047,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(9048,plain,
% 2.04/2.28 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[9047, 9029, 9009])).
% 2.04/2.28 tff(9049,plain,
% 2.04/2.28 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[3228, 9048, 1100])).
% 2.04/2.28 tff(9050,plain,
% 2.04/2.28 (b(s(elem!1), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[659, 9049, 2275])).
% 2.04/2.28 tff(9051,plain,
% 2.04/2.28 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[645, 2271])).
% 2.04/2.28 tff(9052,assumption,(~b(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.04/2.28 tff(9053,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[9052, 9051])).
% 2.04/2.28 tff(9054,plain,((~b(s(elem!1), s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(z)))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(9055,plain,
% 2.04/2.28 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[9054, 9050, 1100])).
% 2.04/2.28 tff(9056,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 2.04/2.28 tff(9057,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(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(9058,plain,
% 2.04/2.28 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(9059,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[9058])).
% 2.04/2.28 tff(9060,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[9059, 9057])).
% 2.04/2.29 tff(9061,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(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(9062,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[9061, 9060])).
% 2.04/2.29 tff(9063,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[9062, 453, 1779, 2611, 9056, 8943])).
% 2.04/2.29 tff(9064,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(9065,plain,
% 2.04/2.29 (~b(s(s(s(z))), s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[9064, 9055, 8929, 9019])).
% 2.04/2.29 tff(9066,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2534, 69, 160, 9065, 9039])).
% 2.04/2.29 tff(9067,plain,((~r(s(z), s(s(s(z))))) | (~(elem!1 = s(z))) | (elem!1 = s(s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(9068,plain,
% 2.04/2.29 (~r(s(z), s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[9067, 1100, 2925, 8852, 299, 1291])).
% 2.04/2.29 tff(9069,plain,
% 2.04/2.29 (~r(elem!1, s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3171, 9068, 3028])).
% 2.04/2.29 tff(9070,plain,
% 2.04/2.29 (b(elem!1, s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1024, 9069, 3102])).
% 2.04/2.29 tff(9071,plain,
% 2.04/2.29 (b(s(z), s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[227, 9068])).
% 2.04/2.29 tff(9072,plain,
% 2.04/2.29 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3782, 9071, 8857, 8866])).
% 2.04/2.29 tff(9073,plain,
% 2.04/2.29 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[518, 9072])).
% 2.04/2.29 tff(9074,plain,
% 2.04/2.29 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 2.04/2.29 inference(symmetry,[status(thm)],[3107])).
% 2.04/2.29 tff(9075,plain,
% 2.04/2.29 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 2.04/2.29 inference(transitivity,[status(thm)],[3105, 9074])).
% 2.04/2.29 tff(9076,plain,
% 2.04/2.29 (b(s(elem!1), elem!1)),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[922, 9075])).
% 2.04/2.29 tff(9077,plain,
% 2.04/2.29 (~b(s(elem!1), s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[918, 9076, 909, 907])).
% 2.04/2.29 tff(9078,plain,
% 2.04/2.29 (r(s(elem!1), s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[440, 9077, 2288])).
% 2.04/2.29 tff(9079,plain,
% 2.04/2.29 (r(s(s(z)), s(s(s(z))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[9078, 2276])).
% 2.04/2.29 tff(9080,plain,
% 2.04/2.29 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2604, 268, 11, 9079])).
% 2.04/2.29 tff(9081,plain,
% 2.04/2.29 (b(s(s(z)), s(z))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[922, 3104])).
% 2.04/2.29 tff(9082,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(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(9083,plain,
% 2.04/2.29 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(9084,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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(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(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[9083])).
% 2.04/2.29 tff(9085,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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(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(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[9084, 9082])).
% 2.04/2.29 tff(9086,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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(9087,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[9086, 9085])).
% 2.04/2.29 tff(9088,plain,
% 2.04/2.29 ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[9087, 453, 1764, 2090])).
% 2.04/2.29 tff(9089,plain,
% 2.04/2.29 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[9088, 9081])).
% 2.04/2.29 tff(9090,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[795, 69, 153, 9089, 9080])).
% 2.04/2.29 tff(9091,plain,((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~(elem!1 = s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(9092,plain,
% 2.04/2.29 (~b(s(s(z)), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[9091, 9073, 1100, 8866, 9071, 8965, 9070])).
% 2.04/2.29 tff(9093,plain,
% 2.04/2.29 (r(s(s(z)), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[782, 9092, 8851])).
% 2.04/2.29 tff(9094,plain,
% 2.04/2.29 (r(s(s(z)), s(z))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[9093, 8846])).
% 2.04/2.29 tff(9095,plain,
% 2.04/2.29 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.29 inference(commutativity,[status(thm)],[])).
% 2.04/2.29 tff(9096,plain,
% 2.04/2.29 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(z)))),
% 2.04/2.29 inference(symmetry,[status(thm)],[9095])).
% 2.04/2.29 tff(9097,plain,
% 2.04/2.29 ((~(s(s(z)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(z))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[9096])).
% 2.04/2.29 tff(9098,plain,
% 2.04/2.29 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[2269])).
% 2.04/2.29 tff(9099,plain,
% 2.04/2.29 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.29 inference(symmetry,[status(thm)],[9098])).
% 2.04/2.29 tff(9100,plain,
% 2.04/2.29 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(z)) = s(s(s(s(s(s(s(z)))))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[9099])).
% 2.04/2.29 tff(9101,plain,
% 2.04/2.29 (~(s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[2552, 9100])).
% 2.04/2.29 tff(9102,plain,
% 2.04/2.29 (~(s(s(s(s(s(s(s(z))))))) = s(s(z)))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[9101, 9097])).
% 2.04/2.29 tff(9103,plain,
% 2.04/2.29 (r(s(s(z)), s(z))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[700, 8846])).
% 2.04/2.29 tff(9104,plain,
% 2.04/2.29 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3782, 2090, 120, 1764])).
% 2.04/2.29 tff(9105,plain,
% 2.04/2.29 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[518, 9104])).
% 2.04/2.29 tff(9106,plain,
% 2.04/2.29 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1982, 256, 9105])).
% 2.04/2.29 tff(9107,plain,
% 2.04/2.29 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[328, 9106])).
% 2.04/2.29 tff(9108,plain,
% 2.04/2.29 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3216, 268, 9105, 256])).
% 2.04/2.29 tff(9109,plain,
% 2.04/2.29 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2463, 69, 9108, 2453])).
% 2.04/2.29 tff(9110,plain,
% 2.04/2.29 (~b(s(z), s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8186, 9109, 1764, 9107])).
% 2.04/2.29 tff(9111,plain,
% 2.04/2.29 (r(s(z), s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[372, 9110])).
% 2.04/2.29 tff(9112,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3314, 268, 2246, 2360, 2787])).
% 2.04/2.29 tff(9113,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(9114,plain,
% 2.04/2.29 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[9113, 9111, 9103])).
% 2.04/2.29 tff(9115,plain,
% 2.04/2.29 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3228, 9114, 1100])).
% 2.04/2.29 tff(9116,plain,
% 2.04/2.29 (b(s(elem!1), s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[659, 9115, 2275])).
% 2.04/2.29 tff(9117,plain,
% 2.04/2.29 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[9054, 9116, 1100])).
% 2.04/2.29 tff(9118,plain,
% 2.04/2.29 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[1100])).
% 2.04/2.29 tff(9119,plain,
% 2.04/2.29 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3822, 2344])).
% 2.04/2.29 tff(9120,plain,
% 2.04/2.29 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3862, 9119])).
% 2.04/2.29 tff(9121,plain,
% 2.04/2.29 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.29 inference(monotonicity,[status(thm)],[2277])).
% 2.04/2.29 tff(9122,plain,
% 2.04/2.29 ((~b(s(s(s(s(s(s(s(z))))))), s(z))) <=> (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[9121])).
% 2.04/2.29 tff(9123,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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~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(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(9124,plain,
% 2.04/2.29 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(9125,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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[9124])).
% 2.04/2.29 tff(9126,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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[9125, 9123])).
% 2.04/2.29 tff(9127,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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(9128,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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[9127, 9126])).
% 2.04/2.29 tff(9129,plain,
% 2.04/2.29 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[9128, 453, 1764, 120, 2090])).
% 2.04/2.29 tff(9130,plain,
% 2.04/2.29 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1656, 9129])).
% 2.04/2.29 tff(9131,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(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(9132,plain,
% 2.04/2.29 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(9133,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(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[9132])).
% 2.04/2.29 tff(9134,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(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[9133, 9131])).
% 2.04/2.29 tff(9135,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(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(9136,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[9135, 9134])).
% 2.04/2.29 tff(9137,plain,
% 2.04/2.29 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[9136, 453, 9107, 9109, 9117])).
% 2.04/2.29 tff(9138,plain,
% 2.04/2.29 (r(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4293, 9137])).
% 2.04/2.29 tff(9139,plain,
% 2.04/2.29 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[607, 8906])).
% 2.04/2.29 tff(9140,plain,
% 2.04/2.29 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[1104, 1105])).
% 2.04/2.29 tff(9141,plain,
% 2.04/2.29 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[3365, 9140])).
% 2.04/2.29 tff(9142,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1648, 9141])).
% 2.04/2.29 tff(9143,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(z))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(9144,plain,
% 2.04/2.29 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[9143, 9129, 1100])).
% 2.04/2.29 tff(9145,plain,
% 2.04/2.29 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[675, 9144, 9139])).
% 2.04/2.29 tff(9146,plain,
% 2.04/2.29 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[1103, 1105])).
% 2.04/2.29 tff(9147,plain,
% 2.04/2.29 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.29 inference(symmetry,[status(thm)],[9146])).
% 2.04/2.29 tff(9148,plain,
% 2.04/2.29 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6600, 453, 9107, 9109, 9117])).
% 2.04/2.29 tff(9149,plain,
% 2.04/2.29 (r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2370, 69, 2359, 9148])).
% 2.04/2.29 tff(9150,plain,
% 2.04/2.29 (r(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[9149, 9147])).
% 2.04/2.29 tff(9151,plain,
% 2.04/2.29 (~r(s(elem!1), s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[670, 9150, 9145])).
% 2.04/2.29 tff(9152,plain,
% 2.04/2.29 (b(s(elem!1), s(s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[440, 9151, 2288])).
% 2.04/2.29 tff(9153,plain,
% 2.04/2.29 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[9152, 2948])).
% 2.04/2.29 tff(9154,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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(9155,plain,
% 2.04/2.29 (((~b(s(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(z))))) | (~b(s(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))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(9156,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(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(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(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))))),
% 2.04/2.30 inference(monotonicity,[status(thm)],[9155])).
% 2.04/2.30 tff(9157,plain,
% 2.04/2.30 (((~![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(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(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(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 2.04/2.30 inference(transitivity,[status(thm)],[9156, 9154])).
% 2.04/2.30 tff(9158,plain,
% 2.04/2.30 ((~![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(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 2.04/2.30 inference(quant_inst,[status(thm)],[])).
% 2.04/2.30 tff(9159,plain,
% 2.04/2.30 ((~![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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))),
% 2.04/2.30 inference(modus_ponens,[status(thm)],[9158, 9157])).
% 2.04/2.30 tff(9160,plain,
% 2.04/2.30 (~b(s(z), s(s(z)))),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[9159, 453, 120, 2090, 9153])).
% 2.04/2.30 tff(9161,plain,
% 2.04/2.30 (r(s(z), s(s(z)))),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[757, 9160])).
% 2.04/2.30 tff(9162,plain,
% 2.04/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.30 inference(rewrite,[status(thm)],[])).
% 2.04/2.30 tff(9163,plain,
% 2.04/2.30 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.30 inference(rewrite,[status(thm)],[])).
% 2.04/2.30 tff(9164,plain,
% 2.04/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.04/2.30 inference(monotonicity,[status(thm)],[9163])).
% 2.04/2.30 tff(9165,plain,
% 2.04/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.30 inference(transitivity,[status(thm)],[9164, 9162])).
% 2.04/2.30 tff(9166,plain,
% 2.04/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(9167,plain,
% 2.14/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[9166, 9165])).
% 2.14/2.30 tff(9168,plain,
% 2.14/2.30 (~r(s(z), s(s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9167, 268, 9105, 9161, 9138])).
% 2.14/2.30 tff(9169,plain,
% 2.14/2.30 (b(s(z), s(s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1677, 69, 9168, 50])).
% 2.14/2.30 tff(9170,assumption,(b(s(s(s(s(s(s(s(z))))))), s(z))), introduced(assumption)).
% 2.14/2.30 tff(9171,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(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(9172,plain,
% 2.14/2.30 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(9173,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), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[9172])).
% 2.14/2.30 tff(9174,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), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[9173, 9171])).
% 2.14/2.30 tff(9175,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), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(9176,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(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[9175, 9174])).
% 2.14/2.30 tff(9177,plain,
% 2.14/2.30 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9176, 453, 1764, 1780, 2497, 1974, 9170])).
% 2.14/2.30 tff(9178,plain,
% 2.14/2.30 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2696, 9177])).
% 2.14/2.30 tff(9179,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(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(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(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(9180,plain,
% 2.14/2.30 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(9181,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), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(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(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[9180])).
% 2.14/2.30 tff(9182,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), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(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(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[9181, 9179])).
% 2.14/2.30 tff(9183,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), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(9184,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(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[9183, 9182])).
% 2.14/2.30 tff(9185,plain,
% 2.14/2.30 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9184, 453, 1974, 120, 9170])).
% 2.14/2.30 tff(9186,plain,
% 2.14/2.30 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[7740, 9185, 3475])).
% 2.14/2.30 tff(9187,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(9188,plain,
% 2.14/2.30 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(9189,plain,
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% 2.14/2.30 inference(monotonicity,[status(thm)],[9188])).
% 2.14/2.30 tff(9190,plain,
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% 2.14/2.30 inference(transitivity,[status(thm)],[9189, 9187])).
% 2.14/2.30 tff(9191,plain,
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% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(9192,plain,
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% 2.14/2.30 inference(modus_ponens,[status(thm)],[9191, 9190])).
% 2.14/2.30 tff(9193,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9192, 268, 300, 9186, 9178])).
% 2.14/2.30 tff(9194,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(9195,plain,
% 2.14/2.30 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9194, 9169, 9130, 120, 1764, 9107, 9109])).
% 2.14/2.30 tff(9196,plain,
% 2.14/2.30 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[9195, 9122])).
% 2.14/2.30 tff(9197,plain,
% 2.14/2.30 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[3875, 9196, 9120])).
% 2.14/2.30 tff(9198,plain,
% 2.14/2.30 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[9197, 9118])).
% 2.14/2.30 tff(9199,plain,
% 2.14/2.30 (~r(s(s(s(s(z)))), elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[4297, 9138, 700])).
% 2.14/2.30 tff(9200,plain,
% 2.14/2.30 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[8862])).
% 2.14/2.30 tff(9201,plain,
% 2.14/2.30 (~(s(s(s(s(z)))) = elem!1)),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[50, 9200])).
% 2.14/2.30 tff(9202,plain,
% 2.14/2.30 (~r(elem!1, s(s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6942, 9149, 700])).
% 2.14/2.30 tff(9203,plain,
% 2.14/2.30 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[6664, 9202, 9107, 9201, 9199, 9109])).
% 2.14/2.30 tff(9204,plain,
% 2.14/2.30 (r(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[643, 9203, 637])).
% 2.14/2.30 tff(9205,plain,
% 2.14/2.30 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[292, 2928])).
% 2.14/2.30 tff(9206,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[722, 9205])).
% 2.14/2.30 tff(9207,plain,(r(s(s(s(s(s(z))))), s(z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(9208,plain,
% 2.14/2.30 (r(s(s(s(s(s(z))))), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9207, 9204, 1100])).
% 2.14/2.30 tff(9209,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(9210,plain,
% 2.14/2.30 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(9211,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[9210])).
% 2.14/2.30 tff(9212,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[9211, 9209])).
% 2.14/2.30 tff(9213,plain,
% 2.14/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(9214,plain,
% 2.14/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[9213, 9212])).
% 2.14/2.30 tff(9215,plain,
% 2.14/2.30 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[9214, 268, 256, 9208, 9198])).
% 2.14/2.30 tff(9216,plain,
% 2.14/2.30 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2732, 69, 2729, 9215])).
% 2.14/2.30 tff(9217,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(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9218,plain,
% 2.14/2.31 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9219,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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9218])).
% 2.14/2.31 tff(9220,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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[9219, 9217])).
% 2.14/2.31 tff(9221,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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(9222,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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[9221, 9220])).
% 2.14/2.31 tff(9223,plain,
% 2.14/2.31 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9222, 453, 9107, 9216, 9117])).
% 2.14/2.31 tff(9224,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9225,plain,
% 2.14/2.31 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9226,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9225])).
% 2.14/2.31 tff(9227,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[9226, 9224])).
% 2.14/2.31 tff(9228,plain,
% 2.14/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(9229,plain,
% 2.14/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[9228, 9227])).
% 2.14/2.31 tff(9230,plain,
% 2.14/2.31 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9229, 268, 9103, 9198])).
% 2.14/2.31 tff(9231,plain,
% 2.14/2.31 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1369, 69, 9230])).
% 2.14/2.31 tff(9232,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9231, 9223, 9102])).
% 2.14/2.31 tff(9233,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~(elem!1 = s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(9234,plain,
% 2.14/2.31 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9233, 1100, 8857, 8866, 9071, 637, 9093])).
% 2.14/2.31 tff(9235,plain,
% 2.14/2.31 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[687, 9234])).
% 2.14/2.31 tff(9236,plain,
% 2.14/2.31 (~b(s(z), s(s(s(s(s(z))))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5584, 453, 9235, 8857, 9071])).
% 2.14/2.31 tff(9237,plain,
% 2.14/2.31 (r(s(z), s(s(s(s(s(z))))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[372, 9236])).
% 2.14/2.31 tff(9238,plain,
% 2.14/2.31 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9113, 9237, 9094])).
% 2.14/2.31 tff(9239,plain,
% 2.14/2.31 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3228, 9238, 1100])).
% 2.14/2.31 tff(9240,plain,
% 2.14/2.31 (b(s(elem!1), s(s(s(s(s(z))))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[659, 9239, 2275])).
% 2.14/2.31 tff(9241,plain,
% 2.14/2.31 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9054, 9240, 1100])).
% 2.14/2.31 tff(9242,plain,
% 2.14/2.31 (~b(s(s(s(s(s(z))))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[7909, 453, 9235, 8857, 9071])).
% 2.14/2.31 tff(9243,plain,
% 2.14/2.31 (r(s(s(s(s(s(z))))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[297, 9242])).
% 2.14/2.31 tff(9244,plain,
% 2.14/2.31 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[6922, 268, 9243, 9094])).
% 2.14/2.31 tff(9245,plain,
% 2.14/2.31 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[4081, 9244])).
% 2.14/2.31 tff(9246,plain,
% 2.14/2.31 (~b(s(s(z)), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8945, 9241, 8857, 9235])).
% 2.14/2.31 tff(9247,plain,
% 2.14/2.31 (~b(s(elem!1), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[8941, 9246, 1100])).
% 2.14/2.31 tff(9248,plain,
% 2.14/2.31 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(z))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[2948, 3043])).
% 2.14/2.31 tff(9249,plain,
% 2.14/2.31 (b(s(elem!1), s(s(s(z))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[910, 9248])).
% 2.14/2.31 tff(9250,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1300, 9249])).
% 2.14/2.31 tff(9251,plain,((~b(s(elem!1), s(s(elem!1)))) | b(s(elem!1), s(s(s(z)))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(9252,plain,
% 2.14/2.31 (~b(s(elem!1), s(s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9251, 9247, 1100])).
% 2.14/2.31 tff(9253,plain,
% 2.14/2.31 (r(s(elem!1), s(s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[440, 9252, 2288])).
% 2.14/2.31 tff(9254,plain,
% 2.14/2.31 (r(s(s(z)), s(s(s(z))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[9253, 2276])).
% 2.14/2.31 tff(9255,plain,
% 2.14/2.31 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2739, 268, 9073, 9254])).
% 2.14/2.31 tff(9256,plain,
% 2.14/2.31 (b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2370, 69, 9255, 2359])).
% 2.14/2.31 tff(9257,plain,
% 2.14/2.31 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2604, 268, 9073, 9254])).
% 2.14/2.31 tff(9258,plain,
% 2.14/2.31 (b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[4293, 9257])).
% 2.14/2.31 tff(9259,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(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9260,plain,
% 2.14/2.31 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9261,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(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9260])).
% 2.14/2.31 tff(9262,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(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[9261, 9259])).
% 2.14/2.31 tff(9263,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(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(9264,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(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[9263, 9262])).
% 2.14/2.31 tff(9265,plain,
% 2.14/2.31 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9264, 453, 9258, 9245, 9241])).
% 2.14/2.31 tff(9266,plain,
% 2.14/2.31 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[328, 9265])).
% 2.14/2.31 tff(9267,plain,
% 2.14/2.31 (~r(s(z), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5380, 9266, 8857, 9235])).
% 2.14/2.31 tff(9268,plain,
% 2.14/2.31 (b(s(z), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1677, 69, 9267, 50])).
% 2.14/2.31 tff(9269,plain,
% 2.14/2.31 ((~(elem!1 = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[8506])).
% 2.14/2.31 tff(9270,plain,
% 2.14/2.31 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[9119, 9269])).
% 2.14/2.31 tff(9271,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(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9272,plain,
% 2.14/2.31 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9273,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(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(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(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9272])).
% 2.14/2.31 tff(9274,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(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(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(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[9273, 9271])).
% 2.14/2.31 tff(9275,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(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(9276,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(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[9275, 9274])).
% 2.14/2.31 tff(9277,plain,
% 2.14/2.31 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9276, 453, 1764, 1974, 2994])).
% 2.14/2.31 tff(9278,plain,
% 2.14/2.31 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[9277, 9122])).
% 2.14/2.31 tff(9279,plain,
% 2.14/2.31 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3875, 9278, 9270])).
% 2.14/2.31 tff(9280,plain,
% 2.14/2.31 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[9279, 9118])).
% 2.14/2.31 tff(9281,plain,
% 2.14/2.31 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9229, 268, 2360, 9280])).
% 2.14/2.31 tff(9282,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(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9283,plain,
% 2.14/2.31 (((~b(s(s(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(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9284,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(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9283])).
% 2.14/2.31 tff(9285,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(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[9284, 9282])).
% 2.14/2.31 tff(9286,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(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(9287,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[9286, 9285])).
% 2.14/2.31 tff(9288,plain,
% 2.14/2.31 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9287, 453, 1764, 2994, 2956])).
% 2.14/2.31 tff(9289,plain,
% 2.14/2.31 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1369, 69, 9288])).
% 2.14/2.31 tff(9290,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9289, 9281, 2553])).
% 2.14/2.31 tff(9291,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~(elem!1 = s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(9292,plain,
% 2.14/2.31 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9291, 9268, 1100, 8866, 9256, 9094])).
% 2.14/2.31 tff(9293,plain,
% 2.14/2.31 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2696, 9292])).
% 2.14/2.31 tff(9294,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9295,plain,
% 2.14/2.31 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(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(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(9296,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(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(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[9295])).
% 2.14/2.31 tff(9297,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(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(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[9296, 9294])).
% 2.14/2.31 tff(9298,plain,
% 2.14/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(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(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(9299,plain,
% 2.14/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[9298, 9297])).
% 2.14/2.31 tff(9300,plain,
% 2.14/2.31 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[9299, 268, 9266, 9293])).
% 2.14/2.31 tff(9301,plain,
% 2.14/2.31 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2732, 69, 2729, 9300])).
% 2.14/2.31 tff(9302,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(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9303,plain,
% 2.14/2.32 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9304,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(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(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9303])).
% 2.14/2.32 tff(9305,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(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(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[9304, 9302])).
% 2.14/2.32 tff(9306,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(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(9307,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(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[9306, 9305])).
% 2.14/2.32 tff(9308,plain,
% 2.14/2.32 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9307, 453, 9258, 9245, 9241])).
% 2.14/2.32 tff(9309,plain,
% 2.14/2.32 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2463, 69, 9308, 2453])).
% 2.14/2.32 tff(9310,plain,
% 2.14/2.32 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8666, 9309, 9073])).
% 2.14/2.32 tff(9311,plain,
% 2.14/2.32 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2570, 9310])).
% 2.14/2.32 tff(9312,plain,
% 2.14/2.32 (~b(s(s(s(z))), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9064, 9311, 9235, 9241])).
% 2.14/2.32 tff(9313,plain,
% 2.14/2.32 (r(s(s(s(z))), s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2534, 69, 160, 9312])).
% 2.14/2.32 tff(9314,plain,
% 2.14/2.32 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9128, 453, 8866, 8857, 9071])).
% 2.14/2.32 tff(9315,plain,
% 2.14/2.32 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1656, 9314])).
% 2.14/2.32 tff(9316,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9317,plain,
% 2.14/2.32 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), 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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9318,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9317])).
% 2.14/2.32 tff(9319,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[9318, 9316])).
% 2.14/2.32 tff(9320,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(9321,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[9320, 9319])).
% 2.14/2.32 tff(9322,plain,
% 2.14/2.32 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9321, 268, 9315, 9293, 9313])).
% 2.14/2.32 tff(9323,plain,
% 2.14/2.32 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1238, 69, 2663, 9322])).
% 2.14/2.32 tff(9324,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(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9325,plain,
% 2.14/2.32 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9326,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(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9325])).
% 2.14/2.32 tff(9327,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(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[9326, 9324])).
% 2.14/2.32 tff(9328,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(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(9329,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[9328, 9327])).
% 2.14/2.32 tff(9330,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9329, 453, 9235, 9311, 9323, 9301, 9245, 9241])).
% 2.14/2.32 tff(9331,plain,((~(elem!1 = s(z))) | (s(s(s(s(s(z))))) = elem!1) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(9332,plain,
% 2.14/2.32 (~(elem!1 = s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9331, 637, 8845, 8837, 8844])).
% 2.14/2.32 tff(9333,plain,
% 2.14/2.32 (r(elem!1, s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1130, 9332, 10])).
% 2.14/2.32 tff(9334,plain,
% 2.14/2.32 (~(elem!1 = s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[4487, 8843])).
% 2.14/2.32 tff(9335,plain,
% 2.14/2.32 (~(s(z) = elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1125, 9332])).
% 2.14/2.32 tff(9336,plain,
% 2.14/2.32 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[547, 9335])).
% 2.14/2.32 tff(9337,plain,
% 2.14/2.32 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(elem!1))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[2284])).
% 2.14/2.32 tff(9338,plain,
% 2.14/2.32 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.32 inference(symmetry,[status(thm)],[9337])).
% 2.14/2.32 tff(9339,plain,
% 2.14/2.32 ((~b(s(s(s(z))), s(elem!1))) <=> (~b(s(s(s(z))), s(s(elem!1))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9338])).
% 2.14/2.32 tff(9340,plain,
% 2.14/2.32 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[6845, 9339])).
% 2.14/2.32 tff(9341,plain,
% 2.14/2.32 (inj_0(s(s(elem!1))) = inj_0(s(elem!1))),
% 2.14/2.32 inference(symmetry,[status(thm)],[1858])).
% 2.14/2.32 tff(9342,plain,
% 2.14/2.32 (s(s(elem!1)) = elem!1),
% 2.14/2.32 inference(transitivity,[status(thm)],[2284, 195, 9341, 85])).
% 2.14/2.32 tff(9343,plain,
% 2.14/2.32 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), elem!1)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9342])).
% 2.14/2.32 tff(9344,plain,
% 2.14/2.32 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.32 inference(symmetry,[status(thm)],[9343])).
% 2.14/2.32 tff(9345,plain,
% 2.14/2.32 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9344])).
% 2.14/2.32 tff(9346,plain,
% 2.14/2.32 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[2, 9345])).
% 2.14/2.32 tff(9347,plain,
% 2.14/2.32 (b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5201, 69, 555])).
% 2.14/2.32 tff(9348,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9347, 9346, 9340])).
% 2.14/2.32 tff(9349,plain,(r(s(s(s(z))), elem!1) | (s(s(s(z))) = s(s(elem!1))) | (~(s(elem!1) = s(s(elem!1)))) | b(s(s(s(z))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(9350,plain,
% 2.14/2.32 (~(s(elem!1) = s(s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9349, 6845, 2, 9336])).
% 2.14/2.32 tff(9351,plain,
% 2.14/2.32 (~(s(elem!1) = elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8905, 9350])).
% 2.14/2.32 tff(9352,plain,
% 2.14/2.32 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[607, 9351])).
% 2.14/2.32 tff(9353,plain,
% 2.14/2.32 (~(elem!1 = s(elem!1))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8957, 9351])).
% 2.14/2.32 tff(9354,plain,
% 2.14/2.32 (~(s(s(s(z))) = elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2267, 299, 2925, 10])).
% 2.14/2.32 tff(9355,plain,
% 2.14/2.32 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[4144, 9354])).
% 2.14/2.32 tff(9356,plain,
% 2.14/2.32 (~(elem!1 = s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9331, 637, 9355, 299, 1291])).
% 2.14/2.32 tff(9357,plain,
% 2.14/2.32 (~(s(z) = elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1125, 9356])).
% 2.14/2.32 tff(9358,plain,
% 2.14/2.32 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[2372])).
% 2.14/2.32 tff(9359,plain,
% 2.14/2.32 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[9355, 9358])).
% 2.14/2.32 tff(9360,plain,
% 2.14/2.32 (~(elem!1 = s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[4487, 9354])).
% 2.14/2.32 tff(9361,plain,
% 2.14/2.32 (r(elem!1, s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1130, 9356, 10])).
% 2.14/2.32 tff(9362,assumption,(~r(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 2.14/2.32 tff(9363,plain,
% 2.14/2.32 (b(s(s(s(s(z)))), elem!1) <=> b(elem!1, elem!1)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[4148])).
% 2.14/2.32 tff(9364,plain,
% 2.14/2.32 (b(elem!1, elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.14/2.32 inference(symmetry,[status(thm)],[9363])).
% 2.14/2.32 tff(9365,plain,
% 2.14/2.32 ((~b(elem!1, elem!1)) <=> (~b(s(s(s(s(z)))), elem!1))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9364])).
% 2.14/2.32 tff(9366,plain,
% 2.14/2.32 (~b(s(s(s(s(z)))), elem!1)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[1707, 9365])).
% 2.14/2.32 tff(9367,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[299, 9366])).
% 2.14/2.32 tff(9368,plain,((~(s(s(s(s(s(z))))) = s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(9369,plain,
% 2.14/2.32 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9368, 299])).
% 2.14/2.32 tff(9370,plain,
% 2.14/2.32 (~(s(s(s(s(z)))) = elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[4108, 9369])).
% 2.14/2.32 tff(9371,plain,
% 2.14/2.32 (~(elem!1 = s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[8, 9370])).
% 2.14/2.32 tff(9372,assumption,(s(elem!1) = s(s(s(z)))), introduced(assumption)).
% 2.14/2.32 tff(9373,plain,
% 2.14/2.32 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9372])).
% 2.14/2.32 tff(9374,plain,
% 2.14/2.32 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 2.14/2.32 inference(symmetry,[status(thm)],[9373])).
% 2.14/2.32 tff(9375,plain,
% 2.14/2.32 (b(s(elem!1), elem!1)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[1291, 9374])).
% 2.14/2.32 tff(9376,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[526, 9375])).
% 2.14/2.32 tff(9377,plain,((~(s(elem!1) = s(s(s(z))))) | b(s(elem!1), elem!1) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(9378,plain,
% 2.14/2.32 (b(s(elem!1), elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9377, 9372, 1291])).
% 2.14/2.32 tff(9379,plain,
% 2.14/2.32 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9380,plain,
% 2.14/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z))))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(9381,plain,
% 2.14/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z)))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[9380, 9379])).
% 2.14/2.32 tff(9382,plain,
% 2.14/2.32 ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9381, 69])).
% 2.14/2.32 tff(9383,plain,
% 2.14/2.32 (b(s(elem!1), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9382, 9362, 79])).
% 2.14/2.32 tff(9384,assumption,(b(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 2.14/2.32 tff(9385,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(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9386,plain,
% 2.14/2.32 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9387,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9386])).
% 2.14/2.32 tff(9388,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[9387, 9385])).
% 2.14/2.32 tff(9389,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(9390,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[9389, 9388])).
% 2.14/2.32 tff(9391,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9390, 453, 629, 299, 9384, 1275])).
% 2.14/2.32 tff(9392,plain,((~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(9393,plain,
% 2.14/2.32 (~b(elem!1, s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9392, 9383, 299, 9378])).
% 2.14/2.32 tff(9394,plain,
% 2.14/2.32 (r(elem!1, s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[4492, 9393, 4489])).
% 2.14/2.32 tff(9395,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9396,plain,
% 2.14/2.32 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9397,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[9396])).
% 2.14/2.32 tff(9398,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[9397, 9395])).
% 2.14/2.32 tff(9399,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(9400,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[9399, 9398])).
% 2.14/2.32 tff(9401,plain,
% 2.14/2.32 (~r(elem!1, s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9400, 268, 11, 9394])).
% 2.14/2.32 tff(9402,plain,
% 2.14/2.32 (b(elem!1, s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1087, 9401, 9371])).
% 2.14/2.32 tff(9403,plain,
% 2.14/2.32 (~b(s(s(z)), elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[6077, 9402, 299, 1291, 11])).
% 2.14/2.32 tff(9404,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(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9405,plain,
% 2.14/2.32 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(9406,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(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9405])).
% 2.14/2.33 tff(9407,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(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[9406, 9404])).
% 2.14/2.33 tff(9408,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(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(9409,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[9408, 9407])).
% 2.14/2.33 tff(9410,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9409, 453, 629, 923, 299, 9384])).
% 2.14/2.33 tff(9411,plain,((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(9412,plain,
% 2.14/2.33 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9411, 9383, 299, 9378])).
% 2.14/2.33 tff(9413,plain,
% 2.14/2.33 (r(elem!1, s(s(s(s(s(z))))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[466, 9412, 2073])).
% 2.14/2.33 tff(9414,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[6153, 268, 412, 1149, 4621])).
% 2.14/2.33 tff(9415,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(9416,plain,
% 2.14/2.33 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9415, 9394, 9413])).
% 2.14/2.33 tff(9417,plain,
% 2.14/2.33 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2570, 9416])).
% 2.14/2.33 tff(9418,plain,
% 2.14/2.33 (~r(s(s(s(s(s(z))))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[3465, 9413, 238])).
% 2.14/2.33 tff(9419,plain,
% 2.14/2.33 (b(s(s(s(s(s(z))))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[297, 9418])).
% 2.14/2.33 tff(9420,plain,
% 2.14/2.33 (r(s(elem!1), s(z)) <=> r(s(s(s(z))), s(z))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9372])).
% 2.14/2.33 tff(9421,plain,
% 2.14/2.33 (r(s(s(s(z))), s(z)) <=> r(s(elem!1), s(z))),
% 2.14/2.33 inference(symmetry,[status(thm)],[9420])).
% 2.14/2.33 tff(9422,plain,
% 2.14/2.33 (r(s(elem!1), s(z))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[233, 9421])).
% 2.14/2.33 tff(9423,plain,
% 2.14/2.33 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9372])).
% 2.14/2.33 tff(9424,plain,
% 2.14/2.33 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 2.14/2.33 inference(symmetry,[status(thm)],[9423])).
% 2.14/2.33 tff(9425,plain,
% 2.14/2.33 (r(elem!1, s(elem!1))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[1149, 9424])).
% 2.14/2.33 tff(9426,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[348, 9425, 9422, 238])).
% 2.14/2.33 tff(9427,plain,((~(s(elem!1) = s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(9428,plain,
% 2.14/2.33 (~r(s(s(s(z))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9427, 9394, 238, 9372])).
% 2.14/2.33 tff(9429,plain,
% 2.14/2.33 (b(s(s(s(z))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[134, 9428])).
% 2.14/2.33 tff(9430,plain,
% 2.14/2.33 (~b(s(z), s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9027, 9429, 9419, 9417])).
% 2.14/2.33 tff(9431,plain,
% 2.14/2.33 (r(s(z), s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[757, 9430])).
% 2.14/2.33 tff(9432,plain,
% 2.14/2.33 (~b(s(z), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[7149, 9402, 9429, 1291])).
% 2.14/2.33 tff(9433,plain,
% 2.14/2.33 (r(s(z), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[506, 9432, 492])).
% 2.14/2.33 tff(9434,plain,
% 2.14/2.33 (~r(s(s(z)), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[741, 9433, 9431])).
% 2.14/2.33 tff(9435,plain,
% 2.14/2.33 (s(s(z)) = elem!1),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[782, 9434, 9403])).
% 2.14/2.33 tff(9436,plain,
% 2.14/2.33 (s(s(s(z))) = s(elem!1)),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9435])).
% 2.14/2.33 tff(9437,plain,
% 2.14/2.33 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9436])).
% 2.14/2.33 tff(9438,plain,
% 2.14/2.33 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.33 inference(symmetry,[status(thm)],[9437])).
% 2.14/2.33 tff(9439,plain,
% 2.14/2.33 ((~r(s(elem!1), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9438])).
% 2.14/2.33 tff(9440,plain,
% 2.14/2.33 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[9362, 9439])).
% 2.14/2.33 tff(9441,plain,
% 2.14/2.33 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1641, 9402, 299, 1291])).
% 2.14/2.33 tff(9442,plain,
% 2.14/2.33 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1656, 9441])).
% 2.14/2.33 tff(9443,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9442, 9440])).
% 2.14/2.33 tff(9444,plain,(r(s(elem!1), s(s(s(s(z))))) | (s(z) = elem!1) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(z))) | (~(s(elem!1) = s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (elem!1 = s(s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(9445,plain,
% 2.14/2.33 (~(s(elem!1) = s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9444, 9362, 299, 1291, 11, 9361, 9357, 9360, 2925, 9359])).
% 2.14/2.33 tff(9446,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1290, 3515])).
% 2.14/2.33 tff(9447,plain,((~(s(s(z)) = elem!1)) | (s(elem!1) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(9448,plain,
% 2.14/2.33 (~(s(s(z)) = elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9447, 9445])).
% 2.14/2.33 tff(9449,plain,
% 2.14/2.33 (b(s(elem!1), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9382, 9362, 9359])).
% 2.14/2.33 tff(9450,plain,
% 2.14/2.33 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[4324, 4103, 1291, 637, 238, 258])).
% 2.14/2.33 tff(9451,plain,
% 2.14/2.33 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[687, 9450])).
% 2.14/2.33 tff(9452,plain,
% 2.14/2.33 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1982, 9451, 11])).
% 2.14/2.33 tff(9453,plain,
% 2.14/2.33 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[328, 9452])).
% 2.14/2.33 tff(9454,plain,
% 2.14/2.33 (~r(s(z), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[276, 9451, 258])).
% 2.14/2.33 tff(9455,plain,
% 2.14/2.33 (b(s(z), s(s(s(z))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[227, 9454])).
% 2.14/2.33 tff(9456,plain,
% 2.14/2.33 (~b(s(z), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[4096, 9455, 1291, 8715])).
% 2.14/2.33 tff(9457,plain,
% 2.14/2.33 (r(s(z), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[506, 9456, 492])).
% 2.14/2.33 tff(9458,plain,
% 2.14/2.33 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[730, 9457, 258])).
% 2.14/2.33 tff(9459,plain,
% 2.14/2.33 (b(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[643, 9458, 637])).
% 2.14/2.33 tff(9460,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(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9461,plain,
% 2.14/2.33 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9462,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(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~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(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9461])).
% 2.14/2.33 tff(9463,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(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~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(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[9462, 9460])).
% 2.14/2.33 tff(9464,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(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(9465,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[9464, 9463])).
% 2.14/2.33 tff(9466,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9465, 453, 8715, 9459, 9453, 299])).
% 2.14/2.33 tff(9467,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (s(z) = elem!1) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(9468,plain,
% 2.14/2.33 (~r(s(s(s(s(s(z))))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9467, 11, 637, 9357, 1291, 299, 9361])).
% 2.14/2.33 tff(9469,plain,
% 2.14/2.33 (b(s(s(s(s(s(z))))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[297, 9468])).
% 2.14/2.33 tff(9470,assumption,(s(s(s(z))) = s(elem!1)), introduced(assumption)).
% 2.14/2.33 tff(9471,plain,
% 2.14/2.33 (s(elem!1) = s(s(s(z)))),
% 2.14/2.33 inference(symmetry,[status(thm)],[9470])).
% 2.14/2.33 tff(9472,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1290, 9471])).
% 2.14/2.33 tff(9473,plain,((~(s(s(s(z))) = s(elem!1))) | (s(elem!1) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(9474,plain,
% 2.14/2.33 (~(s(s(s(z))) = s(elem!1))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9473, 9445])).
% 2.14/2.33 tff(9475,assumption,(~(s(s(s(z))) = s(elem!1))), introduced(assumption)).
% 2.14/2.33 tff(9476,plain,
% 2.14/2.33 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9477,plain,
% 2.14/2.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(9478,plain,
% 2.14/2.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[9477, 9476])).
% 2.14/2.33 tff(9479,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9478, 69, 6845, 7022, 9475])).
% 2.14/2.33 tff(9480,plain,(b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)) | (s(s(s(z))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(9481,plain,
% 2.14/2.33 (r(s(s(s(z))), s(elem!1))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9480, 9474, 6845])).
% 2.14/2.33 tff(9482,plain,
% 2.14/2.33 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 2.14/2.33 inference(symmetry,[status(thm)],[4303])).
% 2.14/2.33 tff(9483,plain,
% 2.14/2.33 (s(s(s(s(z)))) = elem!1),
% 2.14/2.33 inference(transitivity,[status(thm)],[284, 9482, 85])).
% 2.14/2.33 tff(9484,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[3, 9483])).
% 2.14/2.33 tff(9485,plain,((~(s(elem!1) = s(s(s(s(s(z))))))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(9486,plain,
% 2.14/2.33 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9485, 9370])).
% 2.14/2.33 tff(9487,plain,
% 2.14/2.33 (~(elem!1 = s(elem!1))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[8957, 605])).
% 2.14/2.33 tff(9488,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9489,plain,
% 2.14/2.33 (((~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9490,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z)))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9489])).
% 2.14/2.33 tff(9491,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[9490, 9488])).
% 2.14/2.33 tff(9492,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z))))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(9493,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(s(s(z)))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[9492, 9491])).
% 2.14/2.33 tff(9494,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9493, 268, 339, 1149, 7009])).
% 2.14/2.33 tff(9495,plain,((~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(9496,plain,
% 2.14/2.33 (~r(elem!1, s(elem!1))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9495, 1149, 7009])).
% 2.14/2.33 tff(9497,plain,
% 2.14/2.33 (b(elem!1, s(elem!1))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1069, 9496, 9487])).
% 2.14/2.33 tff(9498,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(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9499,plain,
% 2.14/2.33 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9500,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(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9499])).
% 2.14/2.33 tff(9501,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(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[9500, 9498])).
% 2.14/2.33 tff(9502,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(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(9503,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[9502, 9501])).
% 2.14/2.33 tff(9504,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9503, 453, 499, 1071, 1291, 2090])).
% 2.14/2.33 tff(9505,plain,((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(9506,plain,
% 2.14/2.33 (~b(s(z), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9505, 9497, 1291, 8467])).
% 2.14/2.33 tff(9507,plain,
% 2.14/2.33 (r(s(z), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[506, 9506, 492])).
% 2.14/2.33 tff(9508,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(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9509,plain,
% 2.14/2.33 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9510,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(elem!1, s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[9509])).
% 2.14/2.33 tff(9511,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(elem!1, s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.14/2.33 inference(transitivity,[status(thm)],[9510, 9508])).
% 2.14/2.33 tff(9512,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(elem!1, s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(9513,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(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[9512, 9511])).
% 2.14/2.33 tff(9514,plain,
% 2.14/2.33 (~b(s(s(s(z))), s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[9513, 453, 1071, 1291, 922])).
% 2.14/2.33 tff(9515,plain,
% 2.14/2.33 (r(s(s(s(z))), s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[2534, 69, 160, 9514])).
% 2.14/2.33 tff(9516,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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9517,plain,
% 2.14/2.33 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(9518,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(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[9517])).
% 2.14/2.34 tff(9519,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(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.14/2.34 inference(transitivity,[status(thm)],[9518, 9516])).
% 2.14/2.34 tff(9520,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(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(9521,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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[9520, 9519])).
% 2.14/2.34 tff(9522,plain,
% 2.14/2.34 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9521, 453, 1071, 922, 299])).
% 2.14/2.34 tff(9523,plain,
% 2.14/2.34 (r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2370, 69, 2359, 9522])).
% 2.14/2.34 tff(9524,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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9525,plain,
% 2.14/2.34 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9526,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(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[9525])).
% 2.14/2.34 tff(9527,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.14/2.34 inference(transitivity,[status(thm)],[9526, 9524])).
% 2.14/2.34 tff(9528,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(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(9529,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[9528, 9527])).
% 2.14/2.34 tff(9530,plain,
% 2.14/2.34 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9529, 453, 1071, 1291, 299])).
% 2.14/2.34 tff(9531,plain,
% 2.14/2.34 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[1656, 9530])).
% 2.14/2.34 tff(9532,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[6256, 268, 9531, 9523, 9515])).
% 2.14/2.34 tff(9533,plain,((~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(9534,plain,
% 2.14/2.34 (~b(s(s(z)), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9533, 9497, 1291, 299])).
% 2.14/2.34 tff(9535,plain,
% 2.14/2.34 (r(s(s(z)), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[782, 9534, 4060])).
% 2.14/2.34 tff(9536,plain,
% 2.14/2.34 (~r(s(z), s(s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[741, 9535, 9507])).
% 2.14/2.34 tff(9537,plain,
% 2.14/2.34 (b(s(z), s(s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[757, 9536])).
% 2.14/2.34 tff(9538,plain,
% 2.14/2.34 (~(s(z) = s(elem!1))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[4972, 9497, 10])).
% 2.14/2.34 tff(9539,plain,
% 2.14/2.34 (~(s(elem!1) = s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[179, 9538])).
% 2.14/2.34 tff(9540,plain,
% 2.14/2.34 (~r(s(s(z)), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[707, 268, 9507, 9535])).
% 2.14/2.34 tff(9541,plain,
% 2.14/2.34 (b(s(s(z)), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[720, 69, 717, 9540])).
% 2.14/2.34 tff(9542,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(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), 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(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9543,plain,
% 2.14/2.34 (((~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(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9544,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), 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(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z)))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[9543])).
% 2.14/2.34 tff(9545,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), 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(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[9544, 9542])).
% 2.14/2.34 tff(9546,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), 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))))))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(9547,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(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z)))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[9546, 9545])).
% 2.14/2.34 tff(9548,plain,
% 2.14/2.34 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9547, 453, 9537, 374, 9541])).
% 2.14/2.34 tff(9549,plain,
% 2.14/2.34 ((s(s(z)) = s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5711, 69, 9548])).
% 2.14/2.34 tff(9550,plain,
% 2.14/2.34 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9549, 5578])).
% 2.14/2.34 tff(9551,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9552,plain,
% 2.14/2.34 (((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9553,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[9552])).
% 2.14/2.34 tff(9554,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[9553, 9551])).
% 2.14/2.34 tff(9555,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(9556,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[9555, 9554])).
% 2.14/2.34 tff(9557,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9556, 268, 412, 700, 2787])).
% 2.14/2.34 tff(9558,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(9559,plain,
% 2.14/2.34 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9558, 9535, 9550])).
% 2.14/2.34 tff(9560,plain,
% 2.14/2.34 (b(elem!1, s(s(s(s(s(z))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[466, 9559, 2073])).
% 2.14/2.34 tff(9561,plain,
% 2.14/2.34 (~b(s(elem!1), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9411, 9560, 299, 9384])).
% 2.14/2.34 tff(9562,plain,
% 2.14/2.34 (r(s(elem!1), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2440, 9561, 605])).
% 2.14/2.34 tff(9563,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9564,plain,
% 2.14/2.34 (((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9565,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z)))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[9564])).
% 2.14/2.34 tff(9566,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[9565, 9563])).
% 2.14/2.34 tff(9567,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(9568,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z)))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[9567, 9566])).
% 2.14/2.34 tff(9569,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9568, 268, 340, 238, 1892])).
% 2.14/2.34 tff(9570,plain,((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(9571,plain,
% 2.14/2.34 (~r(s(elem!1), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9570, 9562, 238])).
% 2.14/2.34 tff(9572,plain,
% 2.14/2.34 (b(s(elem!1), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[353, 9571, 9539])).
% 2.14/2.34 tff(9573,plain,
% 2.14/2.34 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[4858, 9572, 374, 9537])).
% 2.14/2.34 tff(9574,plain,
% 2.14/2.34 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[659, 9573, 9486])).
% 2.14/2.34 tff(9575,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9576,plain,
% 2.14/2.34 (((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9577,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[9576])).
% 2.14/2.34 tff(9578,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[9577, 9575])).
% 2.14/2.34 tff(9579,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(elem!1))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(9580,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[9579, 9578])).
% 2.14/2.34 tff(9581,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9580, 268, 4621, 3224, 7009])).
% 2.14/2.34 tff(9582,plain,((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(9583,plain,
% 2.14/2.34 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[9582, 9574, 7009])).
% 2.14/2.34 tff(9584,plain,
% 2.14/2.34 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2570, 9583])).
% 2.14/2.34 tff(9585,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), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9586,plain,
% 2.14/2.34 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(9587,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(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[9586])).
% 2.14/2.34 tff(9588,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(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[9587, 9585])).
% 2.14/2.35 tff(9589,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(9590,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[9589, 9588])).
% 2.14/2.35 tff(9591,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9590, 453, 9572, 9497, 1291, 9560, 374, 9584])).
% 2.14/2.35 tff(9592,plain,((~r(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(z))) | (s(elem!1) = elem!1) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(s(z)))))) | (s(s(z)) = elem!1) | (s(z) = elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(9593,plain,
% 2.14/2.35 (~r(elem!1, s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9592, 9481, 9469, 1291, 9361, 605, 299, 9449, 2925, 9448, 9357, 10])).
% 2.14/2.35 tff(9594,plain,
% 2.14/2.35 (b(elem!1, s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[4492, 9593, 9360])).
% 2.14/2.35 tff(9595,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(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9596,plain,
% 2.14/2.35 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9597,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9596])).
% 2.14/2.35 tff(9598,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.14/2.35 inference(transitivity,[status(thm)],[9597, 9595])).
% 2.14/2.35 tff(9599,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(9600,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(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[9599, 9598])).
% 2.14/2.35 tff(9601,plain,
% 2.14/2.35 (~b(s(s(s(z))), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9600, 453, 1291, 922, 1275])).
% 2.14/2.35 tff(9602,plain,
% 2.14/2.35 (r(s(s(s(z))), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2534, 69, 160, 9601])).
% 2.14/2.35 tff(9603,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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9604,plain,
% 2.14/2.35 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9605,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9604])).
% 2.14/2.35 tff(9606,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 2.14/2.35 inference(transitivity,[status(thm)],[9605, 9603])).
% 2.14/2.35 tff(9607,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(9608,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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[9607, 9606])).
% 2.14/2.35 tff(9609,plain,
% 2.14/2.35 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9608, 453, 922, 299, 1275])).
% 2.14/2.35 tff(9610,plain,
% 2.14/2.35 (r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2370, 69, 2359, 9609])).
% 2.14/2.35 tff(9611,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(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9612,plain,
% 2.14/2.35 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9613,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9612])).
% 2.14/2.35 tff(9614,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[9613, 9611])).
% 2.14/2.35 tff(9615,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(9616,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[9615, 9614])).
% 2.14/2.35 tff(9617,plain,
% 2.14/2.35 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9616, 453, 1291, 299, 1275])).
% 2.14/2.35 tff(9618,plain,
% 2.14/2.35 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1656, 9617])).
% 2.14/2.35 tff(9619,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[6256, 268, 9618, 9610, 9602])).
% 2.14/2.35 tff(9620,plain,((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(9621,plain,
% 2.14/2.35 (~b(s(s(z)), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9620, 9594, 1291, 299])).
% 2.14/2.35 tff(9622,plain,
% 2.14/2.35 (r(s(s(z)), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[782, 9621, 9448])).
% 2.14/2.35 tff(9623,plain,
% 2.14/2.35 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9616, 453, 1291, 299, 9594])).
% 2.14/2.35 tff(9624,plain,
% 2.14/2.35 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1656, 9623])).
% 2.14/2.35 tff(9625,plain,
% 2.14/2.35 (b(s(s(s(s(z)))), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[7911, 9624, 9356])).
% 2.14/2.35 tff(9626,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(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9627,plain,
% 2.14/2.35 (((~b(s(z), s(s(z)))) | (~b(s(z), 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(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9628,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(z)))) | (~b(s(z), 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(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9627])).
% 2.14/2.35 tff(9629,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(z)))) | (~b(s(z), 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(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[9628, 9626])).
% 2.14/2.35 tff(9630,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(z)))) | (~b(s(z), 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)))))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(9631,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(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[9630, 9629])).
% 2.14/2.35 tff(9632,plain,
% 2.14/2.35 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9631, 453, 1764, 758, 374])).
% 2.14/2.35 tff(9633,plain,
% 2.14/2.35 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[328, 9632])).
% 2.14/2.35 tff(9634,plain,
% 2.14/2.35 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[1982, 9633, 11])).
% 2.14/2.35 tff(9635,plain,
% 2.14/2.35 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[687, 9634])).
% 2.14/2.35 tff(9636,plain,
% 2.14/2.35 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[777, 700, 701])).
% 2.14/2.35 tff(9637,plain,
% 2.14/2.35 (b(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[643, 9636, 637])).
% 2.14/2.35 tff(9638,plain,
% 2.14/2.35 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(9639,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))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9638])).
% 2.14/2.35 tff(9640,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))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.14/2.35 inference(transitivity,[status(thm)],[9639, 8344])).
% 2.14/2.35 tff(9641,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))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(9642,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[9641, 9640])).
% 2.14/2.35 tff(9643,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9642, 453, 1291, 9637, 9635, 1275])).
% 2.14/2.35 tff(9644,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(9645,plain,
% 2.14/2.35 (~r(s(z), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9644, 9625, 1291, 11, 9594, 9469, 637, 9622])).
% 2.14/2.35 tff(9646,plain,
% 2.14/2.35 (~b(s(z), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5423, 9625, 299, 9594])).
% 2.14/2.35 tff(9647,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[506, 9646, 9645, 9357])).
% 2.14/2.35 tff(9648,plain,(r(s(elem!1), s(s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(s(z))))) = elem!1) | (s(elem!1) = elem!1) | b(elem!1, s(z)) | b(s(s(s(z))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(9649,plain,
% 2.14/2.35 (r(s(elem!1), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9648, 11, 8844, 8837, 637, 9351, 10, 6845])).
% 2.14/2.35 tff(9650,assumption,(r(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 2.14/2.35 tff(9651,plain,
% 2.14/2.35 (~r(s(s(s(s(s(z))))), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9467, 11, 637, 4495, 1291, 299, 238])).
% 2.14/2.35 tff(9652,plain,
% 2.14/2.35 (b(s(s(s(s(s(z))))), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[297, 9651])).
% 2.14/2.35 tff(9653,plain,
% 2.14/2.35 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9470])).
% 2.14/2.35 tff(9654,plain,
% 2.14/2.35 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9653])).
% 2.14/2.35 tff(9655,plain,
% 2.14/2.35 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.35 inference(symmetry,[status(thm)],[9654])).
% 2.14/2.35 tff(9656,plain,
% 2.14/2.35 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.14/2.35 inference(symmetry,[status(thm)],[9653])).
% 2.14/2.35 tff(9657,plain,
% 2.14/2.35 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9656])).
% 2.14/2.35 tff(9658,plain,
% 2.14/2.35 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9657])).
% 2.14/2.35 tff(9659,plain,
% 2.14/2.35 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[9658, 9655])).
% 2.14/2.35 tff(9660,plain,
% 2.14/2.35 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9656, 9657])).
% 2.14/2.35 tff(9661,plain,
% 2.14/2.35 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.14/2.35 inference(symmetry,[status(thm)],[9660])).
% 2.14/2.35 tff(9662,plain,
% 2.14/2.35 (r(s(s(elem!1)), s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9656])).
% 2.14/2.35 tff(9663,plain,
% 2.14/2.35 (r(s(s(elem!1)), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[9662, 9661])).
% 2.14/2.35 tff(9664,plain,
% 2.14/2.35 ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9663])).
% 2.14/2.35 tff(9665,plain,
% 2.14/2.35 (s(elem!1) = s(s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9473, 9470])).
% 2.14/2.35 tff(9666,plain,
% 2.14/2.35 (b(s(elem!1), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[9377, 9665, 1291])).
% 2.14/2.35 tff(9667,plain,
% 2.14/2.35 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9470])).
% 2.14/2.35 tff(9668,plain,
% 2.14/2.35 (b(s(z), s(elem!1))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[2090, 9667])).
% 2.14/2.35 tff(9669,plain,
% 2.14/2.35 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2137, 9668, 9666, 374])).
% 2.14/2.35 tff(9670,plain,
% 2.14/2.35 (r(s(s(s(s(s(z))))), s(elem!1))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[2142, 9669, 4106])).
% 2.14/2.35 tff(9671,plain,
% 2.14/2.35 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9656])).
% 2.14/2.35 tff(9672,plain,
% 2.14/2.35 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.14/2.35 inference(symmetry,[status(thm)],[9671])).
% 2.14/2.35 tff(9673,plain,
% 2.14/2.35 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9470])).
% 2.14/2.35 tff(9674,plain,
% 2.14/2.35 (r(s(s(s(s(z)))), s(elem!1))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[11, 9673])).
% 2.14/2.35 tff(9675,plain,
% 2.14/2.35 (r(s(s(elem!1)), s(elem!1))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[9674, 9672])).
% 2.14/2.35 tff(9676,plain,
% 2.14/2.35 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[3791, 268, 9675, 9670])).
% 2.14/2.35 tff(9677,plain,
% 2.14/2.35 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[9676, 9664])).
% 2.14/2.35 tff(9678,plain,
% 2.14/2.35 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[675, 9677, 617])).
% 2.14/2.35 tff(9679,plain,
% 2.14/2.35 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[9678, 9659])).
% 2.14/2.35 tff(9680,plain,
% 2.14/2.35 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9470])).
% 2.14/2.35 tff(9681,plain,
% 2.14/2.35 (s(s(z)) = elem!1),
% 2.14/2.35 inference(transitivity,[status(thm)],[98, 9680, 85])).
% 2.14/2.35 tff(9682,plain,
% 2.14/2.35 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9470])).
% 2.14/2.35 tff(9683,plain,
% 2.14/2.35 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.35 inference(symmetry,[status(thm)],[9682])).
% 2.14/2.35 tff(9684,plain,
% 2.14/2.35 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[9650, 9683])).
% 2.14/2.35 tff(9685,plain,
% 2.14/2.35 (b(s(s(s(s(z)))), s(z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[7911, 9684, 1123])).
% 2.14/2.35 tff(9686,plain,
% 2.14/2.35 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[3942, 9685, 2090, 9681, 9666, 374])).
% 2.14/2.35 tff(9687,plain,
% 2.14/2.35 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[328, 9686])).
% 2.14/2.35 tff(9688,plain,
% 2.14/2.35 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[9470])).
% 2.14/2.35 tff(9689,plain,
% 2.14/2.35 (r(elem!1, s(elem!1))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[1149, 9688])).
% 2.14/2.35 tff(9690,plain,
% 2.14/2.35 (~r(elem!1, s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[4946, 9674, 9689])).
% 2.14/2.35 tff(9691,plain,
% 2.14/2.35 (~r(s(s(s(s(z)))), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[8475, 1149, 11])).
% 2.14/2.35 tff(9692,plain,
% 2.14/2.35 (~(s(s(s(s(z)))) = elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[4108, 4106])).
% 2.14/2.35 tff(9693,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9694,plain,
% 2.14/2.36 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9695,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9694])).
% 2.14/2.36 tff(9696,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[9695, 9693])).
% 2.14/2.36 tff(9697,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(9698,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[9697, 9696])).
% 2.14/2.36 tff(9699,plain,
% 2.14/2.36 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9698, 268, 9689, 9670])).
% 2.14/2.36 tff(9700,plain,
% 2.14/2.36 (b(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[643, 9699, 637])).
% 2.14/2.36 tff(9701,plain,
% 2.14/2.36 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[6664, 9700, 9692, 9691, 9690, 9687])).
% 2.14/2.36 tff(9702,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9701, 9679])).
% 2.14/2.36 tff(9703,plain,((~(s(s(s(z))) = s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(s(s(z))))) = elem!1) | (s(s(s(s(s(z))))) = s(elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (elem!1 = s(z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(9704,plain,
% 2.14/2.36 (~(s(s(s(z))) = s(elem!1))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9703, 8467, 637, 9369, 617, 9652, 1123, 1149, 9650, 11, 1291])).
% 2.14/2.36 tff(9705,plain,
% 2.14/2.36 (r(s(s(s(z))), s(elem!1))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9480, 9704, 6845])).
% 2.14/2.36 tff(9706,plain,
% 2.14/2.36 (~r(elem!1, s(elem!1))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9495, 9705, 1149])).
% 2.14/2.36 tff(9707,plain,
% 2.14/2.36 (b(elem!1, s(elem!1))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1069, 9706, 1056])).
% 2.14/2.36 tff(9708,plain,
% 2.14/2.36 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9529, 453, 9707, 1291, 299])).
% 2.14/2.36 tff(9709,plain,
% 2.14/2.36 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1656, 9708])).
% 2.14/2.36 tff(9710,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9711,plain,
% 2.14/2.36 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9712,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9711])).
% 2.14/2.36 tff(9713,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[9712, 9710])).
% 2.14/2.36 tff(9714,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(9715,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[9714, 9713])).
% 2.14/2.36 tff(9716,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9715, 268, 9709, 9650, 9705])).
% 2.14/2.36 tff(9717,plain,((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (elem!1 = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = s(z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(9718,plain,
% 2.14/2.36 (~r(elem!1, s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9717, 9649, 8844, 8837, 9353, 6845, 637, 9352, 9332, 11, 9333])).
% 2.14/2.36 tff(9719,plain,
% 2.14/2.36 (b(elem!1, s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[4492, 9718, 9334])).
% 2.14/2.36 tff(9720,plain,
% 2.14/2.36 (~b(s(s(z)), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9620, 9719, 8844, 8837])).
% 2.14/2.36 tff(9721,plain,
% 2.14/2.36 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9616, 453, 8844, 8837, 9719])).
% 2.14/2.36 tff(9722,plain,
% 2.14/2.36 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1656, 9721])).
% 2.14/2.36 tff(9723,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[7911, 9722, 9332])).
% 2.14/2.36 tff(9724,plain,
% 2.14/2.36 (~r(s(s(s(s(s(z))))), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9467, 11, 637, 9335, 8844, 8837, 9333])).
% 2.14/2.36 tff(9725,plain,
% 2.14/2.36 (b(s(s(s(s(s(z))))), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[297, 9724])).
% 2.14/2.36 tff(9726,plain,
% 2.14/2.36 (~b(s(z), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5423, 9723, 8837, 9719])).
% 2.14/2.36 tff(9727,plain,
% 2.14/2.36 (r(s(z), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[506, 9726, 9335])).
% 2.14/2.36 tff(9728,plain,
% 2.14/2.36 (~r(s(s(z)), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9644, 9727, 8844, 11, 9719, 9725, 637, 9723])).
% 2.14/2.36 tff(9729,plain,
% 2.14/2.36 (s(s(z)) = elem!1),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[782, 9728, 9720])).
% 2.14/2.36 tff(9730,plain,
% 2.14/2.36 (s(s(s(z))) = s(elem!1)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9729])).
% 2.14/2.36 tff(9731,plain,
% 2.14/2.36 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9730])).
% 2.14/2.36 tff(9732,plain,
% 2.14/2.36 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.14/2.36 inference(symmetry,[status(thm)],[9731])).
% 2.14/2.36 tff(9733,plain,
% 2.14/2.36 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9732])).
% 2.14/2.36 tff(9734,plain,
% 2.14/2.36 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 2.14/2.36 inference(symmetry,[status(thm)],[9733])).
% 2.14/2.36 tff(9735,plain,
% 2.14/2.36 (~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[3814, 9729])).
% 2.14/2.36 tff(9736,plain,
% 2.14/2.36 (~(s(s(s(s(s(s(s(s(z)))))))) = elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5602, 9729])).
% 2.14/2.36 tff(9737,plain,
% 2.14/2.36 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9731])).
% 2.14/2.36 tff(9738,plain,
% 2.14/2.36 (r(s(elem!1), s(s(elem!1)))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[9649, 9737])).
% 2.14/2.36 tff(9739,plain,
% 2.14/2.36 (s(elem!1) = s(s(s(z)))),
% 2.14/2.36 inference(symmetry,[status(thm)],[9730])).
% 2.14/2.36 tff(9740,plain,
% 2.14/2.36 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(z))), s(elem!1))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9739, 9730])).
% 2.14/2.36 tff(9741,plain,
% 2.14/2.36 (b(s(s(s(z))), s(elem!1)) <=> b(s(elem!1), s(s(s(z))))),
% 2.14/2.36 inference(symmetry,[status(thm)],[9740])).
% 2.14/2.36 tff(9742,plain,
% 2.14/2.36 ((~b(s(s(s(z))), s(elem!1))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9741])).
% 2.14/2.36 tff(9743,plain,
% 2.14/2.36 (~b(s(elem!1), s(s(s(z))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[6845, 9742])).
% 2.14/2.36 tff(9744,plain,
% 2.14/2.36 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9739])).
% 2.14/2.36 tff(9745,plain,
% 2.14/2.36 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 2.14/2.36 inference(symmetry,[status(thm)],[9744])).
% 2.14/2.36 tff(9746,plain,
% 2.14/2.36 (b(elem!1, s(elem!1))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[9719, 9745])).
% 2.14/2.36 tff(9747,plain,
% 2.14/2.36 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9732])).
% 2.14/2.36 tff(9748,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.14/2.36 inference(symmetry,[status(thm)],[9747])).
% 2.14/2.36 tff(9749,plain,
% 2.14/2.36 (b(s(s(elem!1)), elem!1)),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[8837, 9748])).
% 2.14/2.36 tff(9750,plain,
% 2.14/2.36 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[4210, 555, 1071, 59, 909, 2])).
% 2.14/2.36 tff(9751,plain,
% 2.14/2.36 (s(s(s(s(s(z))))) = elem!1),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[643, 9750, 636])).
% 2.14/2.36 tff(9752,plain,
% 2.14/2.36 (elem!1 = s(s(s(s(s(z)))))),
% 2.14/2.36 inference(symmetry,[status(thm)],[9751])).
% 2.14/2.36 tff(9753,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(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9754,plain,
% 2.14/2.36 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9755,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9754])).
% 2.14/2.36 tff(9756,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.14/2.36 inference(transitivity,[status(thm)],[9755, 9753])).
% 2.14/2.36 tff(9757,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(9758,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(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[9757, 9756])).
% 2.14/2.36 tff(9759,plain,
% 2.14/2.36 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9758, 453, 1071, 909, 4165])).
% 2.14/2.36 tff(9760,plain,
% 2.14/2.36 (r(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5203, 555, 9759])).
% 2.14/2.36 tff(9761,plain,
% 2.14/2.36 (~r(s(elem!1), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[7128, 268, 431, 9760])).
% 2.14/2.36 tff(9762,plain,
% 2.14/2.36 ((s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1303, 69, 1300])).
% 2.14/2.36 tff(9763,plain,
% 2.14/2.36 (s(elem!1) = s(s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9762, 9761])).
% 2.14/2.36 tff(9764,plain,
% 2.14/2.36 (s(s(s(z))) = s(elem!1)),
% 2.14/2.36 inference(symmetry,[status(thm)],[9763])).
% 2.14/2.36 tff(9765,plain,
% 2.14/2.36 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9764])).
% 2.14/2.36 tff(9766,plain,
% 2.14/2.36 (s(s(z)) = s(s(s(s(s(z)))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[98, 9765, 85, 9752])).
% 2.14/2.36 tff(9767,plain,
% 2.14/2.36 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9766])).
% 2.14/2.36 tff(9768,plain,
% 2.14/2.36 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(z)))),
% 2.14/2.36 inference(symmetry,[status(thm)],[9767])).
% 2.14/2.36 tff(9769,plain,
% 2.14/2.36 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9764])).
% 2.14/2.36 tff(9770,plain,
% 2.14/2.36 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.14/2.36 inference(symmetry,[status(thm)],[9769])).
% 2.14/2.36 tff(9771,plain,
% 2.14/2.36 (s(s(elem!1)) = s(z)),
% 2.14/2.36 inference(transitivity,[status(thm)],[9770, 284, 9768, 28])).
% 2.14/2.36 tff(9772,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[816, 9771])).
% 2.14/2.36 tff(9773,plain,((s(s(s(z))) = s(s(elem!1))) | b(s(elem!1), s(s(s(z)))) | (~r(s(elem!1), s(s(elem!1)))) | r(s(s(s(s(s(z))))), elem!1) | (~b(elem!1, s(elem!1))) | (s(s(s(z))) = elem!1) | (~b(s(s(elem!1)), elem!1)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(9774,plain,
% 2.14/2.36 (r(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9773, 9749, 2, 8843, 9336, 9746, 9743, 9738])).
% 2.14/2.36 tff(9775,plain,
% 2.14/2.36 (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[6110, 9774, 9727])).
% 2.14/2.36 tff(9776,plain,
% 2.14/2.36 (b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5649, 9775, 9736])).
% 2.14/2.36 tff(9777,plain,
% 2.14/2.36 (s(elem!1) = s(s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9447, 9729])).
% 2.14/2.36 tff(9778,plain,
% 2.14/2.36 (b(s(elem!1), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9377, 9777, 8844])).
% 2.14/2.36 tff(9779,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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9780,plain,
% 2.14/2.36 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9781,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9780])).
% 2.14/2.36 tff(9782,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[9781, 9779])).
% 2.14/2.36 tff(9783,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(9784,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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z))))))))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[9783, 9782])).
% 2.14/2.36 tff(9785,plain,
% 2.14/2.36 (~b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9784, 453, 9778, 9746, 9776])).
% 2.14/2.36 tff(9786,plain,
% 2.14/2.36 (r(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2919, 9785, 9735])).
% 2.14/2.36 tff(9787,assumption,(r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))), introduced(assumption)).
% 2.14/2.36 tff(9788,assumption,(r(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 2.14/2.36 tff(9789,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9790,plain,
% 2.14/2.36 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9791,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9790])).
% 2.14/2.36 tff(9792,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[9791, 9789])).
% 2.14/2.36 tff(9793,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(9794,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[9793, 9792])).
% 2.14/2.36 tff(9795,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9794, 268, 9650, 9788, 9787])).
% 2.14/2.36 tff(9796,plain,((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(s(z))))))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(9797,plain,
% 2.14/2.36 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9796, 9786, 9649])).
% 2.14/2.36 tff(9798,plain,
% 2.14/2.36 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2863, 9797])).
% 2.14/2.36 tff(9799,plain,
% 2.14/2.36 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[9798, 9734])).
% 2.14/2.36 tff(9800,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(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9801,plain,
% 2.14/2.36 (((~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(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(9802,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[9801])).
% 2.14/2.36 tff(9803,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[9802, 9800])).
% 2.14/2.36 tff(9804,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(9805,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[9804, 9803])).
% 2.14/2.36 tff(9806,plain,
% 2.14/2.36 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9805, 453, 9746, 9749, 9776])).
% 2.14/2.36 tff(9807,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[9806, 9799])).
% 2.14/2.36 tff(9808,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | r(s(s(s(z))), elem!1) | b(s(s(s(z))), s(elem!1)) | (s(s(s(s(s(z))))) = elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9809,plain,
% 2.14/2.37 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9808, 6845, 2, 637, 10])).
% 2.14/2.37 tff(9810,plain,
% 2.14/2.37 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[518, 9809])).
% 2.14/2.37 tff(9811,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9812,plain,
% 2.14/2.37 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9813,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(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9812])).
% 2.14/2.37 tff(9814,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(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9813, 9811])).
% 2.14/2.37 tff(9815,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(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(9816,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9815, 9814])).
% 2.14/2.37 tff(9817,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9816, 453, 523, 1291, 923, 299])).
% 2.14/2.37 tff(9818,plain,((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9819,plain,
% 2.14/2.37 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9818, 9810, 8844, 8837])).
% 2.14/2.37 tff(9820,plain,
% 2.14/2.37 (r(elem!1, s(s(s(s(s(z))))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[466, 9819, 2925])).
% 2.14/2.37 tff(9821,plain,
% 2.14/2.37 (~r(s(s(s(s(s(z))))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[3465, 9820, 9333])).
% 2.14/2.37 tff(9822,plain,
% 2.14/2.37 (b(s(s(s(s(s(z))))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[297, 9821])).
% 2.14/2.37 tff(9823,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(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9824,plain,
% 2.14/2.37 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9825,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(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9824])).
% 2.14/2.37 tff(9826,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(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9825, 9823])).
% 2.14/2.37 tff(9827,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(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(9828,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9827, 9826])).
% 2.14/2.37 tff(9829,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9828, 453, 1071, 523, 1291, 299])).
% 2.14/2.37 tff(9830,plain,((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9831,plain,
% 2.14/2.37 (~b(elem!1, s(elem!1))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9830, 9810, 8844, 8837])).
% 2.14/2.37 tff(9832,plain,
% 2.14/2.37 (r(elem!1, s(elem!1))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1069, 9831, 9353])).
% 2.14/2.37 tff(9833,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[7279, 453, 523, 1291, 299, 1275])).
% 2.14/2.37 tff(9834,plain,((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9835,plain,
% 2.14/2.37 (~b(elem!1, s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9834, 9810, 8844, 8837])).
% 2.14/2.37 tff(9836,plain,
% 2.14/2.37 (r(elem!1, s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[4492, 9835, 9334])).
% 2.14/2.37 tff(9837,plain,
% 2.14/2.37 (~r(s(s(s(z))), s(elem!1))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9495, 9836, 9832])).
% 2.14/2.37 tff(9838,plain,
% 2.14/2.37 (s(s(s(z))) = s(elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9480, 9837, 6845])).
% 2.14/2.37 tff(9839,plain,
% 2.14/2.37 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9838])).
% 2.14/2.37 tff(9840,plain,
% 2.14/2.37 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9415, 9836, 9820])).
% 2.14/2.37 tff(9841,plain,
% 2.14/2.37 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2570, 9840])).
% 2.14/2.37 tff(9842,plain,
% 2.14/2.37 (b(s(elem!1), s(s(s(s(s(z))))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9841, 9839])).
% 2.14/2.37 tff(9843,plain,
% 2.14/2.37 (~r(s(z), s(elem!1))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1496, 9832, 9333])).
% 2.14/2.37 tff(9844,plain,
% 2.14/2.37 (s(elem!1) = s(s(s(z)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9473, 9838])).
% 2.14/2.37 tff(9845,plain,
% 2.14/2.37 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9372])).
% 2.14/2.37 tff(9846,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5806, 9845])).
% 2.14/2.37 tff(9847,plain,((~(s(elem!1) = s(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9848,plain,
% 2.14/2.37 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9847, 9844])).
% 2.14/2.37 tff(9849,assumption,(s(s(elem!1)) = s(s(s(s(z))))), introduced(assumption)).
% 2.14/2.37 tff(9850,plain,
% 2.14/2.37 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.14/2.37 inference(symmetry,[status(thm)],[9849])).
% 2.14/2.37 tff(9851,plain,
% 2.14/2.37 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9850])).
% 2.14/2.37 tff(9852,plain,
% 2.14/2.37 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 2.14/2.37 inference(symmetry,[status(thm)],[9851])).
% 2.14/2.37 tff(9853,plain,
% 2.14/2.37 (s(z) = s(s(s(z)))),
% 2.14/2.37 inference(transitivity,[status(thm)],[163, 195, 9852, 37])).
% 2.14/2.37 tff(9854,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[109, 9853])).
% 2.14/2.37 tff(9855,plain,((~(s(s(elem!1)) = s(s(s(s(z)))))) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9856,plain,
% 2.14/2.37 (~(s(z) = s(elem!1))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9855, 9848])).
% 2.14/2.37 tff(9857,plain,
% 2.14/2.37 (b(s(z), s(elem!1))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[397, 9856, 9843])).
% 2.14/2.37 tff(9858,plain,
% 2.14/2.37 (~r(s(elem!1), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[348, 9832, 9333])).
% 2.14/2.37 tff(9859,plain,
% 2.14/2.37 (~(s(elem!1) = s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[179, 9856])).
% 2.14/2.37 tff(9860,plain,
% 2.14/2.37 (b(s(elem!1), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[353, 9859, 9858])).
% 2.14/2.37 tff(9861,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(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9862,plain,
% 2.14/2.37 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9863,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(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9862])).
% 2.14/2.37 tff(9864,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(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9863, 9861])).
% 2.14/2.37 tff(9865,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(9866,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9865, 9864])).
% 2.14/2.37 tff(9867,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9866, 453, 9860, 9857, 9842, 9822])).
% 2.14/2.37 tff(9868,plain,(b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), elem!1) | (s(s(s(s(s(z))))) = elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9869,plain,
% 2.14/2.37 (b(s(s(s(z))), s(elem!1))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9868, 637, 10, 2])).
% 2.14/2.37 tff(9870,plain,
% 2.14/2.37 (b(s(z), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[506, 4495, 4541])).
% 2.14/2.37 tff(9871,plain,
% 2.14/2.37 (r(s(s(s(z))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[8835, 58, 10])).
% 2.14/2.37 tff(9872,plain,
% 2.14/2.37 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[4119, 135, 1132])).
% 2.14/2.37 tff(9873,plain,
% 2.14/2.37 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[518, 9872])).
% 2.14/2.37 tff(9874,plain,
% 2.14/2.37 (b(s(s(s(s(z)))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[4123, 9873, 76])).
% 2.14/2.37 tff(9875,plain,
% 2.14/2.37 (elem!1 = s(s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2267, 9874, 76, 10])).
% 2.14/2.37 tff(9876,plain,
% 2.14/2.37 (s(s(s(s(s(z))))) = elem!1),
% 2.14/2.37 inference(symmetry,[status(thm)],[9875])).
% 2.14/2.37 tff(9877,plain,
% 2.14/2.37 (s(s(s(s(s(z))))) = s(s(s(z)))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9876, 86, 2075, 37])).
% 2.14/2.37 tff(9878,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[111, 9877])).
% 2.14/2.37 tff(9879,plain,((~(s(s(s(z))) = elem!1)) | b(elem!1, s(z)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9880,plain,
% 2.14/2.37 (~(s(s(s(z))) = elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9879, 1099, 10])).
% 2.14/2.37 tff(9881,plain,
% 2.14/2.37 (~(elem!1 = s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[4487, 9880])).
% 2.14/2.37 tff(9882,plain,
% 2.14/2.37 (b(elem!1, s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[4492, 9881, 1200])).
% 2.14/2.37 tff(9883,plain,
% 2.14/2.37 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[4538, 3448, 1099])).
% 2.14/2.37 tff(9884,plain,
% 2.14/2.37 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1656, 9883])).
% 2.14/2.37 tff(9885,plain,
% 2.14/2.37 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[4119, 3448, 1099])).
% 2.14/2.37 tff(9886,plain,
% 2.14/2.37 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[518, 9885])).
% 2.14/2.37 tff(9887,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9888,plain,
% 2.14/2.37 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9889,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(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9888])).
% 2.14/2.37 tff(9890,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(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9889, 9887])).
% 2.14/2.37 tff(9891,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(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(9892,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9891, 9890])).
% 2.14/2.37 tff(9893,plain,
% 2.14/2.37 (~b(s(s(s(s(z)))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9892, 453, 9886, 9884, 1275])).
% 2.14/2.37 tff(9894,plain,
% 2.14/2.37 (r(s(s(s(s(z)))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[254, 9893, 3])).
% 2.14/2.37 tff(9895,plain,
% 2.14/2.37 (r(s(s(s(z))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[74, 58, 9880])).
% 2.14/2.37 tff(9896,plain,
% 2.14/2.37 (~r(elem!1, s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1586, 9895, 233])).
% 2.14/2.37 tff(9897,plain,
% 2.14/2.37 (elem!1 = s(z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1130, 9896, 10])).
% 2.14/2.37 tff(9898,plain,
% 2.14/2.37 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9897])).
% 2.14/2.37 tff(9899,plain,
% 2.14/2.37 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 2.14/2.37 inference(symmetry,[status(thm)],[9898])).
% 2.14/2.37 tff(9900,plain,
% 2.14/2.37 (s(elem!1) = s(s(z))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9897])).
% 2.14/2.37 tff(9901,plain,
% 2.14/2.37 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9900])).
% 2.14/2.37 tff(9902,plain,
% 2.14/2.37 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9897])).
% 2.14/2.37 tff(9903,plain,
% 2.14/2.37 (r(s(elem!1), elem!1) <=> r(s(s(z)), elem!1)),
% 2.14/2.37 inference(transitivity,[status(thm)],[9902, 9901, 9899])).
% 2.14/2.37 tff(9904,plain,
% 2.14/2.37 (~(s(elem!1) = s(s(elem!1)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2287, 9897])).
% 2.14/2.37 tff(9905,plain,
% 2.14/2.37 (~(s(elem!1) = elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[8905, 9904])).
% 2.14/2.37 tff(9906,plain,
% 2.14/2.37 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9897])).
% 2.14/2.37 tff(9907,plain,
% 2.14/2.37 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.37 inference(symmetry,[status(thm)],[9906])).
% 2.14/2.37 tff(9908,plain,
% 2.14/2.37 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1566, 722, 1545])).
% 2.14/2.37 tff(9909,plain,
% 2.14/2.37 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[687, 9908])).
% 2.14/2.37 tff(9910,plain,
% 2.14/2.37 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[1100])).
% 2.14/2.37 tff(9911,plain,
% 2.14/2.37 (r(s(s(s(s(z)))), s(z))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[1159, 9910])).
% 2.14/2.37 tff(9912,plain,
% 2.14/2.37 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1663, 268, 233, 9911])).
% 2.14/2.37 tff(9913,plain,
% 2.14/2.37 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1656, 9912])).
% 2.14/2.37 tff(9914,plain,
% 2.14/2.37 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5352, 9911, 1159, 722])).
% 2.14/2.37 tff(9915,plain,
% 2.14/2.37 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[328, 9914])).
% 2.14/2.37 tff(9916,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[1788, 9915, 9913, 5340, 9909])).
% 2.14/2.37 tff(9917,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~(elem!1 = s(z))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9918,plain,
% 2.14/2.37 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9917, 9897, 233, 1159, 9895])).
% 2.14/2.37 tff(9919,plain,
% 2.14/2.37 (r(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[258, 2927])).
% 2.14/2.37 tff(9920,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[636, 9919])).
% 2.14/2.37 tff(9921,plain,((~(elem!1 = s(z))) | r(s(s(s(s(s(z))))), elem!1) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(9922,plain,
% 2.14/2.37 (~r(s(s(s(s(s(z))))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9921, 9918, 9897])).
% 2.14/2.37 tff(9923,plain,
% 2.14/2.37 (b(s(s(s(s(s(z))))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[297, 9922])).
% 2.14/2.37 tff(9924,plain,
% 2.14/2.37 (b(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9923, 9907])).
% 2.14/2.37 tff(9925,plain,
% 2.14/2.37 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[4119, 233, 1099])).
% 2.14/2.37 tff(9926,plain,
% 2.14/2.37 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[518, 9925])).
% 2.14/2.37 tff(9927,plain,
% 2.14/2.37 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2551, 9897])).
% 2.14/2.37 tff(9928,plain,
% 2.14/2.37 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2821, 9897, 9927])).
% 2.14/2.37 tff(9929,assumption,(r(s(s(s(s(s(s(s(s(z)))))))), s(z))), introduced(assumption)).
% 2.14/2.37 tff(9930,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9931,plain,
% 2.14/2.37 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(9932,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[9931])).
% 2.14/2.37 tff(9933,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[9932, 9930])).
% 2.14/2.37 tff(9934,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(9935,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[9934, 9933])).
% 2.14/2.37 tff(9936,plain,
% 2.14/2.37 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9935, 268, 233])).
% 2.14/2.37 tff(9937,plain,
% 2.14/2.37 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[9936, 9929])).
% 2.14/2.37 tff(9938,plain,
% 2.14/2.37 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2846, 9937, 2835])).
% 2.14/2.37 tff(9939,assumption,(~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(z)))))), introduced(assumption)).
% 2.14/2.37 tff(9940,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9941,plain,
% 2.14/2.38 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9942,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9941])).
% 2.14/2.38 tff(9943,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[9942, 9940])).
% 2.14/2.38 tff(9944,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(9945,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[9944, 9943])).
% 2.14/2.38 tff(9946,plain,
% 2.14/2.38 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9945, 268, 1132])).
% 2.14/2.38 tff(9947,plain,
% 2.14/2.38 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9946, 9929])).
% 2.14/2.38 tff(9948,plain,
% 2.14/2.38 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2862, 9947, 9939])).
% 2.14/2.38 tff(9949,plain,
% 2.14/2.38 ((~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[5660])).
% 2.14/2.38 tff(9950,plain,
% 2.14/2.38 (~(s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[2835, 9949])).
% 2.14/2.38 tff(9951,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9952,plain,
% 2.14/2.38 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9953,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9952])).
% 2.14/2.38 tff(9954,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[9953, 9951])).
% 2.14/2.38 tff(9955,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(9956,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[9955, 9954])).
% 2.14/2.38 tff(9957,plain,
% 2.14/2.38 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9956, 268, 233])).
% 2.14/2.38 tff(9958,plain,
% 2.14/2.38 (~r(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9957, 9929])).
% 2.14/2.38 tff(9959,plain,
% 2.14/2.38 (b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[6485, 9958, 9950])).
% 2.14/2.38 tff(9960,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(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9961,plain,
% 2.14/2.38 (((~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(9962,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(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(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(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9961])).
% 2.14/2.38 tff(9963,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(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(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(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[9962, 9960])).
% 2.14/2.38 tff(9964,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(9965,plain,
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% 2.14/2.38 inference(modus_ponens,[status(thm)],[9964, 9963])).
% 2.14/2.38 tff(9966,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9965, 453, 523, 9959, 9948, 9938])).
% 2.14/2.38 tff(9967,plain,((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(z))))) | (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(9968,plain,
% 2.14/2.38 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9967, 2727])).
% 2.14/2.38 tff(9969,plain,
% 2.14/2.38 (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9968, 9928, 1099, 233, 9926])).
% 2.14/2.38 tff(9970,plain,
% 2.14/2.38 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4538, 233, 1099])).
% 2.14/2.38 tff(9971,plain,
% 2.14/2.38 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1656, 9970])).
% 2.14/2.38 tff(9972,plain,
% 2.14/2.38 (s(z) = elem!1),
% 2.14/2.38 inference(symmetry,[status(thm)],[9897])).
% 2.14/2.38 tff(9973,plain,
% 2.14/2.38 (b(s(s(s(s(s(s(s(s(z)))))))), s(z)) <=> b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9972])).
% 2.14/2.38 tff(9974,plain,
% 2.14/2.38 (b(s(s(s(s(s(s(s(s(z)))))))), elem!1) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.14/2.38 inference(symmetry,[status(thm)],[9973])).
% 2.14/2.38 tff(9975,plain,
% 2.14/2.38 (s(s(s(s(s(s(s(s(z)))))))) = s(z)),
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% 2.14/2.38 tff(9976,plain,
% 2.14/2.38 (inj_0(s(s(s(s(s(s(s(s(z))))))))) = inj_0(s(z))),
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% 2.14/2.38 tff(9977,plain,
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% 2.14/2.38 tff(9978,plain,
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% 2.14/2.38 inference(unit_resolution,[status(thm)],[2882, 9977])).
% 2.14/2.38 tff(9979,plain,((~(s(s(s(s(s(s(s(s(z)))))))) = elem!1)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(9980,plain,
% 2.14/2.38 (~(s(s(s(s(s(s(s(s(z)))))))) = elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9979, 9897])).
% 2.14/2.38 tff(9981,plain,
% 2.14/2.38 (r(s(s(s(s(s(s(s(s(z)))))))), elem!1) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9897])).
% 2.14/2.38 tff(9982,plain,
% 2.14/2.38 (r(s(s(s(s(s(s(s(s(z)))))))), s(z)) <=> r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.14/2.38 inference(symmetry,[status(thm)],[9981])).
% 2.14/2.38 tff(9983,plain,
% 2.14/2.38 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) <=> (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9982])).
% 2.14/2.38 tff(9984,plain,
% 2.14/2.38 (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[9969, 9983])).
% 2.14/2.38 tff(9985,plain,
% 2.14/2.38 (b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5649, 9984, 9980])).
% 2.14/2.38 tff(9986,plain,
% 2.14/2.38 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[9985, 9974])).
% 2.14/2.38 tff(9987,plain,
% 2.14/2.38 (~b(s(s(s(z))), s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5444, 221, 58, 3])).
% 2.14/2.38 tff(9988,plain,
% 2.14/2.38 (b(elem!1, s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2070, 76, 221, 3, 3448])).
% 2.14/2.38 tff(9989,plain,
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% 2.14/2.38 inference(unit_resolution,[status(thm)],[2080, 9988, 76, 128])).
% 2.14/2.38 tff(9990,plain,((~(s(s(s(z))) = elem!1)) | b(s(s(s(z))), s(z)) | b(s(z), s(s(s(z)))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(9991,plain,
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% 2.14/2.38 tff(9992,plain,
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% 2.14/2.38 tff(9993,plain,
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% 2.14/2.38 inference(unit_resolution,[status(thm)],[1586, 1545, 233])).
% 2.14/2.38 tff(9994,plain,
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% 2.14/2.38 inference(unit_resolution,[status(thm)],[1130, 9993, 10])).
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% 2.14/2.38 (s(elem!1) = s(s(z))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9994])).
% 2.14/2.38 tff(9996,plain,
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% 2.14/2.38 (r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9996])).
% 2.14/2.38 tff(9998,plain,
% 2.14/2.38 (r(s(elem!1), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 2.14/2.38 inference(symmetry,[status(thm)],[9997])).
% 2.14/2.38 tff(9999,plain,
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% 2.14/2.38 inference(unit_resolution,[status(thm)],[2343, 9994])).
% 2.14/2.38 tff(10000,plain,
% 2.14/2.38 (b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9996])).
% 2.14/2.38 tff(10001,plain,
% 2.14/2.38 ((~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) <=> (~b(s(elem!1), s(s(s(s(s(s(s(s(z))))))))))),
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% 2.14/2.38 tff(10002,plain,
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% 2.14/2.38 tff(10003,plain,
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% 2.14/2.38 inference(monotonicity,[status(thm)],[10002])).
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% 2.14/2.38 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
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% 2.14/2.38 tff(10005,plain,
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% 2.14/2.38 inference(monotonicity,[status(thm)],[9996, 9994])).
% 2.14/2.38 tff(10006,plain,
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% 2.14/2.38 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9994])).
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% 2.14/2.38 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 2.14/2.38 inference(transitivity,[status(thm)],[10007, 10006])).
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% 2.14/2.38 inference(monotonicity,[status(thm)],[10009])).
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% 2.14/2.38 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[10009, 10010])).
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% 2.14/2.38 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[10009])).
% 2.14/2.38 tff(10013,plain,
% 2.14/2.38 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
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% 2.14/2.38 tff(10014,plain,
% 2.14/2.38 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
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% 2.14/2.38 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
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% 2.14/2.38 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
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% 2.14/2.38 tff(10018,plain,
% 2.14/2.38 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
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% 2.14/2.38 tff(10019,plain,
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% 2.14/2.38 tff(10020,plain,
% 2.14/2.38 (~(s(s(elem!1)) = s(s(s(elem!1))))),
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% 2.14/2.38 tff(10021,plain,
% 2.14/2.38 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(z))),
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% 2.14/2.38 tff(10022,plain,
% 2.14/2.38 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 2.14/2.38 inference(symmetry,[status(thm)],[10021])).
% 2.14/2.38 tff(10023,plain,
% 2.14/2.38 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(z))), s(z))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[10009])).
% 2.14/2.38 tff(10024,plain,
% 2.14/2.38 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.14/2.38 inference(symmetry,[status(thm)],[10023])).
% 2.14/2.38 tff(10025,plain,
% 2.14/2.38 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 2.14/2.38 inference(transitivity,[status(thm)],[10024, 10022])).
% 2.14/2.38 tff(10026,plain,
% 2.14/2.38 (r(s(s(elem!1)), elem!1)),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[233, 10025])).
% 2.14/2.38 tff(10027,plain,
% 2.14/2.38 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[877, 1712, 10026])).
% 2.14/2.38 tff(10028,plain,
% 2.14/2.38 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[675, 10027, 10020])).
% 2.14/2.38 tff(10029,plain,
% 2.14/2.38 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[10028, 10011])).
% 2.14/2.38 tff(10030,plain,
% 2.14/2.38 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[4117, 268, 233, 1099])).
% 2.14/2.38 tff(10031,plain,
% 2.14/2.38 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[518, 10030])).
% 2.14/2.38 tff(10032,plain,
% 2.14/2.38 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[2269])).
% 2.14/2.38 tff(10033,plain,
% 2.14/2.38 ((s(s(s(s(z)))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[10032, 2372])).
% 2.14/2.38 tff(10034,plain,
% 2.14/2.38 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.14/2.38 inference(transitivity,[status(thm)],[10033, 2373])).
% 2.14/2.38 tff(10035,plain,
% 2.14/2.38 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[10034])).
% 2.14/2.38 tff(10036,plain,
% 2.14/2.38 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[153, 10035])).
% 2.14/2.38 tff(10037,plain,
% 2.14/2.38 ((~r(s(s(s(s(z)))), s(s(z)))) <=> (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[2387])).
% 2.14/2.38 tff(10038,plain,
% 2.14/2.38 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[2980, 10037])).
% 2.14/2.38 tff(10039,plain,
% 2.14/2.38 (b(s(s(s(s(z)))), s(elem!1))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2398, 10038, 10036])).
% 2.14/2.38 tff(10040,plain,
% 2.14/2.38 (b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[10039, 2400])).
% 2.14/2.38 tff(10041,plain,
% 2.14/2.38 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[2269])).
% 2.14/2.38 tff(10042,plain,
% 2.14/2.38 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.14/2.38 inference(symmetry,[status(thm)],[10041])).
% 2.14/2.38 tff(10043,plain,
% 2.14/2.38 (~r(s(elem!1), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3055, 3036, 257])).
% 2.14/2.38 tff(10044,plain,
% 2.14/2.38 (b(s(elem!1), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1305, 10043, 3041])).
% 2.14/2.38 tff(10045,plain,
% 2.14/2.38 (b(s(s(z)), s(s(s(z))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[10044, 10042])).
% 2.14/2.38 tff(10046,plain,
% 2.14/2.38 ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[790, 453, 523, 1633])).
% 2.14/2.38 tff(10047,plain,
% 2.14/2.38 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[10046, 10045])).
% 2.14/2.38 tff(10048,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[10047, 10040])).
% 2.14/2.38 tff(10049,plain,(b(s(elem!1), elem!1) | (~(elem!1 = s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(10050,plain,
% 2.14/2.38 (b(s(elem!1), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[10049, 10031, 9994, 10029, 1099, 228])).
% 2.14/2.38 tff(10051,plain,
% 2.14/2.38 (b(s(s(z)), elem!1)),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[10050, 10008])).
% 2.14/2.38 tff(10052,plain,
% 2.14/2.38 (b(s(s(z)), s(z))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[10051, 10004])).
% 2.14/2.38 tff(10053,plain,
% 2.14/2.38 (b(s(s(s(s(s(s(s(s(z)))))))), s(z)) <=> b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.14/2.38 inference(monotonicity,[status(thm)],[10002])).
% 2.14/2.38 tff(10054,plain,
% 2.14/2.38 (b(s(s(s(s(s(s(s(s(z)))))))), elem!1) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.14/2.38 inference(symmetry,[status(thm)],[10053])).
% 2.14/2.38 tff(10055,plain,
% 2.14/2.38 (~(s(s(s(s(s(s(s(s(z)))))))) = elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9979, 9994])).
% 2.14/2.38 tff(10056,plain,
% 2.14/2.38 (r(s(s(s(s(s(s(s(s(z)))))))), elem!1) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9994])).
% 2.14/2.38 tff(10057,plain,
% 2.14/2.38 (r(s(s(s(s(s(s(s(s(z)))))))), s(z)) <=> r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.14/2.38 inference(symmetry,[status(thm)],[10056])).
% 2.14/2.38 tff(10058,plain,
% 2.14/2.38 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) <=> (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[10057])).
% 2.14/2.38 tff(10059,plain,
% 2.14/2.38 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2551, 9994])).
% 2.14/2.38 tff(10060,plain,
% 2.14/2.38 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2821, 10059, 9994])).
% 2.14/2.38 tff(10061,plain,
% 2.14/2.38 (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9968, 10031, 233, 10060, 1099])).
% 2.14/2.38 tff(10062,plain,
% 2.14/2.38 (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[10061, 10058])).
% 2.14/2.38 tff(10063,plain,
% 2.14/2.38 (b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5649, 10062, 10055])).
% 2.14/2.38 tff(10064,plain,
% 2.14/2.38 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[10063, 10054])).
% 2.14/2.38 tff(10065,plain,
% 2.14/2.38 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(z) = s(s(s(s(s(z))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9994])).
% 2.14/2.38 tff(10066,plain,
% 2.14/2.38 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.14/2.38 inference(symmetry,[status(thm)],[10065])).
% 2.14/2.38 tff(10067,plain,
% 2.14/2.38 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.14/2.38 inference(transitivity,[status(thm)],[10066, 56])).
% 2.14/2.38 tff(10068,plain,
% 2.14/2.38 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[10067])).
% 2.14/2.38 tff(10069,plain,
% 2.14/2.38 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[289, 10068])).
% 2.14/2.38 tff(10070,plain,
% 2.14/2.38 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[9994])).
% 2.14/2.38 tff(10071,plain,
% 2.14/2.38 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), elem!1)),
% 2.14/2.38 inference(symmetry,[status(thm)],[10070])).
% 2.14/2.38 tff(10072,plain,
% 2.14/2.38 (r(s(s(s(s(z)))), elem!1)),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[1099, 10071])).
% 2.14/2.38 tff(10073,plain,
% 2.14/2.38 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[9917, 10072, 233, 9994, 1545])).
% 2.14/2.38 tff(10074,plain,
% 2.14/2.38 (b(s(s(s(s(s(z))))), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[643, 10073, 10069])).
% 2.14/2.38 tff(10075,plain,
% 2.14/2.38 (b(s(elem!1), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 2.14/2.38 inference(symmetry,[status(thm)],[2873])).
% 2.14/2.38 tff(10076,plain,
% 2.14/2.38 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2821, 2552, 1100])).
% 2.14/2.38 tff(10077,assumption,(b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))), introduced(assumption)).
% 2.14/2.38 tff(10078,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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10079,plain,
% 2.14/2.39 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10080,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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10079])).
% 2.14/2.39 tff(10081,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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[10080, 10078])).
% 2.14/2.39 tff(10082,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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(10083,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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[10082, 10081])).
% 2.14/2.39 tff(10084,plain,
% 2.14/2.39 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10083, 453, 1633, 1779, 10077])).
% 2.14/2.39 tff(10085,plain,
% 2.14/2.39 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2833, 69, 2688, 10084])).
% 2.14/2.39 tff(10086,plain,
% 2.14/2.39 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10087,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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10086])).
% 2.14/2.39 tff(10088,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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[10087, 2836])).
% 2.14/2.39 tff(10089,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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(10090,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[10089, 10088])).
% 2.14/2.39 tff(10091,plain,
% 2.14/2.39 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10090, 453, 523, 1633, 10077])).
% 2.14/2.39 tff(10092,plain,
% 2.14/2.39 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2863, 10091])).
% 2.14/2.39 tff(10093,plain,
% 2.14/2.39 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[1788, 1779, 523, 1633])).
% 2.14/2.39 tff(10094,plain,
% 2.14/2.39 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[328, 10093])).
% 2.14/2.39 tff(10095,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10096,plain,
% 2.14/2.39 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(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(s(s(s(z)))))))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10097,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(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(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10096])).
% 2.14/2.39 tff(10098,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(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(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[10097, 10095])).
% 2.14/2.39 tff(10099,plain,
% 2.14/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(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(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(10100,plain,
% 2.14/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[10099, 10098])).
% 2.14/2.39 tff(10101,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10100, 268, 10094, 10092, 10085])).
% 2.14/2.39 tff(10102,plain,((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(10103,plain,
% 2.14/2.39 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10102, 1779, 1633, 523])).
% 2.14/2.39 tff(10104,plain,
% 2.14/2.39 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2846, 10103, 10076])).
% 2.14/2.39 tff(10105,plain,
% 2.14/2.39 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[2269])).
% 2.14/2.39 tff(10106,plain,
% 2.14/2.39 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.39 inference(symmetry,[status(thm)],[10105])).
% 2.14/2.39 tff(10107,plain,
% 2.14/2.39 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10033])).
% 2.14/2.39 tff(10108,plain,
% 2.14/2.39 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[153, 10107])).
% 2.14/2.39 tff(10109,plain,
% 2.14/2.39 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[2269])).
% 2.14/2.39 tff(10110,plain,
% 2.14/2.39 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(s(elem!1), s(s(s(s(z))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10109])).
% 2.14/2.39 tff(10111,plain,
% 2.14/2.39 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[2269])).
% 2.14/2.39 tff(10112,plain,
% 2.14/2.39 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.39 inference(symmetry,[status(thm)],[10111])).
% 2.14/2.39 tff(10113,plain,
% 2.14/2.39 (r(s(z), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.14/2.39 inference(symmetry,[status(thm)],[3119])).
% 2.14/2.39 tff(10114,plain,
% 2.14/2.39 ((~r(s(z), s(s(s(s(s(z))))))) <=> (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10113])).
% 2.14/2.39 tff(10115,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10116,plain,
% 2.14/2.39 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10117,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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10116])).
% 2.14/2.39 tff(10118,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[10117, 10115])).
% 2.14/2.39 tff(10119,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(10120,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[10119, 10118])).
% 2.14/2.39 tff(10121,plain,
% 2.14/2.39 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10120, 453, 523, 1633, 1779])).
% 2.14/2.39 tff(10122,plain,
% 2.14/2.39 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2463, 69, 10121])).
% 2.14/2.39 tff(10123,plain,
% 2.14/2.39 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10122, 5338])).
% 2.14/2.39 tff(10124,plain,
% 2.14/2.39 (~r(s(z), s(s(s(s(s(z))))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2254, 10123, 1132])).
% 2.14/2.39 tff(10125,plain,
% 2.14/2.39 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[10124, 10114])).
% 2.14/2.39 tff(10126,plain,
% 2.14/2.39 (b(elem!1, s(s(s(s(s(z))))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[466, 10125, 8879])).
% 2.14/2.39 tff(10127,plain,
% 2.14/2.39 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[3132, 10126, 629, 646])).
% 2.14/2.39 tff(10128,plain,
% 2.14/2.39 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[659, 10127, 2275])).
% 2.14/2.39 tff(10129,plain,
% 2.14/2.39 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[10128, 10112])).
% 2.14/2.39 tff(10130,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10131,plain,
% 2.14/2.39 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10132,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10131])).
% 2.14/2.39 tff(10133,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[10132, 10130])).
% 2.14/2.39 tff(10134,plain,
% 2.14/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(10135,plain,
% 2.14/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[10134, 10133])).
% 2.14/2.39 tff(10136,plain,
% 2.14/2.39 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10135, 268, 1132, 10123, 10129])).
% 2.14/2.39 tff(10137,plain,
% 2.14/2.39 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[10136, 10110])).
% 2.14/2.39 tff(10138,plain,
% 2.14/2.39 (b(s(elem!1), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[9382, 10137, 10108])).
% 2.14/2.39 tff(10139,plain,
% 2.14/2.39 (b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[10138, 10106])).
% 2.14/2.39 tff(10140,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(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(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10141,plain,
% 2.14/2.39 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(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(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10142,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(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(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10141])).
% 2.14/2.39 tff(10143,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(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(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[10142, 10140])).
% 2.14/2.39 tff(10144,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(10145,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(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[10144, 10143])).
% 2.14/2.39 tff(10146,plain,
% 2.14/2.39 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10145, 453, 523, 1633])).
% 2.14/2.39 tff(10147,plain,
% 2.14/2.39 (~b(s(s(z)), s(s(s(z))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[10146, 10139])).
% 2.14/2.39 tff(10148,plain,
% 2.14/2.39 (~b(s(elem!1), s(s(elem!1)))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[10147, 2950])).
% 2.14/2.39 tff(10149,plain,
% 2.14/2.39 (r(s(elem!1), s(s(elem!1)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[440, 10148, 2288])).
% 2.14/2.39 tff(10150,plain,
% 2.14/2.39 (r(s(s(z)), s(s(s(z))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[10149, 2276])).
% 2.14/2.39 tff(10151,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10152,plain,
% 2.14/2.39 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(10153,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[10152])).
% 2.14/2.39 tff(10154,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[10153, 10151])).
% 2.14/2.39 tff(10155,plain,
% 2.14/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(10156,plain,
% 2.24/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[10155, 10154])).
% 2.24/2.40 tff(10157,plain,
% 2.24/2.40 (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10156, 268, 10150, 10104])).
% 2.24/2.40 tff(10158,plain,
% 2.24/2.40 (~r(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[10157, 2346])).
% 2.24/2.40 tff(10159,plain,
% 2.24/2.40 (b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[2919, 10158, 2344])).
% 2.24/2.40 tff(10160,plain,
% 2.24/2.40 (b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[10159, 10075])).
% 2.24/2.40 tff(10161,plain,
% 2.24/2.40 (b(s(s(s(s(s(s(s(s(z)))))))), s(z)) <=> b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.24/2.40 inference(monotonicity,[status(thm)],[2277])).
% 2.24/2.40 tff(10162,plain,
% 2.24/2.40 (b(s(s(s(s(s(s(s(s(z)))))))), elem!1) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.24/2.40 inference(symmetry,[status(thm)],[10161])).
% 2.24/2.40 tff(10163,plain,
% 2.24/2.40 (~(s(s(s(s(s(s(s(s(z)))))))) = elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[9979, 1100])).
% 2.24/2.40 tff(10164,plain,
% 2.24/2.40 (r(s(s(s(s(s(s(s(s(z)))))))), elem!1) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[1100])).
% 2.24/2.40 tff(10165,plain,
% 2.24/2.40 (r(s(s(s(s(s(s(s(s(z)))))))), s(z)) <=> r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.24/2.40 inference(symmetry,[status(thm)],[10164])).
% 2.24/2.40 tff(10166,plain,
% 2.24/2.40 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) <=> (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[10165])).
% 2.24/2.40 tff(10167,assumption,(~r(s(s(s(s(s(s(s(s(z)))))))), s(z))), introduced(assumption)).
% 2.24/2.40 tff(10168,plain,
% 2.24/2.40 (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[10167, 10166])).
% 2.24/2.40 tff(10169,plain,
% 2.24/2.40 (b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[5649, 10168, 10163])).
% 2.24/2.40 tff(10170,plain,
% 2.24/2.40 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[10169, 10162])).
% 2.24/2.40 tff(10171,plain,
% 2.24/2.40 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 2.24/2.40 inference(transitivity,[status(thm)],[3107, 3106])).
% 2.24/2.40 tff(10172,plain,
% 2.24/2.40 (b(s(s(z)), elem!1)),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[629, 10171])).
% 2.24/2.40 tff(10173,plain,
% 2.24/2.40 (b(s(s(z)), s(z))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[10172, 3104])).
% 2.24/2.40 tff(10174,plain,
% 2.24/2.40 (b(s(z), s(s(s(s(s(z))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[372, 10124])).
% 2.24/2.40 tff(10175,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(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(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(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(10176,plain,
% 2.24/2.40 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(10177,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(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(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(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[10176])).
% 2.24/2.40 tff(10178,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(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(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(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[10177, 10175])).
% 2.24/2.40 tff(10179,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(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(10180,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[10179, 10178])).
% 2.24/2.40 tff(10181,plain,
% 2.24/2.40 (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10180, 453, 10174, 10173, 10170])).
% 2.24/2.40 tff(10182,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10181, 10160])).
% 2.24/2.40 tff(10183,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~(elem!1 = s(z))) | r(s(s(s(s(s(s(s(s(z)))))))), s(z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(10184,plain,
% 2.24/2.40 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10183, 10061, 9994, 10029, 10031, 1099, 10050, 10074])).
% 2.24/2.40 tff(10185,plain,
% 2.24/2.40 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[687, 10184])).
% 2.24/2.40 tff(10186,plain,
% 2.24/2.40 (~r(s(z), s(s(s(s(s(z))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[3158, 268, 10185, 228])).
% 2.24/2.40 tff(10187,plain,
% 2.24/2.40 (b(s(z), s(s(s(s(s(z))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[372, 10186])).
% 2.24/2.40 tff(10188,plain,
% 2.24/2.40 ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10180, 453, 10187, 10064])).
% 2.24/2.40 tff(10189,plain,
% 2.24/2.40 (~b(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10188, 10052])).
% 2.24/2.40 tff(10190,plain,
% 2.24/2.40 (~b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[10189, 10001])).
% 2.24/2.40 tff(10191,plain,
% 2.24/2.40 (r(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[2919, 10190, 9999])).
% 2.24/2.40 tff(10192,plain,
% 2.24/2.40 (r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[10191, 9998])).
% 2.24/2.40 tff(10193,plain,
% 2.24/2.40 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[9994])).
% 2.24/2.40 tff(10194,plain,
% 2.24/2.40 ((~r(s(s(s(s(s(z))))), elem!1)) <=> (~r(s(s(s(s(s(z))))), s(z)))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[10193])).
% 2.24/2.40 tff(10195,plain,
% 2.24/2.40 (~r(s(s(s(s(s(z))))), s(z))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[10073, 10194])).
% 2.24/2.40 tff(10196,plain,
% 2.24/2.40 (b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[295, 69, 10195, 291])).
% 2.24/2.40 tff(10197,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(10198,plain,
% 2.24/2.40 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(10199,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[10198])).
% 2.24/2.40 tff(10200,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[10199, 10197])).
% 2.24/2.40 tff(10201,plain,
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% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(10202,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(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[10201, 10200])).
% 2.24/2.40 tff(10203,plain,
% 2.24/2.40 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10202, 453, 10187, 10196, 10064])).
% 2.24/2.40 tff(10204,plain,
% 2.24/2.40 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[2833, 69, 2688, 10203])).
% 2.24/2.40 tff(10205,plain,
% 2.24/2.40 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[9996])).
% 2.24/2.40 tff(10206,plain,
% 2.24/2.40 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.40 inference(symmetry,[status(thm)],[10205])).
% 2.24/2.40 tff(10207,plain,
% 2.24/2.40 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[9996])).
% 2.24/2.40 tff(10208,plain,
% 2.24/2.40 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[10207, 624])).
% 2.24/2.40 tff(10209,plain,
% 2.24/2.40 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(s(s(z)))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[10208])).
% 2.24/2.40 tff(10210,plain,
% 2.24/2.40 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[52, 10209])).
% 2.24/2.40 tff(10211,plain,
% 2.24/2.40 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[10066])).
% 2.24/2.40 tff(10212,plain,
% 2.24/2.40 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[289, 10211])).
% 2.24/2.40 tff(10213,plain,
% 2.24/2.40 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[9994])).
% 2.24/2.40 tff(10214,plain,
% 2.24/2.40 (r(s(z), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.24/2.40 inference(symmetry,[status(thm)],[10213])).
% 2.24/2.40 tff(10215,plain,
% 2.24/2.40 ((~r(s(z), s(s(s(s(s(z))))))) <=> (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[10214])).
% 2.24/2.40 tff(10216,plain,
% 2.24/2.40 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[10186, 10215])).
% 2.24/2.40 tff(10217,plain,
% 2.24/2.40 (b(elem!1, s(s(s(s(s(z))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[466, 10216, 10212])).
% 2.24/2.40 tff(10218,plain,
% 2.24/2.40 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[3132, 10217, 10050, 10074])).
% 2.24/2.40 tff(10219,plain,
% 2.24/2.40 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[659, 10218, 10210])).
% 2.24/2.40 tff(10220,plain,
% 2.24/2.40 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[10219, 10206])).
% 2.24/2.40 tff(10221,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(10222,plain,
% 2.24/2.40 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(10223,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[10222])).
% 2.24/2.40 tff(10224,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[10223, 10221])).
% 2.24/2.40 tff(10225,plain,
% 2.24/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(10226,plain,
% 2.24/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[10225, 10224])).
% 2.24/2.40 tff(10227,plain,
% 2.24/2.40 (~r(s(s(z)), s(s(s(s(s(s(s(s(z)))))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10226, 268, 10220, 10204])).
% 2.24/2.40 tff(10228,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10227, 10192])).
% 2.24/2.40 tff(10229,plain,(b(s(s(s(s(z)))), s(z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | b(s(z), s(s(s(z)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(10230,plain,
% 2.24/2.40 (~r(s(s(s(z))), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10229, 9992, 1057, 10, 221])).
% 2.24/2.40 tff(10231,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[74, 10230, 9991, 58])).
% 2.24/2.40 tff(10232,plain,(b(s(z), s(s(s(z)))) | b(s(s(s(z))), elem!1) | b(s(s(s(s(z)))), s(z)) | b(elem!1, s(z)) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(10233,plain,
% 2.24/2.40 (b(s(z), s(s(s(z))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[10232, 58, 1057, 10, 3])).
% 2.24/2.40 tff(10234,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(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(10235,plain,
% 2.24/2.40 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(10236,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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[10235])).
% 2.24/2.40 tff(10237,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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[10236, 10234])).
% 2.24/2.40 tff(10238,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(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(10239,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(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10238, 10237])).
% 2.24/2.41 tff(10240,plain,
% 2.24/2.41 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10239, 453, 9923, 10233])).
% 2.24/2.41 tff(10241,plain,
% 2.24/2.41 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10240, 9986])).
% 2.24/2.41 tff(10242,plain,
% 2.24/2.41 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2833, 69, 2688, 10241])).
% 2.24/2.41 tff(10243,assumption,(b(s(s(s(s(s(s(s(s(z)))))))), s(z))), introduced(assumption)).
% 2.24/2.41 tff(10244,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(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(10245,plain,
% 2.24/2.41 (((~b(s(s(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(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(10246,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(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(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(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(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10245])).
% 2.24/2.41 tff(10247,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(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(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(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(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[10246, 10244])).
% 2.24/2.41 tff(10248,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(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(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(10249,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10248, 10247])).
% 2.24/2.41 tff(10250,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10249, 453, 1633, 2090, 10077, 10243])).
% 2.24/2.41 tff(10251,plain,((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(10252,plain,
% 2.24/2.41 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10251, 10233, 9971, 9986])).
% 2.24/2.41 tff(10253,plain,
% 2.24/2.41 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2846, 10252, 9928])).
% 2.24/2.41 tff(10254,assumption,(r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.24/2.41 tff(10255,assumption,(r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))), introduced(assumption)).
% 2.24/2.41 tff(10256,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2855, 268, 256, 10255, 10254])).
% 2.24/2.41 tff(10257,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(10258,plain,
% 2.24/2.41 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10257, 10253, 10242])).
% 2.24/2.41 tff(10259,plain,
% 2.24/2.41 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[687, 10258])).
% 2.24/2.41 tff(10260,plain,
% 2.24/2.41 (~b(s(elem!1), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10183, 10259, 9897, 9926, 9971, 1099, 9969, 9924])).
% 2.24/2.41 tff(10261,plain,
% 2.24/2.41 (r(s(elem!1), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2440, 10260, 9905])).
% 2.24/2.41 tff(10262,plain,
% 2.24/2.41 (r(s(s(z)), elem!1)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10261, 9903])).
% 2.24/2.41 tff(10263,plain,
% 2.24/2.41 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.24/2.41 inference(transitivity,[status(thm)],[8877, 56])).
% 2.24/2.41 tff(10264,plain,
% 2.24/2.41 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10263])).
% 2.24/2.41 tff(10265,plain,
% 2.24/2.41 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[289, 10264])).
% 2.24/2.41 tff(10266,plain,
% 2.24/2.41 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[1100])).
% 2.24/2.41 tff(10267,plain,
% 2.24/2.41 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.24/2.41 inference(symmetry,[status(thm)],[10266])).
% 2.24/2.41 tff(10268,plain,
% 2.24/2.41 ((~b(s(s(s(s(s(z))))), s(z))) <=> (~b(s(s(s(s(s(z))))), elem!1))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10267])).
% 2.24/2.41 tff(10269,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(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(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))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(10270,plain,
% 2.24/2.41 (((~b(s(s(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(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(10271,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(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(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(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)))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10270])).
% 2.24/2.41 tff(10272,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(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(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(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))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[10271, 10269])).
% 2.24/2.41 tff(10273,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(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(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(10274,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(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10273, 10272])).
% 2.24/2.41 tff(10275,plain,
% 2.24/2.41 (~b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10274, 453, 1633, 1779, 2090])).
% 2.24/2.41 tff(10276,plain,
% 2.24/2.41 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10275, 10268])).
% 2.24/2.41 tff(10277,plain,
% 2.24/2.41 (r(s(s(s(s(s(z))))), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[643, 10276, 10265])).
% 2.24/2.41 tff(10278,plain,
% 2.24/2.41 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5352, 10277, 1159, 1132])).
% 2.24/2.41 tff(10279,plain,
% 2.24/2.41 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[328, 10278])).
% 2.24/2.41 tff(10280,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(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(10281,plain,
% 2.24/2.41 (((~b(s(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(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(10282,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(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(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10281])).
% 2.24/2.41 tff(10283,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(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(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[10282, 10280])).
% 2.24/2.41 tff(10284,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(10285,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10284, 10283])).
% 2.24/2.41 tff(10286,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10285, 453, 1633, 10279, 1779, 2496])).
% 2.24/2.41 tff(10287,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~(elem!1 = s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(10288,plain,
% 2.24/2.41 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10287, 10259, 9971, 1159, 9897, 1099, 10233])).
% 2.24/2.41 tff(10289,plain,
% 2.24/2.41 (r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[4293, 10288])).
% 2.24/2.41 tff(10290,plain,
% 2.24/2.41 (~r(s(s(z)), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[4297, 10289, 1159])).
% 2.24/2.41 tff(10291,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10290, 10262])).
% 2.24/2.41 tff(10292,plain,(b(s(s(s(z))), elem!1) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(z))) | b(elem!1, s(z)) | b(s(s(s(s(z)))), s(z)) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(10293,plain,
% 2.24/2.41 (b(s(s(s(z))), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10292, 9894, 3448, 10, 1057, 3])).
% 2.24/2.41 tff(10294,plain,
% 2.24/2.41 (~(elem!1 = s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[8856, 10293, 128])).
% 2.24/2.41 tff(10295,plain,
% 2.24/2.41 (~r(elem!1, s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[8173, 10293, 1099, 3448, 9, 1275])).
% 2.24/2.41 tff(10296,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1130, 10295, 10294, 10])).
% 2.24/2.41 tff(10297,plain,(b(s(s(s(z))), s(z)) | b(elem!1, s(z)) | (~b(elem!1, s(s(s(z))))) | b(s(s(s(s(z)))), s(z)) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(10298,plain,
% 2.24/2.41 (b(s(s(s(z))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10297, 9882, 10, 1057, 3])).
% 2.24/2.41 tff(10299,plain,
% 2.24/2.41 (b(s(s(s(z))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10297, 1275, 10, 1057, 3])).
% 2.24/2.41 tff(10300,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, 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), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(10301,plain,
% 2.24/2.41 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(10302,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10301])).
% 2.24/2.41 tff(10303,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[10302, 10300])).
% 2.24/2.41 tff(10304,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(10305,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10304, 10303])).
% 2.24/2.41 tff(10306,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10305, 453, 499, 120, 2090, 1275])).
% 2.24/2.41 tff(10307,plain,((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(10308,plain,
% 2.24/2.41 (~b(s(z), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10307, 10233, 1275, 10299])).
% 2.24/2.41 tff(10309,plain,
% 2.24/2.41 (~(elem!1 = s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[4875, 58, 10299])).
% 2.24/2.41 tff(10310,plain,
% 2.24/2.41 (~(s(z) = elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1125, 10309])).
% 2.24/2.41 tff(10311,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[506, 10310, 10308, 4541])).
% 2.24/2.41 tff(10312,plain,(b(s(s(s(z))), elem!1) | r(s(z), elem!1) | (~b(elem!1, s(s(s(z))))) | b(s(s(s(s(z)))), s(z)) | b(elem!1, s(z)) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(10313,plain,
% 2.24/2.41 (b(s(s(s(z))), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10312, 9882, 4541, 1057, 10, 3])).
% 2.24/2.41 tff(10314,plain,
% 2.24/2.41 (~b(s(z), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5465, 10313, 9882, 10298])).
% 2.24/2.41 tff(10315,plain,
% 2.24/2.41 (s(z) = elem!1),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[506, 10314, 4541])).
% 2.24/2.41 tff(10316,plain,
% 2.24/2.41 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10315])).
% 2.24/2.41 tff(10317,plain,
% 2.24/2.41 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.24/2.41 inference(transitivity,[status(thm)],[10316, 56])).
% 2.24/2.41 tff(10318,plain,
% 2.24/2.41 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10317])).
% 2.24/2.41 tff(10319,plain,
% 2.24/2.41 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[289, 10318])).
% 2.24/2.41 tff(10320,plain,
% 2.24/2.41 (elem!1 = s(z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1125, 10315])).
% 2.24/2.41 tff(10321,plain,
% 2.24/2.41 (s(s(z)) = s(elem!1)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10315])).
% 2.24/2.41 tff(10322,plain,
% 2.24/2.41 (s(s(s(z))) = s(s(elem!1))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10321])).
% 2.24/2.41 tff(10323,plain,
% 2.24/2.41 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10322])).
% 2.24/2.41 tff(10324,plain,
% 2.24/2.41 (b(s(s(elem!1)), elem!1)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10313, 10323])).
% 2.24/2.41 tff(10325,plain,
% 2.24/2.41 (~r(s(s(s(s(s(z))))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2921, 10324, 10313, 1099, 10298, 10320])).
% 2.24/2.41 tff(10326,plain,
% 2.24/2.41 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9207, 10325, 10320])).
% 2.24/2.41 tff(10327,plain,
% 2.24/2.41 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), elem!1)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10315])).
% 2.24/2.41 tff(10328,plain,
% 2.24/2.41 (r(s(s(s(s(z)))), elem!1)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[1099, 10327])).
% 2.24/2.41 tff(10329,plain,
% 2.24/2.41 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10315])).
% 2.24/2.41 tff(10330,plain,
% 2.24/2.41 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10329])).
% 2.24/2.41 tff(10331,plain,
% 2.24/2.41 (~b(s(s(s(s(z)))), elem!1)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[1057, 10330])).
% 2.24/2.41 tff(10332,plain,
% 2.24/2.41 (r(s(s(s(z))), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[8833, 10319, 10, 10331])).
% 2.24/2.41 tff(10333,plain,
% 2.24/2.41 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[4961, 10332, 10328])).
% 2.24/2.41 tff(10334,plain,
% 2.24/2.41 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[518, 10333])).
% 2.24/2.41 tff(10335,plain,
% 2.24/2.41 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10316])).
% 2.24/2.41 tff(10336,plain,
% 2.24/2.41 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[289, 10335])).
% 2.24/2.41 tff(10337,plain,
% 2.24/2.41 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10315])).
% 2.24/2.41 tff(10338,plain,
% 2.24/2.41 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 2.24/2.41 inference(symmetry,[status(thm)],[10337])).
% 2.24/2.41 tff(10339,plain,
% 2.24/2.41 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), s(z))),
% 2.24/2.41 inference(transitivity,[status(thm)],[10323, 10338])).
% 2.24/2.41 tff(10340,plain,
% 2.24/2.41 (b(s(s(elem!1)), s(z))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10313, 10339])).
% 2.24/2.41 tff(10341,plain,
% 2.24/2.41 (b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[297, 10325])).
% 2.24/2.41 tff(10342,plain,
% 2.24/2.41 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3198, 10341, 10320, 10340, 1099, 10298, 10336, 10334, 10313])).
% 2.24/2.41 tff(10343,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[643, 10342, 10326, 10319])).
% 2.24/2.41 tff(10344,plain,(b(s(s(s(s(z)))), s(z)) | b(elem!1, s(z)) | r(s(z), elem!1) | (s(s(s(s(z)))) = elem!1) | r(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(10345,plain,
% 2.24/2.41 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10344, 3, 4541, 10, 1200])).
% 2.24/2.41 tff(10346,plain,
% 2.24/2.41 (~r(elem!1, s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1586, 3448, 9871])).
% 2.24/2.41 tff(10347,plain,
% 2.24/2.41 (elem!1 = s(z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1130, 10346, 10])).
% 2.24/2.41 tff(10348,plain,
% 2.24/2.41 (s(elem!1) = s(s(z))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10347])).
% 2.24/2.41 tff(10349,plain,
% 2.24/2.41 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10348])).
% 2.24/2.41 tff(10350,plain,
% 2.24/2.41 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10347])).
% 2.24/2.41 tff(10351,plain,
% 2.24/2.41 (r(s(elem!1), elem!1) <=> r(s(s(z)), s(z))),
% 2.24/2.41 inference(transitivity,[status(thm)],[10350, 10349])).
% 2.24/2.41 tff(10352,plain,
% 2.24/2.41 (~(s(elem!1) = s(s(elem!1)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2287, 10347])).
% 2.24/2.41 tff(10353,plain,
% 2.24/2.41 (~(s(elem!1) = elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[8905, 10352])).
% 2.24/2.41 tff(10354,plain,
% 2.24/2.41 (~(s(s(s(z))) = elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9990, 221, 128, 3])).
% 2.24/2.41 tff(10355,plain,
% 2.24/2.41 (r(s(s(s(z))), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[74, 58, 59])).
% 2.24/2.41 tff(10356,plain,
% 2.24/2.41 (~b(s(s(s(z))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5444, 58, 221, 3])).
% 2.24/2.41 tff(10357,plain,
% 2.24/2.41 (r(s(s(s(z))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[134, 10356])).
% 2.24/2.41 tff(10358,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1586, 10357, 10355, 238])).
% 2.24/2.41 tff(10359,plain,(b(s(s(s(z))), elem!1) | (~r(elem!1, s(z))) | (s(s(s(z))) = elem!1) | b(s(z), s(s(s(z)))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(10360,plain,
% 2.24/2.41 (~r(elem!1, s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10359, 221, 3, 10354, 58])).
% 2.24/2.41 tff(10361,plain,
% 2.24/2.41 (elem!1 = s(z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1130, 10360, 10])).
% 2.24/2.41 tff(10362,plain,
% 2.24/2.41 ((~r(elem!1, s(s(s(z))))) <=> (~r(s(z), s(s(s(z)))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[3163])).
% 2.24/2.41 tff(10363,plain,
% 2.24/2.41 (~r(s(z), s(s(s(z))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[1200, 10362])).
% 2.24/2.41 tff(10364,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[257, 10363])).
% 2.24/2.41 tff(10365,plain,((~(s(z) = elem!1)) | (~r(s(z), s(s(s(z))))) | r(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(10366,plain,
% 2.24/2.41 (~(s(z) = elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10365, 228, 1200])).
% 2.24/2.41 tff(10367,plain,
% 2.24/2.41 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[547, 10366])).
% 2.24/2.41 tff(10368,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3026, 10367, 10361])).
% 2.24/2.41 tff(10369,plain,(b(s(z), s(s(s(z)))) | b(elem!1, s(z)) | r(elem!1, s(s(s(z)))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(z))), elem!1) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(10370,plain,
% 2.24/2.41 (b(s(z), s(s(s(z))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[10369, 128, 1200, 3, 58, 10])).
% 2.24/2.41 tff(10371,plain,
% 2.24/2.41 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9485, 3])).
% 2.24/2.41 tff(10372,plain,
% 2.24/2.41 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[4499, 10371])).
% 2.24/2.41 tff(10373,plain,
% 2.24/2.41 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[1104, 1103])).
% 2.24/2.41 tff(10374,plain,
% 2.24/2.41 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 2.24/2.41 inference(symmetry,[status(thm)],[10373])).
% 2.24/2.41 tff(10375,assumption,(~b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 2.24/2.41 tff(10376,plain,
% 2.24/2.41 (r(s(s(s(z))), s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2534, 69, 160, 10375])).
% 2.24/2.41 tff(10377,plain,
% 2.24/2.41 (b(s(elem!1), elem!1) <=> b(s(s(z)), s(z))),
% 2.24/2.41 inference(transitivity,[status(thm)],[3107, 8897])).
% 2.24/2.41 tff(10378,plain,
% 2.24/2.41 ((s(s(s(z))) = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 2.24/2.41 inference(commutativity,[status(thm)],[])).
% 2.24/2.41 tff(10379,plain,
% 2.24/2.41 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.24/2.41 inference(symmetry,[status(thm)],[10378])).
% 2.24/2.41 tff(10380,plain,
% 2.24/2.41 ((s(s(s(z))) = s(s(z))) <=> (s(s(s(z))) = s(elem!1))),
% 2.24/2.41 inference(transitivity,[status(thm)],[3039, 10379])).
% 2.24/2.41 tff(10381,plain,
% 2.24/2.41 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10380])).
% 2.24/2.41 tff(10382,plain,
% 2.24/2.41 (~(s(s(s(z))) = s(elem!1))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[160, 10381])).
% 2.24/2.41 tff(10383,plain,
% 2.24/2.41 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[1103])).
% 2.24/2.41 tff(10384,plain,
% 2.24/2.41 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(elem!1))),
% 2.24/2.41 inference(symmetry,[status(thm)],[10383])).
% 2.24/2.41 tff(10385,plain,
% 2.24/2.41 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(s(s(z))), s(elem!1)))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[10384])).
% 2.24/2.41 tff(10386,plain,
% 2.24/2.41 (~b(s(s(s(z))), s(elem!1))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10375, 10385])).
% 2.24/2.41 tff(10387,plain,
% 2.24/2.41 (r(s(s(s(z))), s(elem!1))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[9480, 10386, 10382])).
% 2.24/2.41 tff(10388,plain,
% 2.24/2.41 (~r(s(elem!1), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[7017, 10387, 1545])).
% 2.24/2.41 tff(10389,plain,
% 2.24/2.41 (b(s(elem!1), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2440, 10388, 8906])).
% 2.24/2.41 tff(10390,plain,
% 2.24/2.41 (b(s(s(z)), s(z))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[10389, 10377])).
% 2.24/2.41 tff(10391,assumption,(~b(elem!1, s(elem!1))), introduced(assumption)).
% 2.24/2.41 tff(10392,plain,
% 2.24/2.41 (r(elem!1, s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1069, 10391, 1056])).
% 2.24/2.42 tff(10393,plain,
% 2.24/2.42 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[9470])).
% 2.24/2.42 tff(10394,plain,
% 2.24/2.42 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 2.24/2.42 inference(symmetry,[status(thm)],[10393])).
% 2.24/2.42 tff(10395,plain,
% 2.24/2.42 ((~b(elem!1, s(elem!1))) <=> (~b(elem!1, s(s(s(z)))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10394])).
% 2.24/2.42 tff(10396,plain,
% 2.24/2.42 (~b(elem!1, s(s(s(z))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10391, 10395])).
% 2.24/2.42 tff(10397,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1275, 10396])).
% 2.24/2.42 tff(10398,plain,((~(s(s(s(z))) = s(elem!1))) | (~b(elem!1, s(s(s(z))))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(10399,plain,
% 2.24/2.42 (~(s(s(s(z))) = s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10398, 10391, 1275])).
% 2.24/2.42 tff(10400,plain,
% 2.24/2.42 (r(s(s(s(z))), s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9480, 10399, 6845])).
% 2.24/2.42 tff(10401,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10402,plain,
% 2.24/2.42 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10403,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10402])).
% 2.24/2.42 tff(10404,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 2.24/2.42 inference(transitivity,[status(thm)],[10403, 10401])).
% 2.24/2.42 tff(10405,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1)))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(10406,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), elem!1))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10405, 10404])).
% 2.24/2.42 tff(10407,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10406, 268, 339, 1545, 7009])).
% 2.24/2.42 tff(10408,plain,((~r(s(s(s(z))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(10409,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10408, 10400, 10392, 1545])).
% 2.24/2.42 tff(10410,plain,(b(elem!1, s(elem!1)) | (~r(s(s(s(z))), elem!1)) | b(s(s(s(z))), s(elem!1)) | (elem!1 = s(elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(10411,plain,
% 2.24/2.42 (b(elem!1, s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10410, 10386, 1275, 1545, 8958])).
% 2.24/2.42 tff(10412,plain,
% 2.24/2.42 (b(s(z), s(elem!1))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[8974, 10411, 1100])).
% 2.24/2.42 tff(10413,plain,
% 2.24/2.42 (b(s(z), s(s(z)))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10412, 8968])).
% 2.24/2.42 tff(10414,plain,
% 2.24/2.42 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[4290, 453, 1764, 10413, 10390])).
% 2.24/2.42 tff(10415,plain,
% 2.24/2.42 (r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[4293, 10414])).
% 2.24/2.42 tff(10416,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10417,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(10418,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10417, 10416])).
% 2.24/2.42 tff(10419,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10418, 268, 11, 233, 10415, 10376])).
% 2.24/2.42 tff(10420,plain,(b(s(s(s(z))), s(s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~(elem!1 = s(z))) | (~r(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(10421,plain,
% 2.24/2.42 (b(s(s(s(z))), s(s(z)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10420, 11, 233, 1764, 1100, 1545, 1275])).
% 2.24/2.42 tff(10422,plain,
% 2.24/2.42 (b(s(s(elem!1)), s(elem!1))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10421, 10374])).
% 2.24/2.42 tff(10423,plain,
% 2.24/2.42 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[1100])).
% 2.24/2.42 tff(10424,plain,
% 2.24/2.42 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.24/2.42 inference(symmetry,[status(thm)],[10423])).
% 2.24/2.42 tff(10425,plain,
% 2.24/2.42 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[1104])).
% 2.24/2.42 tff(10426,plain,
% 2.24/2.42 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 2.24/2.42 inference(symmetry,[status(thm)],[10425])).
% 2.24/2.42 tff(10427,plain,
% 2.24/2.42 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.24/2.42 inference(transitivity,[status(thm)],[10426, 10424])).
% 2.24/2.42 tff(10428,plain,
% 2.24/2.42 (b(elem!1, s(s(elem!1)))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[2090, 10427])).
% 2.24/2.42 tff(10429,plain,
% 2.24/2.42 (b(s(s(z)), s(z)) <=> b(s(elem!1), s(z))),
% 2.24/2.42 inference(symmetry,[status(thm)],[8897])).
% 2.24/2.42 tff(10430,plain,
% 2.24/2.42 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 2.24/2.42 inference(transitivity,[status(thm)],[8895, 10429, 9074])).
% 2.24/2.42 tff(10431,plain,
% 2.24/2.42 (~r(s(s(s(s(s(z))))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9921, 5003, 1100])).
% 2.24/2.42 tff(10432,plain,
% 2.24/2.42 (b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[297, 10431])).
% 2.24/2.42 tff(10433,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(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10434,plain,
% 2.24/2.42 (((~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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10435,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(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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10434])).
% 2.24/2.42 tff(10436,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(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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[10435, 10433])).
% 2.24/2.42 tff(10437,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(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)))))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(10438,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10437, 10436])).
% 2.24/2.42 tff(10439,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10438, 453, 1764, 1984, 10432, 2090])).
% 2.24/2.42 tff(10440,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~(elem!1 = s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(10441,plain,
% 2.24/2.42 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10440, 11, 2090, 1100, 1764, 1545])).
% 2.24/2.42 tff(10442,plain,
% 2.24/2.42 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[687, 10441])).
% 2.24/2.42 tff(10443,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(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10444,plain,
% 2.24/2.42 (((~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(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10445,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(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10444])).
% 2.24/2.42 tff(10446,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(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[10445, 10443])).
% 2.24/2.42 tff(10447,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(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(10448,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10447, 10446])).
% 2.24/2.42 tff(10449,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10448, 453, 1779, 374, 2090, 9056])).
% 2.24/2.42 tff(10450,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(10451,plain,
% 2.24/2.42 (~b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10450, 10421, 10442, 2090])).
% 2.24/2.42 tff(10452,plain,
% 2.24/2.42 (r(s(s(s(s(s(z))))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[297, 10451])).
% 2.24/2.42 tff(10453,plain,
% 2.24/2.42 (r(s(s(s(s(s(z))))), elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[9921, 10452, 1100])).
% 2.24/2.42 tff(10454,plain,
% 2.24/2.42 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1566, 1545, 722])).
% 2.24/2.42 tff(10455,plain,
% 2.24/2.42 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[687, 10454])).
% 2.24/2.42 tff(10456,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10457,plain,
% 2.24/2.42 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10458,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(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(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10457])).
% 2.24/2.42 tff(10459,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(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(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(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[10458, 10456])).
% 2.24/2.42 tff(10460,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(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(10461,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10460, 10459])).
% 2.24/2.42 tff(10462,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10461, 453, 10455, 5690, 7167, 6595])).
% 2.24/2.42 tff(10463,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(10464,plain,
% 2.24/2.42 (~r(s(s(z)), elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[10463, 10453, 1545])).
% 2.24/2.42 tff(10465,plain,
% 2.24/2.42 (b(s(s(z)), elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[782, 10464, 8851])).
% 2.24/2.42 tff(10466,plain,
% 2.24/2.42 (b(s(elem!1), elem!1)),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[10465, 10430])).
% 2.24/2.42 tff(10467,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(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10468,plain,
% 2.24/2.42 (((~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(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(10469,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(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(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[10468])).
% 2.24/2.42 tff(10470,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(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(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[10469, 10467])).
% 2.24/2.43 tff(10471,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(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)))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(10472,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10471, 10470])).
% 2.24/2.43 tff(10473,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10472, 453, 629, 1071, 907, 6555])).
% 2.24/2.43 tff(10474,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(10475,plain,
% 2.24/2.43 (~b(elem!1, s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10474, 10466, 10428, 10422])).
% 2.24/2.43 tff(10476,plain,
% 2.24/2.43 (r(elem!1, s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1069, 10475, 8958])).
% 2.24/2.43 tff(10477,plain,
% 2.24/2.43 (r(s(z), s(elem!1))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10476, 2445])).
% 2.24/2.43 tff(10478,plain,
% 2.24/2.43 (s(s(elem!1)) = s(s(s(z)))),
% 2.24/2.43 inference(symmetry,[status(thm)],[3165])).
% 2.24/2.43 tff(10479,plain,
% 2.24/2.43 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10478])).
% 2.24/2.43 tff(10480,plain,
% 2.24/2.43 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.24/2.43 inference(symmetry,[status(thm)],[10479])).
% 2.24/2.43 tff(10481,plain,
% 2.24/2.43 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[1779, 10480])).
% 2.24/2.43 tff(10482,assumption,(~b(s(s(s(s(s(z))))), s(s(elem!1)))), introduced(assumption)).
% 2.24/2.43 tff(10483,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10482, 10481])).
% 2.24/2.43 tff(10484,plain,(b(s(s(s(s(s(z))))), s(s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(10485,plain,
% 2.24/2.43 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10484, 10442, 3028])).
% 2.24/2.43 tff(10486,assumption,(b(s(s(s(s(s(z))))), s(s(elem!1)))), introduced(assumption)).
% 2.24/2.43 tff(10487,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(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10488,plain,
% 2.24/2.43 (((~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(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10489,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10488])).
% 2.24/2.43 tff(10490,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[10489, 10487])).
% 2.24/2.43 tff(10491,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(10492,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10491, 10490])).
% 2.24/2.43 tff(10493,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10492, 453, 629, 6555, 2129, 10486])).
% 2.24/2.43 tff(10494,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(10495,plain,
% 2.24/2.43 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10494, 10422, 10485, 10466])).
% 2.24/2.43 tff(10496,plain,
% 2.24/2.43 (r(s(s(s(s(s(z))))), s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2142, 10495, 4106])).
% 2.24/2.43 tff(10497,plain,
% 2.24/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10498,plain,
% 2.24/2.43 (((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10499,plain,
% 2.24/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10498])).
% 2.24/2.43 tff(10500,plain,
% 2.24/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[10499, 10497])).
% 2.24/2.43 tff(10501,plain,
% 2.24/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(10502,plain,
% 2.24/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10501, 10500])).
% 2.24/2.43 tff(10503,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10502, 268, 388, 258, 2480])).
% 2.24/2.43 tff(10504,plain,((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(10505,plain,
% 2.24/2.43 (~r(s(z), s(elem!1))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10504, 10496, 10452])).
% 2.24/2.43 tff(10506,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10505, 10477])).
% 2.24/2.43 tff(10507,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~(elem!1 = s(z))) | (s(s(s(s(s(z))))) = s(elem!1)) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(10508,plain,
% 2.24/2.43 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10507, 10347, 10372, 9871, 10370, 3448, 1764, 1275])).
% 2.24/2.43 tff(10509,plain,
% 2.24/2.43 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[518, 10508])).
% 2.24/2.43 tff(10510,plain,
% 2.24/2.43 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2102, 10509, 1764, 10370])).
% 2.24/2.43 tff(10511,plain,
% 2.24/2.43 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1656, 10510])).
% 2.24/2.43 tff(10512,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10438, 453, 1764, 5914, 10432, 2090])).
% 2.24/2.43 tff(10513,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~(elem!1 = s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(10514,plain,
% 2.24/2.43 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10513, 10370, 1764, 10347, 10511, 9871])).
% 2.24/2.43 tff(10515,plain,
% 2.24/2.43 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[687, 10514])).
% 2.24/2.43 tff(10516,plain,
% 2.24/2.43 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10347])).
% 2.24/2.43 tff(10517,plain,
% 2.24/2.43 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.24/2.43 inference(symmetry,[status(thm)],[10516])).
% 2.24/2.43 tff(10518,plain,
% 2.24/2.43 (s(s(elem!1)) = s(s(s(z)))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10348])).
% 2.24/2.43 tff(10519,plain,
% 2.24/2.43 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10518])).
% 2.24/2.43 tff(10520,plain,
% 2.24/2.43 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 2.24/2.43 inference(symmetry,[status(thm)],[10519])).
% 2.24/2.43 tff(10521,plain,
% 2.24/2.43 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.24/2.43 inference(transitivity,[status(thm)],[10520, 10517])).
% 2.24/2.43 tff(10522,plain,
% 2.24/2.43 (b(elem!1, s(s(elem!1)))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10370, 10521])).
% 2.24/2.43 tff(10523,plain,
% 2.24/2.43 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[1103])).
% 2.24/2.43 tff(10524,plain,
% 2.24/2.43 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[2376])).
% 2.24/2.43 tff(10525,plain,
% 2.24/2.43 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[153, 10524])).
% 2.24/2.43 tff(10526,plain,
% 2.24/2.43 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 2.24/2.43 inference(monotonicity,[status(thm)],[1121])).
% 2.24/2.43 tff(10527,plain,
% 2.24/2.43 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 2.24/2.43 inference(symmetry,[status(thm)],[10526])).
% 2.24/2.43 tff(10528,plain,
% 2.24/2.43 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(s(z)))), s(z)))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10527])).
% 2.24/2.43 tff(10529,plain,
% 2.24/2.43 (~b(s(s(s(s(z)))), s(z))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[249, 10528])).
% 2.24/2.43 tff(10530,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1764, 10529])).
% 2.24/2.43 tff(10531,plain,(b(s(s(s(s(z)))), elem!1) | (~b(s(s(s(s(z)))), s(z))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(10532,plain,
% 2.24/2.43 (b(s(s(s(s(z)))), elem!1)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10531, 3028, 1764])).
% 2.24/2.43 tff(10533,plain,
% 2.24/2.43 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9392, 629, 1275, 10532])).
% 2.24/2.43 tff(10534,plain,
% 2.24/2.43 (r(s(elem!1), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9382, 10533, 10525])).
% 2.24/2.43 tff(10535,plain,
% 2.24/2.43 (r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10534, 10523])).
% 2.24/2.43 tff(10536,plain,
% 2.24/2.43 (~r(s(s(s(z))), s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6256, 268, 300, 10535])).
% 2.24/2.43 tff(10537,plain,
% 2.24/2.43 (b(s(s(s(z))), s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2534, 69, 160, 10536])).
% 2.24/2.43 tff(10538,plain,
% 2.24/2.43 (b(s(s(elem!1)), s(elem!1))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10537, 10374])).
% 2.24/2.43 tff(10539,plain,
% 2.24/2.43 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10484, 1779, 1121])).
% 2.24/2.43 tff(10540,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(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10541,plain,
% 2.24/2.43 (((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10542,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(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10541])).
% 2.24/2.43 tff(10543,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(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[10542, 10540])).
% 2.24/2.43 tff(10544,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(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(10545,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10544, 10543])).
% 2.24/2.43 tff(10546,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10545, 453, 629, 923, 645, 10486])).
% 2.24/2.43 tff(10547,plain,((~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(10548,plain,
% 2.24/2.43 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10547, 923, 629, 10539])).
% 2.24/2.43 tff(10549,plain,
% 2.24/2.43 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[659, 10548, 3700])).
% 2.24/2.43 tff(10550,plain,
% 2.24/2.43 (b(s(z), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[1121])).
% 2.24/2.43 tff(10551,plain,
% 2.24/2.43 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 2.24/2.43 inference(symmetry,[status(thm)],[10550])).
% 2.24/2.43 tff(10552,plain,
% 2.24/2.43 (b(s(z), s(s(s(s(s(z))))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[923, 10551])).
% 2.24/2.43 tff(10553,plain,
% 2.24/2.43 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[4526, 10552, 1779, 1764])).
% 2.24/2.43 tff(10554,assumption,(~b(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.24/2.43 tff(10555,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2463, 69, 433, 10554, 2453])).
% 2.24/2.43 tff(10556,plain,(r(s(s(s(s(z)))), s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(10557,plain,
% 2.24/2.43 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10556, 10553])).
% 2.24/2.43 tff(10558,plain,
% 2.24/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10559,plain,
% 2.24/2.43 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10560,plain,
% 2.24/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10559])).
% 2.24/2.43 tff(10561,plain,
% 2.24/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[10560, 10558])).
% 2.24/2.43 tff(10562,plain,
% 2.24/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(10563,plain,
% 2.24/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10562, 10561])).
% 2.24/2.43 tff(10564,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10563, 268, 10557, 9650, 10549])).
% 2.24/2.43 tff(10565,plain,((~b(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~(s(z) = elem!1)) | (s(elem!1) = s(s(s(s(s(z)))))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(10566,plain,
% 2.24/2.43 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[10565, 10534, 1764, 3028, 1779, 3700, 629])).
% 2.24/2.43 tff(10567,plain,
% 2.24/2.43 (r(elem!1, s(s(s(s(s(z))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[466, 10566, 8879])).
% 2.24/2.43 tff(10568,plain,
% 2.24/2.43 (elem!1 = s(z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1125, 1121])).
% 2.24/2.43 tff(10569,plain,
% 2.24/2.43 (~(s(elem!1) = s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2287, 10568])).
% 2.24/2.43 tff(10570,plain,
% 2.24/2.43 (~(s(s(elem!1)) = s(elem!1))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10569, 3330])).
% 2.24/2.43 tff(10571,plain,
% 2.24/2.43 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10478])).
% 2.24/2.43 tff(10572,plain,
% 2.24/2.43 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10571])).
% 2.24/2.43 tff(10573,plain,
% 2.24/2.43 (~(s(elem!1) = elem!1)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[8905, 10569])).
% 2.24/2.43 tff(10574,plain,
% 2.24/2.43 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[607, 10573])).
% 2.24/2.43 tff(10575,plain,
% 2.24/2.43 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1788, 1780, 1779, 523])).
% 2.24/2.43 tff(10576,plain,
% 2.24/2.43 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[9143, 10575, 10568])).
% 2.24/2.43 tff(10577,plain,
% 2.24/2.43 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[675, 10576, 10574])).
% 2.24/2.43 tff(10578,plain,
% 2.24/2.43 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[10577, 10572])).
% 2.24/2.43 tff(10579,plain,
% 2.24/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10580,plain,
% 2.24/2.43 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(10581,plain,
% 2.24/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[10580])).
% 2.24/2.43 tff(10582,plain,
% 2.24/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[10581, 10579])).
% 2.24/2.43 tff(10583,plain,
% 2.24/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(10584,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10583, 10582])).
% 2.24/2.44 tff(10585,plain,
% 2.24/2.44 (~r(s(s(elem!1)), s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10584, 268, 10578, 9650])).
% 2.24/2.44 tff(10586,plain,
% 2.24/2.44 ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1874, 69, 10585])).
% 2.24/2.44 tff(10587,plain,
% 2.24/2.44 (b(s(s(elem!1)), s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10586, 10570])).
% 2.24/2.44 tff(10588,plain,
% 2.24/2.44 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[3165])).
% 2.24/2.44 tff(10589,plain,
% 2.24/2.44 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[523, 10588])).
% 2.24/2.44 tff(10590,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(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(10591,plain,
% 2.24/2.44 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(10592,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(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~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(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10591])).
% 2.24/2.44 tff(10593,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(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~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(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[10592, 10590])).
% 2.24/2.44 tff(10594,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(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(10595,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10594, 10593])).
% 2.24/2.44 tff(10596,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10595, 453, 10589, 10587, 1780, 10539])).
% 2.24/2.44 tff(10597,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~(s(z) = elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(10598,plain,
% 2.24/2.44 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10597, 10534, 3028, 523, 1779])).
% 2.24/2.44 tff(10599,plain,
% 2.24/2.44 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[328, 10598])).
% 2.24/2.44 tff(10600,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(10601,plain,
% 2.24/2.44 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(10602,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10601])).
% 2.24/2.44 tff(10603,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[10602, 10600])).
% 2.24/2.44 tff(10604,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(10605,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10604, 10603])).
% 2.24/2.44 tff(10606,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10605, 268, 301, 9650, 3224])).
% 2.24/2.44 tff(10607,plain,((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(10608,plain,
% 2.24/2.44 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10607, 10599, 10534])).
% 2.24/2.44 tff(10609,plain,
% 2.24/2.44 (b(s(elem!1), s(s(s(s(s(z))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[659, 10608, 3700])).
% 2.24/2.44 tff(10610,plain,
% 2.24/2.44 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9054, 10609, 1100])).
% 2.24/2.44 tff(10611,plain,
% 2.24/2.44 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9064, 10537, 1779, 10610])).
% 2.24/2.44 tff(10612,plain,
% 2.24/2.44 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2570, 10611])).
% 2.24/2.44 tff(10613,plain,
% 2.24/2.44 (~r(elem!1, s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[5151, 10612, 1545, 10567])).
% 2.24/2.44 tff(10614,plain,
% 2.24/2.44 (b(elem!1, s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1069, 10613, 8958])).
% 2.24/2.44 tff(10615,plain,
% 2.24/2.44 (~b(s(s(elem!1)), s(elem!1))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10474, 10614, 907, 629])).
% 2.24/2.44 tff(10616,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10615, 10538])).
% 2.24/2.44 tff(10617,plain,((~b(s(elem!1), elem!1)) | (~(elem!1 = s(z))) | (~b(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(10618,plain,
% 2.24/2.44 (~b(s(elem!1), elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10617, 10347, 10522, 9871, 10515, 10511, 10371, 10509, 1764, 1275])).
% 2.24/2.44 tff(10619,plain,
% 2.24/2.44 (r(s(elem!1), elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2440, 10618, 10353])).
% 2.24/2.44 tff(10620,plain,
% 2.24/2.44 (r(s(s(z)), s(z))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10619, 10351])).
% 2.24/2.44 tff(10621,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(10622,plain,
% 2.24/2.44 (((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(10623,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z)))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10622])).
% 2.24/2.44 tff(10624,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[10623, 10621])).
% 2.24/2.44 tff(10625,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(10626,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z)))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10625, 10624])).
% 2.24/2.44 tff(10627,plain,
% 2.24/2.44 (~r(s(s(s(z))), s(s(z)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10626, 268, 3448, 10620])).
% 2.24/2.44 tff(10628,plain,
% 2.24/2.44 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10347])).
% 2.24/2.44 tff(10629,plain,
% 2.24/2.44 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 2.24/2.44 inference(symmetry,[status(thm)],[10628])).
% 2.24/2.44 tff(10630,plain,
% 2.24/2.44 (r(s(elem!1), elem!1) <=> r(s(s(z)), elem!1)),
% 2.24/2.44 inference(transitivity,[status(thm)],[10350, 10349, 10629])).
% 2.24/2.44 tff(10631,plain,
% 2.24/2.44 (r(s(s(z)), elem!1)),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10619, 10630])).
% 2.24/2.44 tff(10632,plain,
% 2.24/2.44 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10463, 10631, 9871])).
% 2.24/2.44 tff(10633,plain,
% 2.24/2.44 (~r(s(s(s(s(s(z))))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[9921, 10632, 10347])).
% 2.24/2.44 tff(10634,plain,
% 2.24/2.44 (b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[297, 10633])).
% 2.24/2.44 tff(10635,plain,
% 2.24/2.44 (~b(s(s(s(z))), s(s(z)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10450, 10634, 10515, 10370])).
% 2.24/2.44 tff(10636,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2534, 69, 160, 10635, 10627])).
% 2.24/2.44 tff(10637,plain,(b(s(s(s(z))), s(z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(z))))) | b(elem!1, s(z)) | r(elem!1, s(s(s(z)))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(10638,plain,
% 2.24/2.44 (b(s(s(s(z))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10637, 1275, 10345, 10, 1200, 3, 58])).
% 2.24/2.44 tff(10639,plain,
% 2.24/2.44 (b(s(z), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[5444, 10638, 58, 3])).
% 2.24/2.44 tff(10640,plain,
% 2.24/2.44 (~b(s(z), elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10307, 10639, 1275, 10638])).
% 2.24/2.44 tff(10641,plain,
% 2.24/2.44 (~(elem!1 = s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[4875, 10638, 58])).
% 2.24/2.44 tff(10642,plain,
% 2.24/2.44 (~(s(z) = elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1125, 10641])).
% 2.24/2.44 tff(10643,plain,
% 2.24/2.44 ($false),
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% 2.24/2.44 tff(10645,plain,
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% 2.24/2.44 tff(10646,plain,
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% 2.24/2.44 inference(unit_resolution,[status(thm)],[4492, 10645, 1200])).
% 2.24/2.44 tff(10647,plain,
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% 2.24/2.44 inference(unit_resolution,[status(thm)],[4487, 10646])).
% 2.24/2.44 tff(10648,plain,
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% 2.24/2.44 inference(unit_resolution,[status(thm)],[122, 10647, 10])).
% 2.24/2.44 tff(10649,plain,
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% 2.24/2.44 inference(unit_resolution,[status(thm)],[2086, 10647, 10648])).
% 2.24/2.44 tff(10650,plain,
% 2.24/2.44 (r(s(s(s(z))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[134, 10648])).
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% 2.24/2.44 inference(unit_resolution,[status(thm)],[1586, 10650, 10649, 9871])).
% 2.24/2.44 tff(10652,plain,(b(s(s(s(z))), elem!1) | b(elem!1, s(z)) | r(elem!1, s(s(s(z)))) | r(s(z), elem!1) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(10653,plain,
% 2.24/2.44 (b(s(s(s(z))), elem!1)),
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% 2.24/2.44 tff(10654,plain,
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% 2.24/2.44 inference(unit_resolution,[status(thm)],[506, 492, 4541])).
% 2.24/2.44 tff(10655,plain,
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% 2.24/2.44 inference(unit_resolution,[status(thm)],[9990, 123, 221, 76])).
% 2.24/2.44 tff(10656,plain,
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% 2.24/2.44 inference(unit_resolution,[status(thm)],[4492, 1200, 4490])).
% 2.24/2.44 tff(10657,plain,
% 2.24/2.44 (s(s(s(z))) = elem!1),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[4487, 10656])).
% 2.24/2.44 tff(10658,plain,
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% 2.24/2.44 inference(unit_resolution,[status(thm)],[10365, 1200, 228])).
% 2.24/2.44 tff(10659,plain,
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% 2.24/2.44 inference(unit_resolution,[status(thm)],[506, 10658, 4541])).
% 2.24/2.44 tff(10660,plain,
% 2.24/2.44 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[501, 10659, 221])).
% 2.24/2.44 tff(10661,plain,
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% 2.24/2.44 inference(unit_resolution,[status(thm)],[81, 10660, 10657])).
% 2.24/2.44 tff(10662,plain,(r(elem!1, s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), elem!1) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(10663,plain,
% 2.24/2.44 (r(elem!1, s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10662, 4541, 221, 4490])).
% 2.24/2.44 tff(10664,plain,
% 2.24/2.44 (~r(elem!1, s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1157, 1149, 228])).
% 2.24/2.44 tff(10665,plain,
% 2.24/2.44 (~(s(s(s(z))) = elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2086, 128, 10664])).
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% 2.24/2.44 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(s(z)), elem!1)),
% 2.24/2.44 inference(monotonicity,[status(thm)],[7334])).
% 2.24/2.44 tff(10667,plain,
% 2.24/2.44 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.44 inference(symmetry,[status(thm)],[10666])).
% 2.24/2.44 tff(10668,plain,
% 2.24/2.44 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.24/2.44 inference(monotonicity,[status(thm)],[7334])).
% 2.24/2.44 tff(10669,plain,
% 2.24/2.44 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.24/2.44 inference(symmetry,[status(thm)],[10668])).
% 2.24/2.44 tff(10670,plain,
% 2.24/2.44 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.24/2.44 inference(monotonicity,[status(thm)],[7334])).
% 2.24/2.44 tff(10671,plain,
% 2.24/2.44 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[10670, 3858])).
% 2.24/2.44 tff(10672,plain,
% 2.24/2.44 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.24/2.44 inference(transitivity,[status(thm)],[10671, 8506])).
% 2.24/2.44 tff(10673,plain,
% 2.24/2.44 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10672])).
% 2.24/2.44 tff(10674,plain,
% 2.24/2.44 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[2729, 10673])).
% 2.24/2.44 tff(10675,plain,
% 2.24/2.44 ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) <=> (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[7689])).
% 2.24/2.44 tff(10676,plain,
% 2.24/2.44 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[5965])).
% 2.24/2.44 tff(10677,plain,
% 2.24/2.44 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10676])).
% 2.24/2.44 tff(10678,plain,
% 2.24/2.44 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[2, 10677])).
% 2.24/2.44 tff(10679,plain,
% 2.24/2.44 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2570, 10678])).
% 2.24/2.44 tff(10680,plain,
% 2.24/2.44 (r(elem!1, s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[5965])).
% 2.24/2.44 tff(10681,plain,
% 2.24/2.44 ((~r(elem!1, s(z))) <=> (~r(s(s(s(s(s(z))))), s(z)))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10680])).
% 2.24/2.44 tff(10682,plain,
% 2.24/2.44 (~r(s(s(s(s(s(z))))), s(z))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[2076, 10681])).
% 2.24/2.44 tff(10683,plain,
% 2.24/2.44 (b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[295, 69, 10682, 291])).
% 2.24/2.44 tff(10684,plain,
% 2.24/2.44 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[5787])).
% 2.24/2.44 tff(10685,plain,
% 2.24/2.44 (r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.24/2.44 inference(symmetry,[status(thm)],[10684])).
% 2.24/2.44 tff(10686,plain,
% 2.24/2.44 ((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10685])).
% 2.24/2.44 tff(10687,plain,
% 2.24/2.44 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[5787])).
% 2.24/2.44 tff(10688,plain,
% 2.24/2.44 ((~b(s(s(s(s(s(s(s(z))))))), s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[5789])).
% 2.24/2.44 tff(10689,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.24/2.44 tff(10690,plain,
% 2.24/2.44 ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[3097, 453, 443, 374])).
% 2.24/2.44 tff(10691,plain,
% 2.24/2.44 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10690, 10689])).
% 2.24/2.44 tff(10692,plain,
% 2.24/2.44 (~b(s(s(elem!1)), s(z))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10691, 10688])).
% 2.24/2.44 tff(10693,plain,
% 2.24/2.44 (r(s(s(elem!1)), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1047, 10692])).
% 2.24/2.44 tff(10694,plain,
% 2.24/2.44 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10693, 10687])).
% 2.24/2.44 tff(10695,plain,
% 2.24/2.44 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[7971, 268, 233, 10694])).
% 2.24/2.44 tff(10696,plain,
% 2.24/2.44 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10695, 10686])).
% 2.24/2.44 tff(10697,plain,
% 2.24/2.44 ((s(z) = elem!1) <=> (s(z) = s(s(s(s(s(z))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[5529])).
% 2.24/2.44 tff(10698,plain,
% 2.24/2.44 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = elem!1)),
% 2.24/2.44 inference(symmetry,[status(thm)],[10697])).
% 2.24/2.44 tff(10699,plain,
% 2.24/2.44 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(z) = elem!1))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10698])).
% 2.24/2.44 tff(10700,plain,
% 2.24/2.44 (~(s(z) = elem!1)),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[289, 10699])).
% 2.24/2.44 tff(10701,plain,
% 2.24/2.44 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[547, 10700])).
% 2.24/2.44 tff(10702,plain,
% 2.24/2.44 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[5787])).
% 2.24/2.44 tff(10703,plain,
% 2.24/2.44 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.24/2.44 inference(symmetry,[status(thm)],[10702])).
% 2.24/2.44 tff(10704,plain,
% 2.24/2.44 ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(s(z))), s(s(elem!1))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10703])).
% 2.24/2.44 tff(10705,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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(10706,plain,
% 2.24/2.44 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(10707,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(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(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(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10706])).
% 2.24/2.44 tff(10708,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(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(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(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[10707, 10705])).
% 2.24/2.44 tff(10709,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(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(10710,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10709, 10708])).
% 2.24/2.44 tff(10711,plain,
% 2.24/2.44 ((~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10710, 453, 374, 2611])).
% 2.24/2.44 tff(10712,plain,
% 2.24/2.44 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10711, 10689])).
% 2.24/2.44 tff(10713,plain,
% 2.24/2.44 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10712, 10704])).
% 2.24/2.44 tff(10714,plain,
% 2.24/2.44 (r(s(s(s(z))), s(s(elem!1)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[5203, 10713, 10701])).
% 2.24/2.44 tff(10715,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10714, 10696])).
% 2.24/2.44 tff(10716,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~(elem!1 = s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(10717,plain,
% 2.24/2.44 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[10716, 5965, 233, 10683, 10679, 6379])).
% 2.24/2.44 tff(10718,plain,
% 2.24/2.44 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10717, 10675])).
% 2.24/2.44 tff(10719,plain,
% 2.24/2.44 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[3875, 10718, 10674])).
% 2.24/2.44 tff(10720,plain,
% 2.24/2.44 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[10719, 10669])).
% 2.24/2.44 tff(10721,plain,
% 2.24/2.44 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[5965, 7338])).
% 2.24/2.44 tff(10722,plain,
% 2.24/2.44 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[10721, 5915])).
% 2.24/2.44 tff(10723,plain,
% 2.24/2.44 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(elem!1)))),
% 2.24/2.44 inference(symmetry,[status(thm)],[10722])).
% 2.24/2.44 tff(10724,plain,
% 2.24/2.44 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10723])).
% 2.24/2.44 tff(10725,plain,
% 2.24/2.44 (~(elem!1 = s(s(elem!1)))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[2729, 10724])).
% 2.24/2.44 tff(10726,plain,
% 2.24/2.44 (~(s(elem!1) = elem!1)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[3351, 10725])).
% 2.24/2.44 tff(10727,plain,
% 2.24/2.44 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[5965])).
% 2.24/2.44 tff(10728,plain,
% 2.24/2.44 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(s(elem!1), elem!1)),
% 2.24/2.44 inference(symmetry,[status(thm)],[10727])).
% 2.24/2.44 tff(10729,plain,
% 2.24/2.44 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 2.24/2.44 inference(symmetry,[status(thm)],[7337])).
% 2.24/2.44 tff(10730,plain,
% 2.24/2.44 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10729, 5965])).
% 2.24/2.44 tff(10731,plain,
% 2.24/2.44 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.24/2.44 inference(monotonicity,[status(thm)],[7334])).
% 2.24/2.44 tff(10732,plain,
% 2.24/2.44 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) <=> b(s(elem!1), elem!1)),
% 2.24/2.44 inference(transitivity,[status(thm)],[10731, 10730, 10728])).
% 2.24/2.44 tff(10733,plain,
% 2.24/2.44 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) <=> (~b(s(elem!1), elem!1))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10732])).
% 2.24/2.44 tff(10734,plain,
% 2.24/2.44 (b(s(elem!1), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[5786])).
% 2.24/2.44 tff(10735,plain,
% 2.24/2.44 (b(s(s(s(s(s(s(z)))))), s(z)) <=> b(s(elem!1), s(z))),
% 2.24/2.44 inference(symmetry,[status(thm)],[10734])).
% 2.24/2.44 tff(10736,plain,
% 2.24/2.44 ((~b(s(s(s(s(s(s(z)))))), s(z))) <=> (~b(s(elem!1), s(z)))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[10735])).
% 2.24/2.44 tff(10737,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.24/2.44 tff(10738,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(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(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(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10739,plain,
% 2.24/2.45 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10740,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(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10739])).
% 2.24/2.45 tff(10741,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(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[10740, 10738])).
% 2.24/2.45 tff(10742,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(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(10743,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(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[10742, 10741])).
% 2.24/2.45 tff(10744,plain,
% 2.24/2.45 ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10743, 453, 443, 374])).
% 2.24/2.45 tff(10745,plain,
% 2.24/2.45 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10744, 10737])).
% 2.24/2.45 tff(10746,plain,
% 2.24/2.45 (~b(s(elem!1), s(z))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[10745, 10736])).
% 2.24/2.45 tff(10747,plain,
% 2.24/2.45 (r(s(elem!1), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[353, 10746, 197])).
% 2.24/2.45 tff(10748,plain,
% 2.24/2.45 (~(s(elem!1) = s(s(s(z))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[9847, 5795])).
% 2.24/2.45 tff(10749,plain,
% 2.24/2.45 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[5786])).
% 2.24/2.45 tff(10750,plain,
% 2.24/2.45 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.24/2.45 inference(symmetry,[status(thm)],[10749])).
% 2.24/2.45 tff(10751,plain,
% 2.24/2.45 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10750])).
% 2.24/2.45 tff(10752,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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10753,plain,
% 2.24/2.45 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10754,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(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10753])).
% 2.24/2.45 tff(10755,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(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[10754, 10752])).
% 2.24/2.45 tff(10756,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(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(10757,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[10756, 10755])).
% 2.24/2.45 tff(10758,plain,
% 2.24/2.45 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10757, 453, 374, 2611])).
% 2.24/2.45 tff(10759,plain,
% 2.24/2.45 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10758, 10737])).
% 2.24/2.45 tff(10760,plain,
% 2.24/2.45 (~b(s(elem!1), s(s(s(z))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[10759, 10751])).
% 2.24/2.45 tff(10761,plain,
% 2.24/2.45 (r(s(elem!1), s(s(s(z))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1305, 10760, 10748])).
% 2.24/2.45 tff(10762,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3055, 10761, 10747, 257])).
% 2.24/2.45 tff(10763,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (s(elem!1) = s(z)) | (~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(10764,plain,
% 2.24/2.45 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10763, 6231, 257, 5965, 10683, 10679, 6379])).
% 2.24/2.45 tff(10765,plain,
% 2.24/2.45 (~b(s(elem!1), elem!1)),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[10764, 10733])).
% 2.24/2.45 tff(10766,plain,
% 2.24/2.45 (r(s(elem!1), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[2440, 10765, 10726])).
% 2.24/2.45 tff(10767,plain,
% 2.24/2.45 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[5786])).
% 2.24/2.45 tff(10768,plain,
% 2.24/2.45 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[5529])).
% 2.24/2.45 tff(10769,plain,
% 2.24/2.45 (r(s(elem!1), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[10768, 10767])).
% 2.24/2.45 tff(10770,plain,
% 2.24/2.45 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[1892, 10769])).
% 2.24/2.45 tff(10771,assumption,(~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.24/2.45 tff(10772,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10771, 10770])).
% 2.24/2.45 tff(10773,plain,((~r(s(elem!1), elem!1)) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(10774,plain,
% 2.24/2.45 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10773, 10766, 5965])).
% 2.24/2.45 tff(10775,plain,
% 2.24/2.45 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[5788])).
% 2.24/2.45 tff(10776,plain,
% 2.24/2.45 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 2.24/2.45 inference(symmetry,[status(thm)],[10775])).
% 2.24/2.45 tff(10777,plain,
% 2.24/2.45 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(z)) = s(s(s(s(s(s(s(z)))))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10776])).
% 2.24/2.45 tff(10778,plain,
% 2.24/2.45 (~(s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[4227, 10777])).
% 2.24/2.45 tff(10779,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.24/2.45 tff(10780,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.24/2.45 tff(10781,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10782,plain,
% 2.24/2.45 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10783,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10782])).
% 2.24/2.45 tff(10784,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[10783, 10781])).
% 2.24/2.45 tff(10785,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(10786,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[10785, 10784])).
% 2.24/2.45 tff(10787,plain,
% 2.24/2.45 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10786, 268, 10780])).
% 2.24/2.45 tff(10788,plain,
% 2.24/2.45 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10787, 10779])).
% 2.24/2.45 tff(10789,plain,
% 2.24/2.45 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[5787])).
% 2.24/2.45 tff(10790,plain,
% 2.24/2.45 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(elem!1)))),
% 2.24/2.45 inference(symmetry,[status(thm)],[10789])).
% 2.24/2.45 tff(10791,plain,
% 2.24/2.45 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 2.24/2.45 inference(symmetry,[status(thm)],[5786])).
% 2.24/2.45 tff(10792,plain,
% 2.24/2.45 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10791])).
% 2.24/2.45 tff(10793,plain,
% 2.24/2.45 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[10792, 1307])).
% 2.24/2.45 tff(10794,plain,
% 2.24/2.45 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) <=> (s(elem!1) = s(s(elem!1)))),
% 2.24/2.45 inference(transitivity,[status(thm)],[10793, 10790])).
% 2.24/2.45 tff(10795,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 2.24/2.45 tff(10796,plain,
% 2.24/2.45 (s(elem!1) = s(s(elem!1))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[10795, 10794])).
% 2.24/2.45 tff(10797,plain,
% 2.24/2.45 (~(s(elem!1) = s(s(elem!1)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1861, 6035])).
% 2.24/2.45 tff(10798,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10797, 10796])).
% 2.24/2.45 tff(10799,plain,((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z)))))))) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(10800,plain,
% 2.24/2.45 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z)))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10799, 5529])).
% 2.24/2.45 tff(10801,plain,
% 2.24/2.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10802,plain,
% 2.24/2.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(10803,plain,
% 2.24/2.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[10802, 10801])).
% 2.24/2.45 tff(10804,plain,
% 2.24/2.45 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10803, 69, 10800, 10788])).
% 2.24/2.45 tff(10805,plain,
% 2.24/2.45 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(z)))))))),
% 2.24/2.45 inference(commutativity,[status(thm)],[])).
% 2.24/2.45 tff(10806,plain,
% 2.24/2.45 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 2.24/2.45 inference(symmetry,[status(thm)],[10805])).
% 2.24/2.45 tff(10807,plain,
% 2.24/2.45 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(z))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10806])).
% 2.24/2.45 tff(10808,plain,
% 2.24/2.45 (~(s(s(s(s(s(s(z)))))) = s(s(z)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[2661, 10807])).
% 2.24/2.45 tff(10809,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10810,plain,
% 2.24/2.45 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10811,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[10810])).
% 2.24/2.45 tff(10812,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[10811, 10809])).
% 2.24/2.45 tff(10813,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(10814,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[10813, 10812])).
% 2.24/2.45 tff(10815,plain,
% 2.24/2.45 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10814, 268, 10780, 2787])).
% 2.24/2.45 tff(10816,plain,
% 2.24/2.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10817,plain,
% 2.24/2.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(10818,plain,
% 2.24/2.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[10817, 10816])).
% 2.24/2.45 tff(10819,plain,
% 2.24/2.45 ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10818, 69, 10815])).
% 2.24/2.45 tff(10820,plain,
% 2.24/2.45 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[10819, 10808])).
% 2.24/2.45 tff(10821,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(10822,plain,
% 2.24/2.45 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10823,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10822])).
% 2.24/2.46 tff(10824,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[10823, 10821])).
% 2.24/2.46 tff(10825,plain,
% 2.24/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(10826,plain,
% 2.24/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[10825, 10824])).
% 2.24/2.46 tff(10827,plain,
% 2.24/2.46 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10826, 268, 10780, 2787])).
% 2.24/2.46 tff(10828,plain,
% 2.24/2.46 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[822, 69, 2661, 10827])).
% 2.24/2.46 tff(10829,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(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10830,plain,
% 2.24/2.46 (((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10831,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(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(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(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10830])).
% 2.24/2.46 tff(10832,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(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(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(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[10831, 10829])).
% 2.24/2.46 tff(10833,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(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(10834,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(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[10833, 10832])).
% 2.24/2.46 tff(10835,plain,
% 2.24/2.46 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10834, 453, 10828, 10820, 10804])).
% 2.24/2.46 tff(10836,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10837,plain,
% 2.24/2.46 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10838,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10837])).
% 2.24/2.46 tff(10839,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[10838, 10836])).
% 2.24/2.46 tff(10840,plain,
% 2.24/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(10841,plain,
% 2.24/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[10840, 10839])).
% 2.24/2.46 tff(10842,plain,
% 2.24/2.46 ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10841, 268, 2787])).
% 2.24/2.46 tff(10843,plain,
% 2.24/2.46 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10842, 10779])).
% 2.24/2.46 tff(10844,plain,
% 2.24/2.46 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[8583, 69, 10843])).
% 2.24/2.46 tff(10845,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10844, 10835, 10778])).
% 2.24/2.46 tff(10846,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (s(s(z)) = s(s(elem!1))) | (~(elem!1 = s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(10847,plain,
% 2.24/2.46 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10846, 10774, 5965, 10720, 6232])).
% 2.24/2.46 tff(10848,plain,
% 2.24/2.46 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[5529])).
% 2.24/2.46 tff(10849,plain,
% 2.24/2.46 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[700, 10848])).
% 2.24/2.46 tff(10850,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3226, 10849])).
% 2.24/2.46 tff(10851,plain,((~r(s(s(z)), elem!1)) | r(s(s(z)), s(s(s(s(s(z)))))) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(10852,plain,
% 2.24/2.46 (~r(s(s(z)), elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10851, 10847, 5965])).
% 2.24/2.46 tff(10853,plain,
% 2.24/2.46 (b(s(s(z)), elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[782, 10852, 4060])).
% 2.24/2.46 tff(10854,plain,
% 2.24/2.46 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[10853, 10667])).
% 2.24/2.46 tff(10855,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(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10856,plain,
% 2.24/2.46 (((~b(s(s(s(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(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10857,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(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(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10856])).
% 2.24/2.46 tff(10858,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(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(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[10857, 10855])).
% 2.24/2.46 tff(10859,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(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(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(10860,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(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[10859, 10858])).
% 2.24/2.46 tff(10861,plain,
% 2.24/2.46 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10860, 453, 10683, 10679])).
% 2.24/2.46 tff(10862,plain,
% 2.24/2.46 (~b(s(s(s(z))), s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10861, 10854])).
% 2.24/2.46 tff(10863,plain,
% 2.24/2.46 (r(s(s(s(z))), s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2534, 69, 160, 10862])).
% 2.24/2.46 tff(10864,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(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10865,plain,
% 2.24/2.46 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10866,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(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z)))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10865])).
% 2.24/2.46 tff(10867,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(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[10866, 10864])).
% 2.24/2.46 tff(10868,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(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(10869,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z)))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[10868, 10867])).
% 2.24/2.46 tff(10870,plain,
% 2.24/2.46 ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10869, 453, 6379, 10683])).
% 2.24/2.46 tff(10871,plain,
% 2.24/2.46 (~b(s(s(z)), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10870, 10854])).
% 2.24/2.46 tff(10872,plain,
% 2.24/2.46 (r(s(s(z)), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[720, 69, 717, 10871])).
% 2.24/2.46 tff(10873,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10626, 268, 233, 10872, 10863])).
% 2.24/2.46 tff(10874,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~r(s(s(s(z))), s(z))) | (s(s(z)) = elem!1) | (~r(s(z), s(s(s(z))))) | r(s(s(s(z))), elem!1) | r(elem!1, s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(10875,plain,
% 2.24/2.46 (r(s(z), elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10874, 2, 233, 257, 5168, 2076, 5988])).
% 2.24/2.46 tff(10876,plain,
% 2.24/2.46 (b(s(s(s(z))), elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[74, 2, 59])).
% 2.24/2.46 tff(10877,plain,
% 2.24/2.46 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[5959, 3609])).
% 2.24/2.46 tff(10878,plain,
% 2.24/2.46 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10877])).
% 2.24/2.46 tff(10879,plain,
% 2.24/2.46 (~(elem!1 = s(s(s(s(z)))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[319, 10878])).
% 2.24/2.46 tff(10880,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(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10881,plain,
% 2.24/2.46 (((~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(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10882,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(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(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10881])).
% 2.24/2.46 tff(10883,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(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(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[10882, 10880])).
% 2.24/2.46 tff(10884,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(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)))))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(10885,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(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[10884, 10883])).
% 2.24/2.46 tff(10886,plain,
% 2.24/2.46 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[10885, 453, 1764, 758, 721])).
% 2.24/2.46 tff(10887,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(elem!1, s(z))) | (~b(elem!1, s(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(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10888,plain,
% 2.24/2.46 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(10889,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(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[10888])).
% 2.24/2.46 tff(10890,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(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[10889, 10887])).
% 2.24/2.46 tff(10891,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(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(10892,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[10891, 10890])).
% 2.24/2.47 tff(10893,plain,
% 2.24/2.47 (~b(elem!1, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10892, 453, 2077, 1764, 758])).
% 2.24/2.47 tff(10894,plain,
% 2.24/2.47 (r(elem!1, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1087, 10893, 1055])).
% 2.24/2.47 tff(10895,plain,
% 2.24/2.47 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6942, 10894, 700])).
% 2.24/2.47 tff(10896,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2370, 69, 10895, 2359, 10886])).
% 2.24/2.47 tff(10897,plain,((~r(s(s(z)), elem!1)) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(10898,plain,
% 2.24/2.47 (~r(s(s(z)), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10897, 8419, 10879, 2077, 701])).
% 2.24/2.47 tff(10899,plain,
% 2.24/2.47 (b(s(s(z)), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[782, 10898, 5988])).
% 2.24/2.47 tff(10900,plain,
% 2.24/2.47 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[5170])).
% 2.24/2.47 tff(10901,plain,
% 2.24/2.47 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[5171])).
% 2.24/2.47 tff(10902,plain,
% 2.24/2.47 ((~b(s(s(elem!1)), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[10901])).
% 2.24/2.47 tff(10903,plain,
% 2.24/2.47 (~r(s(s(elem!1)), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[3393, 869, 701])).
% 2.24/2.47 tff(10904,plain,
% 2.24/2.47 (b(s(s(elem!1)), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1047, 10903])).
% 2.24/2.47 tff(10905,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(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), 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(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10906,plain,
% 2.24/2.47 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10907,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(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[10906])).
% 2.24/2.47 tff(10908,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(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[10907, 10905])).
% 2.24/2.47 tff(10909,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(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(10910,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(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[10909, 10908])).
% 2.24/2.47 tff(10911,plain,
% 2.24/2.47 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10910, 453, 10904, 8419, 3675])).
% 2.24/2.47 tff(10912,plain,
% 2.24/2.47 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[10911, 10902])).
% 2.24/2.47 tff(10913,plain,
% 2.24/2.47 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2696, 10912])).
% 2.24/2.47 tff(10914,plain,
% 2.24/2.47 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[10913, 10900])).
% 2.24/2.47 tff(10915,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10916,plain,
% 2.24/2.47 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10917,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[10916])).
% 2.24/2.47 tff(10918,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[10917, 10915])).
% 2.24/2.47 tff(10919,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(10920,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[10919, 10918])).
% 2.24/2.47 tff(10921,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10920, 268, 869, 1159, 10914])).
% 2.24/2.47 tff(10922,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~(s(s(s(s(s(z))))) = elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(10923,plain,
% 2.24/2.47 (~r(s(s(elem!1)), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10922, 1159, 5168, 701])).
% 2.24/2.47 tff(10924,plain,
% 2.24/2.47 (b(s(s(elem!1)), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2240, 10923, 5180])).
% 2.24/2.47 tff(10925,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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10926,plain,
% 2.24/2.47 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10927,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), 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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[10926])).
% 2.24/2.47 tff(10928,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), 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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 2.24/2.47 inference(transitivity,[status(thm)],[10927, 10925])).
% 2.24/2.47 tff(10929,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(10930,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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[10929, 10928])).
% 2.24/2.47 tff(10931,plain,
% 2.24/2.47 (~b(s(s(z)), s(s(elem!1)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10930, 453, 2077, 10924, 10899])).
% 2.24/2.47 tff(10932,plain,
% 2.24/2.47 (r(s(s(z)), s(s(elem!1)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[4239, 69, 6232, 10931])).
% 2.24/2.47 tff(10933,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(elem!1, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10934,plain,
% 2.24/2.47 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10935,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[10934])).
% 2.24/2.47 tff(10936,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.24/2.47 inference(transitivity,[status(thm)],[10935, 10933])).
% 2.24/2.47 tff(10937,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(10938,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(elem!1, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[10937, 10936])).
% 2.24/2.47 tff(10939,plain,
% 2.24/2.47 (~b(s(s(z)), s(s(s(z))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10938, 453, 2077, 1291, 10899])).
% 2.24/2.47 tff(10940,plain,
% 2.24/2.47 ((s(s(z)) = s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1350, 69, 10939])).
% 2.24/2.47 tff(10941,plain,
% 2.24/2.47 (r(s(s(z)), s(s(s(z))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10940, 1243])).
% 2.24/2.47 tff(10942,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(z))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10943,plain,
% 2.24/2.47 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10944,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[10943])).
% 2.24/2.47 tff(10945,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.24/2.47 inference(transitivity,[status(thm)],[10944, 10942])).
% 2.24/2.47 tff(10946,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(10947,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(z))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[10946, 10945])).
% 2.24/2.47 tff(10948,plain,
% 2.24/2.47 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10947, 453, 2077, 10924, 1291])).
% 2.24/2.47 tff(10949,plain,
% 2.24/2.47 (r(s(s(s(z))), s(s(elem!1)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5203, 10948, 5952])).
% 2.24/2.47 tff(10950,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10951,plain,
% 2.24/2.47 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10952,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[10951])).
% 2.24/2.47 tff(10953,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[10952, 10950])).
% 2.24/2.47 tff(10954,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(10955,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[10954, 10953])).
% 2.24/2.47 tff(10956,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10955, 268, 10949, 10941, 10932])).
% 2.24/2.47 tff(10957,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~(s(s(s(s(s(z))))) = elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(10958,plain,
% 2.24/2.47 (~r(s(s(s(s(z)))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10957, 10876, 6396, 5168, 10875])).
% 2.24/2.47 tff(10959,plain,
% 2.24/2.47 (b(s(s(s(s(z)))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[254, 10958, 5961])).
% 2.24/2.47 tff(10960,plain,
% 2.24/2.47 (~b(s(s(z)), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[7330, 10959, 6396, 10876])).
% 2.24/2.47 tff(10961,plain,
% 2.24/2.47 (r(s(s(z)), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[782, 10960, 5988])).
% 2.24/2.47 tff(10962,plain,
% 2.24/2.47 (~b(s(s(s(s(z)))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10897, 10961, 10879, 6396, 10875])).
% 2.24/2.47 tff(10963,plain,
% 2.24/2.47 (r(s(s(s(s(z)))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1098, 10962])).
% 2.24/2.47 tff(10964,plain,
% 2.24/2.47 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[4119, 10963, 233])).
% 2.24/2.47 tff(10965,plain,
% 2.24/2.47 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[518, 10964])).
% 2.24/2.47 tff(10966,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[7265, 453, 6396, 10965, 10876, 10959])).
% 2.24/2.47 tff(10967,plain,(r(s(s(s(z))), elem!1) | (~r(s(s(s(z))), s(z))) | (~(s(s(s(s(s(z))))) = elem!1)) | (~r(s(z), s(s(s(z))))) | r(elem!1, s(z)) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(10968,plain,
% 2.24/2.47 (r(s(s(s(z))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[10967, 5168, 233, 257, 2076, 59])).
% 2.24/2.47 tff(10969,plain,
% 2.24/2.47 (~r(s(z), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[4885, 1545, 257])).
% 2.24/2.47 tff(10970,plain,
% 2.24/2.47 (b(s(z), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[506, 10969, 5951])).
% 2.24/2.47 tff(10971,plain,
% 2.24/2.47 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5574, 299, 922, 499, 2077])).
% 2.24/2.47 tff(10972,plain,
% 2.24/2.47 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1098, 10971])).
% 2.24/2.47 tff(10973,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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10974,plain,
% 2.24/2.47 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(10975,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[10974])).
% 2.24/2.48 tff(10976,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[10975, 10973])).
% 2.24/2.48 tff(10977,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(10978,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[10977, 10976])).
% 2.24/2.48 tff(10979,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10978, 453, 499, 2077, 10972, 299])).
% 2.24/2.48 tff(10980,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(10981,plain,
% 2.24/2.48 (~b(s(s(s(s(z)))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10980, 922, 2077, 499])).
% 2.24/2.48 tff(10982,plain,
% 2.24/2.48 (r(s(s(s(s(z)))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[254, 10981, 5961])).
% 2.24/2.48 tff(10983,plain,
% 2.24/2.48 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10920, 268, 869, 1159])).
% 2.24/2.48 tff(10984,plain,
% 2.24/2.48 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5232, 69, 5229, 10983])).
% 2.24/2.48 tff(10985,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(10986,plain,
% 2.24/2.48 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(10987,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[10986])).
% 2.24/2.48 tff(10988,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[10987, 10985])).
% 2.24/2.48 tff(10989,plain,
% 2.24/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(10990,plain,
% 2.24/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[10989, 10988])).
% 2.24/2.48 tff(10991,plain,
% 2.24/2.48 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10990, 268, 869, 1159])).
% 2.24/2.48 tff(10992,plain,
% 2.24/2.48 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[10991, 5238])).
% 2.24/2.48 tff(10993,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6308, 10992])).
% 2.24/2.48 tff(10994,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[10993, 5236])).
% 2.24/2.48 tff(10995,plain,
% 2.24/2.48 (b(s(s(s(z))), s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5203, 6719, 5952])).
% 2.24/2.48 tff(10996,plain,
% 2.24/2.48 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5290, 268, 1545, 1159])).
% 2.24/2.48 tff(10997,plain,
% 2.24/2.48 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1656, 10996])).
% 2.24/2.48 tff(10998,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(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(10999,plain,
% 2.24/2.48 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(11000,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(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[10999])).
% 2.24/2.48 tff(11001,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(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[11000, 10998])).
% 2.24/2.48 tff(11002,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(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(11003,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[11002, 11001])).
% 2.24/2.48 tff(11004,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11003, 453, 5340, 10997, 10995, 10994, 10984])).
% 2.24/2.48 tff(11005,plain,((~r(s(s(elem!1)), elem!1)) | (~(s(s(s(s(s(z))))) = elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(11006,plain,
% 2.24/2.48 (~r(s(s(elem!1)), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11005, 10982, 5168, 1545])).
% 2.24/2.48 tff(11007,plain,
% 2.24/2.48 (b(s(s(elem!1)), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2240, 11006, 5180])).
% 2.24/2.48 tff(11008,plain,
% 2.24/2.48 (~b(s(s(z)), s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10930, 453, 2077, 11007, 922])).
% 2.24/2.48 tff(11009,plain,
% 2.24/2.48 (r(s(s(z)), s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[4239, 69, 6232, 11008])).
% 2.24/2.48 tff(11010,plain,
% 2.24/2.48 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(11011,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[11010])).
% 2.24/2.48 tff(11012,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 2.24/2.48 inference(transitivity,[status(thm)],[11011, 5182])).
% 2.24/2.48 tff(11013,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(11014,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[11013, 11012])).
% 2.24/2.48 tff(11015,plain,
% 2.24/2.48 (~b(s(s(elem!1)), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11014, 453, 499, 2077, 11007])).
% 2.24/2.48 tff(11016,plain,
% 2.24/2.48 (r(s(s(elem!1)), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1047, 11015])).
% 2.24/2.48 tff(11017,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[7068, 268, 11016, 5572, 11009])).
% 2.24/2.48 tff(11018,plain,((~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~(s(s(s(s(s(z))))) = elem!1)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(11019,plain,
% 2.24/2.48 (~b(s(s(z)), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11018, 2077, 10970, 5168, 1545])).
% 2.24/2.48 tff(11020,plain,
% 2.24/2.48 (r(s(s(z)), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[782, 11019, 5988])).
% 2.24/2.48 tff(11021,plain,
% 2.24/2.48 (~r(s(s(z)), s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[4235, 268, 5189, 700])).
% 2.24/2.48 tff(11022,plain,
% 2.24/2.48 (b(s(s(z)), s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[4239, 69, 4227, 11021])).
% 2.24/2.48 tff(11023,plain,
% 2.24/2.48 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5213, 5189, 1545])).
% 2.24/2.48 tff(11024,plain,
% 2.24/2.48 (b(s(s(s(z))), s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5203, 11023, 555])).
% 2.24/2.48 tff(11025,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(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(11026,plain,
% 2.24/2.48 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(11027,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(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[11026])).
% 2.24/2.48 tff(11028,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(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[11027, 11025])).
% 2.24/2.48 tff(11029,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(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(11030,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[11029, 11028])).
% 2.24/2.48 tff(11031,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11030, 453, 1050, 11024, 7167, 11022])).
% 2.24/2.48 tff(11032,plain,((~b(s(s(elem!1)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(z)), elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (s(s(elem!1)) = elem!1) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(11033,plain,
% 2.24/2.48 (~b(s(s(elem!1)), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11032, 6232, 11020, 5952, 1545, 5180, 10970, 2077])).
% 2.24/2.48 tff(11034,plain,
% 2.24/2.48 (r(s(s(elem!1)), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1047, 11033])).
% 2.24/2.48 tff(11035,plain,
% 2.24/2.48 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5282, 299, 257, 5168, 2077, 5952, 1545, 11034, 10970])).
% 2.24/2.48 tff(11036,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1098, 11035])).
% 2.24/2.48 tff(11037,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10978, 453, 10970, 2077, 11036, 299])).
% 2.24/2.48 tff(11038,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~(s(s(s(s(s(z))))) = elem!1)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(11039,plain,
% 2.24/2.48 (~b(s(s(s(s(z)))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11038, 6396, 257, 5168, 10968])).
% 2.24/2.48 tff(11040,plain,
% 2.24/2.48 (r(s(s(s(s(z)))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[254, 11039, 5961])).
% 2.24/2.48 tff(11041,plain,
% 2.24/2.48 (~r(s(z), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[4885, 10968, 257])).
% 2.24/2.48 tff(11042,plain,
% 2.24/2.48 (b(s(z), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[506, 11041, 5951])).
% 2.24/2.48 tff(11043,plain,
% 2.24/2.48 (~b(s(s(z)), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11018, 6396, 11042, 5168, 10968])).
% 2.24/2.48 tff(11044,plain,
% 2.24/2.48 (r(s(s(z)), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[782, 11043, 5988])).
% 2.24/2.48 tff(11045,plain,
% 2.24/2.48 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2058, 268, 11044, 11040])).
% 2.24/2.48 tff(11046,plain,
% 2.24/2.48 (~r(s(s(s(z))), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5861, 268, 11044, 10968])).
% 2.24/2.48 tff(11047,plain,
% 2.24/2.48 (b(s(s(s(z))), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2534, 69, 160, 11046])).
% 2.24/2.48 tff(11048,plain,
% 2.24/2.48 (~r(s(s(z)), s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5719, 268, 11044, 10968])).
% 2.24/2.48 tff(11049,plain,
% 2.24/2.48 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1350, 69, 11048])).
% 2.24/2.48 tff(11050,plain,
% 2.24/2.48 (b(s(s(z)), s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11049, 1243])).
% 2.24/2.48 tff(11051,plain,
% 2.24/2.48 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[4961, 11040, 10968])).
% 2.24/2.48 tff(11052,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[518, 11051])).
% 2.24/2.48 tff(11053,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(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(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(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(z)), s(s(s(z))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(11054,plain,
% 2.24/2.48 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(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(z)), s(s(s(z))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(11055,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(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(z)), s(s(s(z)))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[11054])).
% 2.24/2.48 tff(11056,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(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(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(z)), s(s(s(z))))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[11055, 11053])).
% 2.24/2.48 tff(11057,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(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(11058,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[11057, 11056])).
% 2.24/2.48 tff(11059,plain,
% 2.24/2.48 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11058, 453, 11052, 11050, 11047])).
% 2.24/2.48 tff(11060,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[795, 69, 153, 11059, 11045])).
% 2.24/2.48 tff(11061,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | r(elem!1, s(z)) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(11062,plain,
% 2.24/2.48 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11061, 3448, 228, 10664, 10665])).
% 2.24/2.48 tff(11063,plain,
% 2.24/2.48 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8839, 11062])).
% 2.24/2.48 tff(11064,plain,
% 2.24/2.48 (~r(elem!1, s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1157, 1149, 257])).
% 2.24/2.48 tff(11065,plain,
% 2.24/2.48 (~(s(s(s(z))) = elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2086, 128, 11064])).
% 2.24/2.48 tff(11066,plain,
% 2.24/2.48 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11061, 3448, 257, 11064, 11065])).
% 2.24/2.48 tff(11067,plain,
% 2.24/2.48 (~(elem!1 = s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[8856, 1291, 128])).
% 2.24/2.48 tff(11068,plain,
% 2.24/2.48 (~(s(z) = elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1125, 11067])).
% 2.24/2.48 tff(11069,plain,
% 2.24/2.48 (b(s(z), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[506, 11068, 4541])).
% 2.24/2.48 tff(11070,plain,
% 2.24/2.48 (b(elem!1, s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1130, 11067, 11064])).
% 2.24/2.48 tff(11071,plain,
% 2.24/2.48 (~b(s(s(s(z))), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[7324, 453, 6754, 1291, 922])).
% 2.24/2.48 tff(11072,plain,
% 2.24/2.48 (r(s(s(s(z))), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2534, 69, 160, 11071])).
% 2.24/2.48 tff(11073,plain,
% 2.24/2.48 (~b(s(s(z)), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5570, 453, 9870, 6754, 922])).
% 2.24/2.48 tff(11074,plain,
% 2.24/2.48 (r(s(s(z)), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[720, 69, 717, 11073])).
% 2.24/2.48 tff(11075,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[10626, 268, 233, 11074, 11072])).
% 2.24/2.48 tff(11076,plain,((elem!1 = s(z)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | r(s(z), elem!1) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(11077,plain,
% 2.24/2.48 (elem!1 = s(z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11076, 1291, 3448, 922, 4541, 2076])).
% 2.24/2.48 tff(11078,plain,
% 2.24/2.48 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(z))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[11077])).
% 2.24/2.48 tff(11079,plain,
% 2.24/2.48 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 2.24/2.48 inference(symmetry,[status(thm)],[11078])).
% 2.24/2.48 tff(11080,plain,
% 2.24/2.48 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(s(z))), elem!1))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[11079])).
% 2.24/2.48 tff(11081,plain,
% 2.24/2.48 (~b(s(s(s(z))), elem!1)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[128, 11080])).
% 2.24/2.48 tff(11082,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1291, 11081])).
% 2.24/2.48 tff(11083,plain,((~b(s(s(s(z))), elem!1)) | b(s(s(s(z))), s(z)) | (~b(s(s(z)), elem!1)) | r(s(z), elem!1) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(11084,plain,
% 2.24/2.48 (~b(s(s(z)), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[11083, 1291, 128, 4541, 11064])).
% 2.24/2.48 tff(11085,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(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11086,plain,
% 2.24/2.49 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11087,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(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[11086])).
% 2.24/2.49 tff(11088,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(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[11087, 11085])).
% 2.24/2.49 tff(11089,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(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(11090,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[11089, 11088])).
% 2.24/2.49 tff(11091,plain,
% 2.24/2.49 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11090, 453, 2077, 8909, 298])).
% 2.24/2.49 tff(11092,plain,
% 2.24/2.49 (r(elem!1, s(s(s(s(s(z))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[466, 11091, 8840])).
% 2.24/2.49 tff(11093,plain,
% 2.24/2.49 (r(s(s(z)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[3468])).
% 2.24/2.49 tff(11094,plain,
% 2.24/2.49 (r(elem!1, s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 2.24/2.49 inference(symmetry,[status(thm)],[11093])).
% 2.24/2.49 tff(11095,plain,
% 2.24/2.49 (r(s(s(z)), s(s(s(z))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[1149, 11094])).
% 2.24/2.49 tff(11096,plain,
% 2.24/2.49 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[3468])).
% 2.24/2.49 tff(11097,plain,
% 2.24/2.49 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.49 inference(symmetry,[status(thm)],[11096])).
% 2.24/2.49 tff(11098,plain,
% 2.24/2.49 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[412, 11097])).
% 2.24/2.49 tff(11099,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2795, 11098, 11095, 256])).
% 2.24/2.49 tff(11100,plain,((~(s(s(z)) = elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(11101,plain,
% 2.24/2.49 (~(s(s(z)) = elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11100, 256, 11092, 1149])).
% 2.24/2.49 tff(11102,plain,
% 2.24/2.49 (r(s(s(z)), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[782, 11101, 4])).
% 2.24/2.49 tff(11103,plain,
% 2.24/2.49 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[9558, 11102, 11092])).
% 2.24/2.49 tff(11104,plain,
% 2.24/2.49 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5711, 69, 11103, 54])).
% 2.24/2.49 tff(11105,plain,
% 2.24/2.49 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5331, 298, 2077, 499])).
% 2.24/2.49 tff(11106,plain,
% 2.24/2.49 (r(s(s(s(s(s(z))))), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[643, 11105, 637])).
% 2.24/2.49 tff(11107,plain,
% 2.24/2.49 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[775, 268, 11102, 11106])).
% 2.24/2.49 tff(11108,plain,
% 2.24/2.49 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[4081, 11107])).
% 2.24/2.49 tff(11109,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(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11110,plain,
% 2.24/2.49 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11111,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(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[11110])).
% 2.24/2.49 tff(11112,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(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[11111, 11109])).
% 2.24/2.49 tff(11113,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(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(11114,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(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[11113, 11112])).
% 2.24/2.49 tff(11115,plain,
% 2.24/2.49 (~b(s(z), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11114, 453, 8909, 11108, 11104])).
% 2.24/2.49 tff(11116,plain,
% 2.24/2.49 (r(s(z), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[757, 11115])).
% 2.24/2.49 tff(11117,plain,
% 2.24/2.49 (~r(s(s(s(z))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[9038, 11116, 257])).
% 2.24/2.49 tff(11118,plain,
% 2.24/2.49 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[9415, 11092, 1149])).
% 2.24/2.49 tff(11119,plain,
% 2.24/2.49 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2570, 11118])).
% 2.24/2.49 tff(11120,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(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11121,plain,
% 2.24/2.49 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11122,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(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[11121])).
% 2.24/2.49 tff(11123,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(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[11122, 11120])).
% 2.24/2.49 tff(11124,plain,
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% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(11125,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[11124, 11123])).
% 2.24/2.49 tff(11126,plain,
% 2.24/2.49 (~b(s(s(s(z))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11125, 453, 11119, 11108, 11104])).
% 2.24/2.49 tff(11127,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2534, 69, 160, 11126, 11117])).
% 2.24/2.49 tff(11128,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | b(s(s(z)), elem!1) | (~r(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (s(s(s(s(s(z))))) = elem!1) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(11129,plain,
% 2.24/2.49 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11128, 11084, 257, 1149, 11070, 11066, 11069])).
% 2.24/2.49 tff(11130,plain,
% 2.24/2.49 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[687, 11129])).
% 2.24/2.49 tff(11131,plain,
% 2.24/2.49 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[8475, 1159, 1149])).
% 2.24/2.49 tff(11132,plain,
% 2.24/2.49 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[518, 11131])).
% 2.24/2.49 tff(11133,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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11134,plain,
% 2.24/2.49 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11135,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(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[11134])).
% 2.24/2.49 tff(11136,plain,
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% 2.24/2.49 inference(transitivity,[status(thm)],[11135, 11133])).
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% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
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% 2.24/2.49 inference(modus_ponens,[status(thm)],[11137, 11136])).
% 2.24/2.49 tff(11139,plain,
% 2.24/2.49 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11138, 453, 11132, 1291, 1779])).
% 2.24/2.49 tff(11140,plain,
% 2.24/2.49 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[328, 11139])).
% 2.24/2.49 tff(11141,plain,
% 2.24/2.49 (~r(s(s(s(s(s(z))))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2414, 301, 1132])).
% 2.24/2.49 tff(11142,plain,
% 2.24/2.49 (b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[297, 11141])).
% 2.24/2.49 tff(11143,plain,
% 2.24/2.49 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5352, 301, 1159, 1132])).
% 2.24/2.49 tff(11144,plain,
% 2.24/2.49 (b(s(s(s(s(s(z))))), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[643, 11143, 637])).
% 2.24/2.49 tff(11145,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5331, 11144, 11142, 499, 2077])).
% 2.24/2.49 tff(11146,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(11147,plain,
% 2.24/2.49 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11146, 11140, 637, 499, 2077, 1159])).
% 2.24/2.49 tff(11148,plain,
% 2.24/2.49 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1098, 11147])).
% 2.24/2.49 tff(11149,plain,
% 2.24/2.49 (~b(elem!1, s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5442, 453, 499, 2077, 11148])).
% 2.24/2.49 tff(11150,plain,
% 2.24/2.49 (r(elem!1, s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1087, 11149, 1055])).
% 2.24/2.49 tff(11151,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, 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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11152,plain,
% 2.24/2.49 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11153,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[11152])).
% 2.24/2.49 tff(11154,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[11153, 11151])).
% 2.24/2.49 tff(11155,plain,
% 2.24/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(11156,plain,
% 2.24/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[11155, 11154])).
% 2.24/2.49 tff(11157,plain,
% 2.24/2.49 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[11156, 268, 11140, 11150])).
% 2.24/2.49 tff(11158,plain,
% 2.24/2.49 (b(s(s(s(s(s(z))))), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[643, 11157, 637])).
% 2.24/2.49 tff(11159,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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(11160,plain,
% 2.24/2.49 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.24/2.50 inference(rewrite,[status(thm)],[])).
% 2.24/2.50 tff(11161,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.24/2.50 inference(monotonicity,[status(thm)],[11160])).
% 2.24/2.50 tff(11162,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.24/2.50 inference(transitivity,[status(thm)],[11161, 11159])).
% 2.24/2.50 tff(11163,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.50 inference(quant_inst,[status(thm)],[])).
% 2.24/2.50 tff(11164,plain,
% 2.24/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.24/2.50 inference(modus_ponens,[status(thm)],[11163, 11162])).
% 2.24/2.50 tff(11165,plain,
% 2.24/2.50 ($false),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[11164, 453, 499, 2077, 443, 646])).
% 2.24/2.50 tff(11166,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.50 tff(11167,plain,
% 2.24/2.50 (~b(s(z), s(s(s(s(s(z))))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[11166, 11158, 2077, 499])).
% 2.24/2.50 tff(11168,plain,
% 2.24/2.50 (r(s(z), s(s(s(s(s(z))))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[372, 11167])).
% 2.24/2.50 tff(11169,plain,
% 2.24/2.50 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[9017, 11168, 257])).
% 2.24/2.50 tff(11170,plain,
% 2.24/2.50 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[2570, 11169])).
% 2.24/2.50 tff(11171,plain,
% 2.24/2.50 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[2596, 11132, 1291, 1779])).
% 2.24/2.50 tff(11172,plain,
% 2.24/2.50 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[2463, 69, 11171, 2453])).
% 2.24/2.50 tff(11173,plain,
% 2.24/2.50 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[427, 11150, 11172])).
% 2.24/2.50 tff(11174,plain,
% 2.24/2.50 (b(elem!1, s(s(s(s(s(z))))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[466, 11173, 8840])).
% 2.24/2.50 tff(11175,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(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.24/2.50 inference(rewrite,[status(thm)],[])).
% 2.24/2.50 tff(11176,plain,
% 2.24/2.50 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(11177,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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[11176])).
% 2.34/2.50 tff(11178,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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.34/2.50 inference(transitivity,[status(thm)],[11177, 11175])).
% 2.34/2.50 tff(11179,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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(11180,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[11179, 11178])).
% 2.34/2.50 tff(11181,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[11180, 453, 1291, 11174, 1779, 11170])).
% 2.34/2.50 tff(11182,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (elem!1 = s(s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(11183,plain,
% 2.34/2.50 (~r(s(s(s(s(z)))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[11182, 1291, 11130, 257, 11070, 11069, 11066, 9, 1149])).
% 2.34/2.50 tff(11184,plain,
% 2.34/2.50 (b(s(s(s(s(z)))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[254, 11183, 3])).
% 2.34/2.50 tff(11185,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(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, 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(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(11186,plain,
% 2.34/2.50 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(11187,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[11186])).
% 2.34/2.50 tff(11188,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.34/2.50 inference(transitivity,[status(thm)],[11187, 11185])).
% 2.34/2.50 tff(11189,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(11190,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[11189, 11188])).
% 2.34/2.50 tff(11191,plain,
% 2.34/2.50 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[11190, 453, 11070, 1291, 11184])).
% 2.34/2.50 tff(11192,plain,
% 2.34/2.50 (~b(s(s(s(s(z)))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[10978, 453, 11069, 11070, 11184])).
% 2.34/2.50 tff(11193,plain,
% 2.34/2.50 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7911, 11192, 11067])).
% 2.34/2.50 tff(11194,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1656, 11193, 11191])).
% 2.34/2.50 tff(11195,plain,((~b(s(s(s(z))), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | r(s(z), elem!1) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(11196,plain,
% 2.34/2.50 (~b(s(s(s(z))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[11195, 128, 228, 1149, 4541, 3])).
% 2.34/2.50 tff(11197,plain,
% 2.34/2.50 (r(s(s(s(z))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[74, 11196, 10665])).
% 2.34/2.50 tff(11198,plain,
% 2.34/2.50 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[4144, 10665])).
% 2.34/2.50 tff(11199,plain,
% 2.34/2.50 (r(s(z), s(s(z))) <=> r(elem!1, s(elem!1))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[1121, 3164])).
% 2.34/2.50 tff(11200,plain,
% 2.34/2.50 (r(elem!1, s(elem!1)) <=> r(s(z), s(s(z)))),
% 2.34/2.50 inference(symmetry,[status(thm)],[11199])).
% 2.34/2.50 tff(11201,plain,
% 2.34/2.50 (~(elem!1 = s(elem!1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[8957, 10573])).
% 2.34/2.50 tff(11202,plain,
% 2.34/2.50 (b(elem!1, s(z)) <=> b(elem!1, elem!1)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[1121])).
% 2.34/2.50 tff(11203,plain,
% 2.34/2.50 (b(elem!1, elem!1) <=> b(elem!1, s(z))),
% 2.34/2.50 inference(symmetry,[status(thm)],[11202])).
% 2.34/2.50 tff(11204,plain,
% 2.34/2.50 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(z)))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[11203])).
% 2.34/2.50 tff(11205,plain,
% 2.34/2.50 (~b(elem!1, s(z))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[1707, 11204])).
% 2.34/2.50 tff(11206,plain,
% 2.34/2.50 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[10229, 11205, 221, 1545, 233])).
% 2.34/2.50 tff(11207,plain,
% 2.34/2.50 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[4499, 3700])).
% 2.34/2.50 tff(11208,plain,
% 2.34/2.50 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[10478])).
% 2.34/2.50 tff(11209,plain,
% 2.34/2.50 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 2.34/2.50 inference(symmetry,[status(thm)],[11208])).
% 2.34/2.50 tff(11210,plain,
% 2.34/2.50 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2551, 10568])).
% 2.34/2.50 tff(11211,plain,
% 2.34/2.50 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2821, 10568, 11210])).
% 2.34/2.50 tff(11212,plain,
% 2.34/2.50 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[10478])).
% 2.34/2.50 tff(11213,plain,
% 2.34/2.50 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) <=> (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[11212])).
% 2.34/2.50 tff(11214,plain,
% 2.34/2.50 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[3165])).
% 2.34/2.50 tff(11215,plain,
% 2.34/2.50 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[11214])).
% 2.34/2.50 tff(11216,plain,
% 2.34/2.50 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[8918, 11215])).
% 2.34/2.50 tff(11217,plain,
% 2.34/2.50 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[10478])).
% 2.34/2.50 tff(11218,plain,
% 2.34/2.50 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.34/2.50 inference(transitivity,[status(thm)],[11217, 10014])).
% 2.34/2.50 tff(11219,plain,
% 2.34/2.50 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 2.34/2.50 inference(symmetry,[status(thm)],[11218])).
% 2.34/2.50 tff(11220,plain,
% 2.34/2.50 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[11219])).
% 2.34/2.50 tff(11221,plain,
% 2.34/2.50 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[142, 11220])).
% 2.34/2.50 tff(11222,plain,
% 2.34/2.50 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[5232, 69, 11221, 11216])).
% 2.34/2.50 tff(11223,plain,
% 2.34/2.50 (b(s(s(s(s(z)))), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[10531, 1764, 1121])).
% 2.34/2.50 tff(11224,plain,
% 2.34/2.50 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3122, 8908, 10568])).
% 2.34/2.50 tff(11225,plain,
% 2.34/2.50 (b(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[466, 11224, 8840])).
% 2.34/2.50 tff(11226,plain,
% 2.34/2.50 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[9465, 453, 11225, 5323, 11223])).
% 2.34/2.50 tff(11227,plain,
% 2.34/2.50 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[328, 11226])).
% 2.34/2.50 tff(11228,plain,
% 2.34/2.50 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[3164])).
% 2.34/2.50 tff(11229,plain,
% 2.34/2.50 ((s(s(s(s(z)))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.34/2.50 inference(transitivity,[status(thm)],[11228, 2372])).
% 2.34/2.50 tff(11230,plain,
% 2.34/2.50 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[11229])).
% 2.34/2.50 tff(11231,plain,
% 2.34/2.50 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[153, 11230])).
% 2.34/2.50 tff(11232,plain,
% 2.34/2.50 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1982, 11227, 256])).
% 2.34/2.50 tff(11233,plain,
% 2.34/2.50 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[518, 11232])).
% 2.34/2.50 tff(11234,plain,
% 2.34/2.50 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[11233, 10588])).
% 2.34/2.50 tff(11235,plain,
% 2.34/2.50 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[3165])).
% 2.34/2.50 tff(11236,plain,
% 2.34/2.50 (r(s(s(elem!1)), elem!1)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[1545, 11235])).
% 2.34/2.50 tff(11237,plain,
% 2.34/2.50 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 2.34/2.50 inference(monotonicity,[status(thm)],[3164])).
% 2.34/2.50 tff(11238,plain,
% 2.34/2.50 ((s(z) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[1121])).
% 2.34/2.50 tff(11239,plain,
% 2.34/2.50 ((s(z) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.34/2.50 inference(transitivity,[status(thm)],[11238, 144])).
% 2.34/2.50 tff(11240,plain,
% 2.34/2.50 ((~(s(z) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[11239])).
% 2.34/2.50 tff(11241,plain,
% 2.34/2.50 (~(s(s(z)) = elem!1)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[752, 11240])).
% 2.34/2.50 tff(11242,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(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(11243,plain,
% 2.34/2.50 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(11244,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(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[11243])).
% 2.34/2.50 tff(11245,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(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.34/2.50 inference(transitivity,[status(thm)],[11244, 11242])).
% 2.34/2.50 tff(11246,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(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(11247,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(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[11246, 11245])).
% 2.34/2.50 tff(11248,plain,
% 2.34/2.50 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[11247, 453, 11225, 5323, 11223])).
% 2.34/2.50 tff(11249,plain,
% 2.34/2.50 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2463, 69, 11248, 2453])).
% 2.34/2.50 tff(11250,plain,
% 2.34/2.50 (~b(s(s(z)), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[947, 11249, 11223, 11225, 5323])).
% 2.34/2.50 tff(11251,plain,
% 2.34/2.50 (r(s(s(z)), elem!1)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[782, 11250, 11241])).
% 2.34/2.50 tff(11252,plain,
% 2.34/2.50 (r(s(elem!1), elem!1)),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[11251, 11237])).
% 2.34/2.50 tff(11253,plain,
% 2.34/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(11254,plain,
% 2.34/2.50 (((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(11255,plain,
% 2.34/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1))))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[11254])).
% 2.34/2.50 tff(11256,plain,
% 2.34/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.34/2.50 inference(transitivity,[status(thm)],[11255, 11253])).
% 2.34/2.50 tff(11257,plain,
% 2.34/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(11258,plain,
% 2.34/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[11257, 11256])).
% 2.34/2.50 tff(11259,plain,
% 2.34/2.50 (~r(s(elem!1), s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[11258, 268, 11252, 11236])).
% 2.34/2.50 tff(11260,plain,
% 2.34/2.50 (b(s(elem!1), s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[440, 11259, 10569])).
% 2.34/2.50 tff(11261,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(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(11262,plain,
% 2.34/2.50 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(11263,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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[11262])).
% 2.34/2.51 tff(11264,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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[11263, 11261])).
% 2.34/2.51 tff(11265,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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(11266,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(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11265, 11264])).
% 2.34/2.51 tff(11267,plain,
% 2.34/2.51 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11266, 453, 11260, 11234, 11222])).
% 2.34/2.51 tff(11268,plain,
% 2.34/2.51 (r(s(elem!1), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[9382, 11267, 11231])).
% 2.34/2.51 tff(11269,plain,
% 2.34/2.51 (~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2343, 10568])).
% 2.34/2.51 tff(11270,plain,
% 2.34/2.51 (~(s(s(s(s(s(s(s(s(z)))))))) = s(elem!1))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11269, 6159])).
% 2.34/2.51 tff(11271,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11272,plain,
% 2.34/2.51 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11273,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[11272])).
% 2.34/2.51 tff(11274,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[11273, 11271])).
% 2.34/2.51 tff(11275,plain,
% 2.34/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(11276,plain,
% 2.34/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11275, 11274])).
% 2.34/2.51 tff(11277,plain,
% 2.34/2.51 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11276, 268, 11227, 11268])).
% 2.34/2.51 tff(11278,plain,
% 2.34/2.51 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2142, 11277, 4106])).
% 2.34/2.51 tff(11279,plain,
% 2.34/2.51 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[10100, 268, 301, 9787])).
% 2.34/2.51 tff(11280,plain,
% 2.34/2.51 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2833, 69, 2688, 11279])).
% 2.34/2.51 tff(11281,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11282,plain,
% 2.34/2.51 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11283,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[11282])).
% 2.34/2.51 tff(11284,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[11283, 11281])).
% 2.34/2.51 tff(11285,plain,
% 2.34/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(11286,plain,
% 2.34/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11285, 11284])).
% 2.34/2.51 tff(11287,plain,
% 2.34/2.51 (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11286, 268, 1892, 9650, 9787])).
% 2.34/2.51 tff(11288,plain,
% 2.34/2.51 (b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6187, 11287, 6176])).
% 2.34/2.51 tff(11289,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(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11290,plain,
% 2.34/2.51 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11291,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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[11290])).
% 2.34/2.51 tff(11292,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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[11291, 11289])).
% 2.34/2.51 tff(11293,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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(11294,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11293, 11292])).
% 2.34/2.51 tff(11295,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11294, 453, 910, 2129, 11288, 11280])).
% 2.34/2.51 tff(11296,plain,((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (s(s(s(s(s(s(s(s(z)))))))) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(11297,plain,
% 2.34/2.51 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11296, 11260, 11278, 11270, 11252, 11268, 11227])).
% 2.34/2.51 tff(11298,plain,
% 2.34/2.51 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2863, 11297])).
% 2.34/2.51 tff(11299,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11300,plain,
% 2.34/2.51 (((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11301,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[11300])).
% 2.34/2.51 tff(11302,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 2.34/2.51 inference(transitivity,[status(thm)],[11301, 11299])).
% 2.34/2.51 tff(11303,plain,
% 2.34/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(11304,plain,
% 2.34/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11303, 11302])).
% 2.34/2.51 tff(11305,plain,
% 2.34/2.51 (~r(s(s(elem!1)), s(elem!1))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11304, 268, 11252, 11236])).
% 2.34/2.51 tff(11306,plain,
% 2.34/2.51 ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1874, 69, 11305])).
% 2.34/2.51 tff(11307,plain,
% 2.34/2.51 (b(s(s(elem!1)), s(elem!1))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11306, 10570])).
% 2.34/2.51 tff(11308,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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11309,plain,
% 2.34/2.51 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11310,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(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[11309])).
% 2.34/2.51 tff(11311,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(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[11310, 11308])).
% 2.34/2.51 tff(11312,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(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(11313,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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11312, 11311])).
% 2.34/2.51 tff(11314,plain,
% 2.34/2.51 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11313, 453, 11260, 11234, 11307, 11298, 11222])).
% 2.34/2.51 tff(11315,plain,
% 2.34/2.51 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11314, 11213])).
% 2.34/2.51 tff(11316,plain,
% 2.34/2.51 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2846, 11315, 11211])).
% 2.34/2.51 tff(11317,plain,
% 2.34/2.51 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11316, 11209])).
% 2.34/2.51 tff(11318,plain,
% 2.34/2.51 (~(s(s(s(s(s(s(s(s(z)))))))) = elem!1)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[9979, 10568])).
% 2.34/2.51 tff(11319,plain,
% 2.34/2.51 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[3164])).
% 2.34/2.51 tff(11320,plain,
% 2.34/2.51 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.51 inference(symmetry,[status(thm)],[11319])).
% 2.34/2.51 tff(11321,plain,
% 2.34/2.51 (r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11268, 11320])).
% 2.34/2.51 tff(11322,plain,
% 2.34/2.51 (~r(elem!1, s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6942, 11321, 11251])).
% 2.34/2.51 tff(11323,plain,
% 2.34/2.51 (b(elem!1, s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1087, 11322, 1055])).
% 2.34/2.51 tff(11324,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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11325,plain,
% 2.34/2.51 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11326,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(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[11325])).
% 2.34/2.51 tff(11327,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(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.34/2.51 inference(transitivity,[status(thm)],[11326, 11324])).
% 2.34/2.51 tff(11328,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(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(11329,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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[11328, 11327])).
% 2.34/2.51 tff(11330,plain,
% 2.34/2.51 (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[11329, 453, 11234, 11323, 11298])).
% 2.34/2.51 tff(11331,plain,
% 2.34/2.51 (r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[5649, 11330, 11318])).
% 2.34/2.51 tff(11332,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(11333,plain,
% 2.34/2.51 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(11334,plain,
% 2.34/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11333])).
% 2.34/2.52 tff(11335,plain,
% 2.34/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[11334, 11332])).
% 2.34/2.52 tff(11336,plain,
% 2.34/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(11337,plain,
% 2.34/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11336, 11335])).
% 2.34/2.52 tff(11338,plain,
% 2.34/2.52 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11337, 268, 11236, 11331])).
% 2.34/2.52 tff(11339,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11338, 11317])).
% 2.34/2.52 tff(11340,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~(s(z) = elem!1)) | (elem!1 = s(s(s(s(z))))) | (s(s(s(s(s(z))))) = s(elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(11341,plain,
% 2.34/2.52 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11340, 1121, 1055, 11207, 637, 1545, 228, 11206])).
% 2.34/2.52 tff(11342,plain,
% 2.34/2.52 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[687, 11341])).
% 2.34/2.52 tff(11343,plain,
% 2.34/2.52 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10484, 11342, 1121])).
% 2.34/2.52 tff(11344,plain,
% 2.34/2.52 (b(s(s(s(s(z)))), elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10531, 11206, 1121])).
% 2.34/2.52 tff(11345,plain,
% 2.34/2.52 (b(s(z), s(s(z))) <=> b(elem!1, s(elem!1))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[1121, 3164])).
% 2.34/2.52 tff(11346,plain,
% 2.34/2.52 (b(elem!1, s(elem!1)) <=> b(s(z), s(s(z)))),
% 2.34/2.52 inference(symmetry,[status(thm)],[11345])).
% 2.34/2.52 tff(11347,plain,
% 2.34/2.52 ((~b(elem!1, s(elem!1))) <=> (~b(s(z), s(s(z))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11346])).
% 2.34/2.52 tff(11348,plain,
% 2.34/2.52 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[3164])).
% 2.34/2.52 tff(11349,plain,
% 2.34/2.52 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.52 inference(symmetry,[status(thm)],[11348])).
% 2.34/2.52 tff(11350,plain,
% 2.34/2.52 (b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[9384, 11349])).
% 2.34/2.52 tff(11351,plain,
% 2.34/2.52 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[10478])).
% 2.34/2.52 tff(11352,plain,
% 2.34/2.52 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(z))))))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[11351, 3473])).
% 2.34/2.52 tff(11353,plain,
% 2.34/2.52 ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.34/2.52 inference(symmetry,[status(thm)],[11352])).
% 2.34/2.52 tff(11354,plain,
% 2.34/2.52 ((~(s(s(s(z))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11353])).
% 2.34/2.52 tff(11355,plain,
% 2.34/2.52 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[3475, 11354])).
% 2.34/2.52 tff(11356,plain,
% 2.34/2.52 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 2.34/2.52 inference(monotonicity,[status(thm)],[1121])).
% 2.34/2.52 tff(11357,plain,
% 2.34/2.52 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 2.34/2.52 inference(symmetry,[status(thm)],[11356])).
% 2.34/2.52 tff(11358,plain,
% 2.34/2.52 (r(s(elem!1), elem!1) <=> r(s(s(z)), elem!1)),
% 2.34/2.52 inference(symmetry,[status(thm)],[11237])).
% 2.34/2.52 tff(11359,plain,
% 2.34/2.52 (r(s(elem!1), elem!1) <=> r(s(s(z)), s(z))),
% 2.34/2.52 inference(transitivity,[status(thm)],[11358, 11357])).
% 2.34/2.52 tff(11360,plain,
% 2.34/2.52 (r(s(s(z)), s(z))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[1892, 11359])).
% 2.34/2.52 tff(11361,plain,
% 2.34/2.52 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[1121])).
% 2.34/2.52 tff(11362,plain,
% 2.34/2.52 (b(elem!1, s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 2.34/2.52 inference(symmetry,[status(thm)],[11361])).
% 2.34/2.52 tff(11363,plain,
% 2.34/2.52 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[10478])).
% 2.34/2.52 tff(11364,plain,
% 2.34/2.52 ((~b(s(s(elem!1)), s(s(s(s(z)))))) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11363])).
% 2.34/2.52 tff(11365,assumption,(s(s(elem!1)) = s(elem!1)), introduced(assumption)).
% 2.34/2.52 tff(11366,plain,
% 2.34/2.52 (s(elem!1) = s(s(elem!1))),
% 2.34/2.52 inference(symmetry,[status(thm)],[11365])).
% 2.34/2.52 tff(11367,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1997, 11366])).
% 2.34/2.52 tff(11368,plain,((~(s(s(elem!1)) = s(elem!1))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(11369,plain,
% 2.34/2.52 (~(s(s(elem!1)) = s(elem!1))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11368, 10569])).
% 2.34/2.52 tff(11370,plain,
% 2.34/2.52 (~r(s(s(elem!1)), s(elem!1))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11304, 268, 1892, 11236])).
% 2.34/2.52 tff(11371,plain,
% 2.34/2.52 (b(s(s(elem!1)), s(elem!1))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1874, 69, 11370, 11369])).
% 2.34/2.52 tff(11372,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11258, 268, 1892, 869, 431])).
% 2.34/2.52 tff(11373,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(11374,plain,
% 2.34/2.52 (~r(s(elem!1), s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11373, 1892, 11236])).
% 2.34/2.52 tff(11375,plain,
% 2.34/2.52 (b(s(elem!1), s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[440, 11374, 10569])).
% 2.34/2.52 tff(11376,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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(11377,plain,
% 2.34/2.52 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(11378,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(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11377])).
% 2.34/2.52 tff(11379,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(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[11378, 11376])).
% 2.34/2.52 tff(11380,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(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(11381,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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11380, 11379])).
% 2.34/2.52 tff(11382,plain,
% 2.34/2.52 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11381, 453, 11375, 11371, 10539])).
% 2.34/2.52 tff(11383,plain,
% 2.34/2.52 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[659, 11382, 3700])).
% 2.34/2.52 tff(11384,plain,
% 2.34/2.52 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[3228, 11383, 10568])).
% 2.34/2.52 tff(11385,plain,
% 2.34/2.52 (~r(s(z), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[9113, 11384, 11360])).
% 2.34/2.52 tff(11386,plain,
% 2.34/2.52 (b(s(z), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[372, 11385])).
% 2.34/2.52 tff(11387,plain,
% 2.34/2.52 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[4526, 11386, 1779, 1764])).
% 2.34/2.52 tff(11388,plain,
% 2.34/2.52 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2463, 69, 11387, 2453])).
% 2.34/2.52 tff(11389,plain,
% 2.34/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(11390,plain,
% 2.34/2.52 (((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(11391,plain,
% 2.34/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11390])).
% 2.34/2.52 tff(11392,plain,
% 2.34/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[11391, 11389])).
% 2.34/2.52 tff(11393,plain,
% 2.34/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(11394,plain,
% 2.34/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11393, 11392])).
% 2.34/2.52 tff(11395,plain,
% 2.34/2.52 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11394, 268, 1892, 11388, 11383])).
% 2.34/2.52 tff(11396,plain,
% 2.34/2.52 (b(s(s(s(s(z)))), s(elem!1))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2398, 11395, 8852])).
% 2.34/2.52 tff(11397,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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(11398,plain,
% 2.34/2.52 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(11399,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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11398])).
% 2.34/2.52 tff(11400,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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[11399, 11397])).
% 2.34/2.52 tff(11401,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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(11402,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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11401, 11400])).
% 2.34/2.52 tff(11403,plain,
% 2.34/2.52 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11402, 453, 11375, 11371, 11396])).
% 2.34/2.52 tff(11404,plain,
% 2.34/2.52 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11403, 11364])).
% 2.34/2.52 tff(11405,plain,
% 2.34/2.52 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1656, 11404])).
% 2.34/2.52 tff(11406,plain,
% 2.34/2.52 (~r(elem!1, s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[5432, 11405, 1149, 1545])).
% 2.34/2.52 tff(11407,plain,
% 2.34/2.52 (b(elem!1, s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1087, 11406, 1055])).
% 2.34/2.52 tff(11408,plain,
% 2.34/2.52 (b(s(z), s(s(s(s(z)))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11407, 11362])).
% 2.34/2.52 tff(11409,plain,
% 2.34/2.52 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[9291, 11408, 10568, 1764, 2956, 11360])).
% 2.34/2.52 tff(11410,plain,
% 2.34/2.52 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2696, 11409])).
% 2.34/2.52 tff(11411,plain,
% 2.34/2.52 (r(s(s(z)), elem!1)),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[1892, 11358])).
% 2.34/2.52 tff(11412,plain,
% 2.34/2.52 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[10463, 11411, 1545])).
% 2.34/2.52 tff(11413,plain,
% 2.34/2.52 (b(s(s(s(s(s(z))))), elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[643, 11412, 637])).
% 2.34/2.52 tff(11414,plain,
% 2.34/2.52 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[9558, 11384, 11411])).
% 2.34/2.52 tff(11415,plain,
% 2.34/2.52 (b(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[466, 11414, 8840])).
% 2.34/2.52 tff(11416,plain,
% 2.34/2.52 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[9465, 453, 11415, 11413, 11223])).
% 2.34/2.52 tff(11417,plain,
% 2.34/2.52 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[328, 11416])).
% 2.34/2.52 tff(11418,plain,
% 2.34/2.52 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[9299, 268, 11417, 11410])).
% 2.34/2.52 tff(11419,assumption,(~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.34/2.52 tff(11420,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.34/2.52 tff(11421,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2732, 69, 2729, 11420, 11419])).
% 2.34/2.52 tff(11422,plain,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(11423,plain,
% 2.34/2.52 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11422, 11418])).
% 2.34/2.52 tff(11424,plain,
% 2.34/2.52 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[3165])).
% 2.34/2.52 tff(11425,plain,
% 2.34/2.52 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.52 inference(symmetry,[status(thm)],[10588])).
% 2.34/2.52 tff(11426,plain,
% 2.34/2.52 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11425])).
% 2.34/2.52 tff(11427,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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(11428,plain,
% 2.34/2.52 (((~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(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), 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(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(11429,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(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(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[11428])).
% 2.34/2.52 tff(11430,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(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(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[11429, 11427])).
% 2.34/2.52 tff(11431,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(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(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(11432,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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11431, 11430])).
% 2.34/2.52 tff(11433,plain,
% 2.34/2.52 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[11432, 453, 11375, 11371, 11396])).
% 2.34/2.52 tff(11434,plain,
% 2.34/2.52 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11433, 11426])).
% 2.34/2.52 tff(11435,plain,
% 2.34/2.52 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[518, 11434])).
% 2.34/2.52 tff(11436,plain,
% 2.34/2.52 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[8666, 11435, 11388])).
% 2.34/2.52 tff(11437,plain,
% 2.34/2.52 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2570, 11436])).
% 2.34/2.52 tff(11438,plain,
% 2.34/2.52 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[11437, 11424])).
% 2.34/2.52 tff(11439,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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(11440,plain,
% 2.34/2.53 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11441,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(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11440])).
% 2.34/2.53 tff(11442,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(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[11441, 11439])).
% 2.34/2.53 tff(11443,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(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(11444,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(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11443, 11442])).
% 2.34/2.53 tff(11445,plain,
% 2.34/2.53 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11444, 453, 11413, 11438, 11423])).
% 2.34/2.53 tff(11446,plain,
% 2.34/2.53 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[5232, 69, 11221, 11403])).
% 2.34/2.53 tff(11447,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11448,plain,
% 2.34/2.53 (((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11449,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11448])).
% 2.34/2.53 tff(11450,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[11449, 11447])).
% 2.34/2.53 tff(11451,plain,
% 2.34/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(11452,plain,
% 2.34/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11451, 11450])).
% 2.34/2.53 tff(11453,plain,
% 2.34/2.53 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11452, 268, 11236, 11446, 11410])).
% 2.34/2.53 tff(11454,plain,
% 2.34/2.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11455,plain,
% 2.34/2.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(11456,plain,
% 2.34/2.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11455, 11454])).
% 2.34/2.53 tff(11457,plain,
% 2.34/2.53 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11456, 69, 11453])).
% 2.34/2.53 tff(11458,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11457, 11445, 11355])).
% 2.34/2.53 tff(11459,plain,((~r(s(elem!1), elem!1)) | (~(s(z) = elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (s(elem!1) = s(s(s(s(s(z)))))) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(11460,plain,
% 2.34/2.53 (~r(s(elem!1), elem!1)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11459, 11350, 1764, 1121, 1055, 1149, 1545, 8852, 1779, 3700, 637])).
% 2.34/2.53 tff(11461,plain,
% 2.34/2.53 (b(s(elem!1), elem!1)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2440, 11460, 10573])).
% 2.34/2.53 tff(11462,plain,
% 2.34/2.53 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[9411, 11461, 11223, 9384])).
% 2.34/2.53 tff(11463,plain,
% 2.34/2.53 (r(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[466, 11462, 8840])).
% 2.34/2.53 tff(11464,plain,
% 2.34/2.53 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10571])).
% 2.34/2.53 tff(11465,plain,
% 2.34/2.53 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.53 inference(symmetry,[status(thm)],[11464])).
% 2.34/2.53 tff(11466,plain,
% 2.34/2.53 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.34/2.53 inference(symmetry,[status(thm)],[11363])).
% 2.34/2.53 tff(11467,plain,
% 2.34/2.53 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[10571])).
% 2.34/2.53 tff(11468,plain,
% 2.34/2.53 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.34/2.53 inference(symmetry,[status(thm)],[11467])).
% 2.34/2.53 tff(11469,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(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11470,plain,
% 2.34/2.53 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11471,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11470])).
% 2.34/2.53 tff(11472,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.34/2.53 inference(transitivity,[status(thm)],[11471, 11469])).
% 2.34/2.53 tff(11473,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(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(11474,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(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11473, 11472])).
% 2.34/2.53 tff(11475,plain,
% 2.34/2.53 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11474, 453, 629, 1071, 11223])).
% 2.34/2.53 tff(11476,plain,
% 2.34/2.53 (r(s(elem!1), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[9382, 11475, 11231])).
% 2.34/2.53 tff(11477,plain,
% 2.34/2.53 (r(s(elem!1), s(s(s(elem!1))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11476, 11468])).
% 2.34/2.53 tff(11478,plain,
% 2.34/2.53 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[9415, 412, 1149])).
% 2.34/2.53 tff(11479,plain,
% 2.34/2.53 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2570, 11478])).
% 2.34/2.53 tff(11480,plain,
% 2.34/2.53 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11479, 11424])).
% 2.34/2.53 tff(11481,plain,
% 2.34/2.53 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 2.34/2.53 inference(symmetry,[status(thm)],[11212])).
% 2.34/2.53 tff(11482,plain,
% 2.34/2.53 ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) <=> (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11208])).
% 2.34/2.53 tff(11483,assumption,(b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))), introduced(assumption)).
% 2.34/2.53 tff(11484,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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11485,plain,
% 2.34/2.53 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11486,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11485])).
% 2.34/2.53 tff(11487,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[11486, 11484])).
% 2.34/2.53 tff(11488,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(11489,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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11488, 11487])).
% 2.34/2.53 tff(11490,plain,
% 2.34/2.53 (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11489, 453, 629, 1071, 11483])).
% 2.34/2.53 tff(11491,plain,
% 2.34/2.53 (r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[5649, 11490, 11318])).
% 2.34/2.53 tff(11492,plain,
% 2.34/2.53 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11337, 268, 869, 11491])).
% 2.34/2.53 tff(11493,plain,
% 2.34/2.53 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11492, 11482])).
% 2.34/2.53 tff(11494,plain,
% 2.34/2.53 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2846, 11493, 11211])).
% 2.34/2.53 tff(11495,plain,
% 2.34/2.53 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11494, 11481])).
% 2.34/2.53 tff(11496,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(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11497,plain,
% 2.34/2.53 (((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11498,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(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11497])).
% 2.34/2.53 tff(11499,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(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[11498, 11496])).
% 2.34/2.53 tff(11500,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(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(11501,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(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[11500, 11499])).
% 2.34/2.53 tff(11502,plain,
% 2.34/2.53 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11501, 453, 5798, 10486])).
% 2.34/2.53 tff(11503,plain,
% 2.34/2.53 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[11502, 11495])).
% 2.34/2.53 tff(11504,plain,
% 2.34/2.53 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2833, 69, 2688, 11503])).
% 2.34/2.53 tff(11505,plain,
% 2.34/2.53 ((s(z) = s(s(s(s(s(s(s(s(z))))))))) <=> (elem!1 = s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[1121])).
% 2.34/2.53 tff(11506,plain,
% 2.34/2.53 ((~(s(z) = s(s(s(s(s(s(s(s(z)))))))))) <=> (~(elem!1 = s(s(s(s(s(s(s(s(z))))))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11505])).
% 2.34/2.53 tff(11507,plain,
% 2.34/2.53 (~(elem!1 = s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[2884, 11506])).
% 2.34/2.53 tff(11508,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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11509,plain,
% 2.34/2.53 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(11510,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~b(elem!1, s(s(s(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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[11509])).
% 2.34/2.53 tff(11511,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~b(elem!1, s(s(s(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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[11510, 11508])).
% 2.34/2.53 tff(11512,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(11513,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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11512, 11511])).
% 2.34/2.54 tff(11514,plain,
% 2.34/2.54 (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11513, 453, 629, 1071, 11483])).
% 2.34/2.54 tff(11515,plain,
% 2.34/2.54 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(s(s(z))))))))) | b(elem!1, s(s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(s(z))))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(s(s(z))))))))) | b(elem!1, s(s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(s(z))))))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11516,plain,
% 2.34/2.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(s(s(z))))))))) | b(elem!1, s(s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(s(z))))))))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(11517,plain,
% 2.34/2.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(s(s(z))))))))) | b(elem!1, s(s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11516, 11515])).
% 2.34/2.54 tff(11518,plain,
% 2.34/2.54 ((elem!1 = s(s(s(s(s(s(s(s(z))))))))) | b(elem!1, s(s(s(s(s(s(s(s(z))))))))) | r(elem!1, s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11517, 69])).
% 2.34/2.54 tff(11519,plain,
% 2.34/2.54 (r(elem!1, s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11518, 11514, 11507])).
% 2.34/2.54 tff(11520,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11521,plain,
% 2.34/2.54 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11522,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11521])).
% 2.34/2.54 tff(11523,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[11522, 11520])).
% 2.34/2.54 tff(11524,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(11525,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11524, 11523])).
% 2.34/2.54 tff(11526,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11525, 268, 412, 11519, 11504])).
% 2.34/2.54 tff(11527,plain,((~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~(s(z) = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(11528,plain,
% 2.34/2.54 (~b(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11527, 412, 11480, 10539, 1121, 869, 629, 1071])).
% 2.34/2.54 tff(11529,plain,
% 2.34/2.54 (r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[6187, 11528, 11270])).
% 2.34/2.54 tff(11530,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11531,plain,
% 2.34/2.54 (((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11532,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11531])).
% 2.34/2.54 tff(11533,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[11532, 11530])).
% 2.34/2.54 tff(11534,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(11535,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11534, 11533])).
% 2.34/2.54 tff(11536,plain,
% 2.34/2.54 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11535, 268, 2389, 11529])).
% 2.34/2.54 tff(11537,plain,
% 2.34/2.54 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2863, 11536])).
% 2.34/2.54 tff(11538,plain,
% 2.34/2.54 (r(elem!1, s(s(elem!1)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[1149, 3166])).
% 2.34/2.54 tff(11539,plain,
% 2.34/2.54 (r(s(z), s(s(s(s(s(z))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[3122, 412, 10568])).
% 2.34/2.54 tff(11540,plain,
% 2.34/2.54 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[10478])).
% 2.34/2.54 tff(11541,plain,
% 2.34/2.54 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.34/2.54 inference(symmetry,[status(thm)],[11540])).
% 2.34/2.54 tff(11542,plain,
% 2.34/2.54 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10597, 1780, 1121, 1779, 9650])).
% 2.34/2.54 tff(11543,plain,
% 2.34/2.54 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[518, 11542])).
% 2.34/2.54 tff(11544,plain,
% 2.34/2.54 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11543, 11541])).
% 2.34/2.54 tff(11545,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11546,plain,
% 2.34/2.54 (((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11547,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11546])).
% 2.34/2.54 tff(11548,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[11547, 11545])).
% 2.34/2.54 tff(11549,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(11550,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11549, 11548])).
% 2.34/2.54 tff(11551,plain,
% 2.34/2.54 ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11550, 268, 1032])).
% 2.34/2.54 tff(11552,plain,
% 2.34/2.54 (~r(elem!1, s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11551, 11544])).
% 2.34/2.54 tff(11553,plain,
% 2.34/2.54 (b(elem!1, s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1087, 11552, 1055])).
% 2.34/2.54 tff(11554,plain,
% 2.34/2.54 (b(s(z), s(s(s(s(z)))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11553, 11362])).
% 2.34/2.54 tff(11555,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(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11556,plain,
% 2.34/2.54 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11557,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(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(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(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11556])).
% 2.34/2.54 tff(11558,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(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(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(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[11557, 11555])).
% 2.34/2.54 tff(11559,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(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(11560,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(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11559, 11558])).
% 2.34/2.54 tff(11561,plain,
% 2.34/2.54 (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11560, 453, 1764, 1974, 2823])).
% 2.34/2.54 tff(11562,plain,
% 2.34/2.54 (r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[6101, 69, 2884, 11561])).
% 2.34/2.54 tff(11563,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11564,plain,
% 2.34/2.54 (((~b(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(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11565,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(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(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[11564])).
% 2.34/2.54 tff(11566,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(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(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[11565, 11563])).
% 2.34/2.54 tff(11567,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(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(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(11568,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z)))))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[11567, 11566])).
% 2.34/2.54 tff(11569,plain,
% 2.34/2.54 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11568, 453, 1764, 1780, 2823])).
% 2.34/2.54 tff(11570,plain,
% 2.34/2.54 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2833, 69, 2688, 11569])).
% 2.34/2.54 tff(11571,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7357, 268, 2246, 11570, 11562])).
% 2.34/2.54 tff(11572,plain,((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(11573,plain,
% 2.34/2.54 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11572, 1780, 1764, 2246, 2823])).
% 2.34/2.54 tff(11574,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11573, 11554])).
% 2.34/2.54 tff(11575,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~(s(z) = elem!1)) | (elem!1 = s(s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(11576,plain,
% 2.34/2.54 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[11575, 11539, 1055, 11538, 1764, 1121, 11537, 1779, 11476])).
% 2.34/2.54 tff(11577,plain,
% 2.34/2.54 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[328, 11576])).
% 2.34/2.54 tff(11578,plain,
% 2.34/2.54 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[10607, 11577, 11476])).
% 2.34/2.54 tff(11579,plain,
% 2.34/2.54 (b(s(elem!1), s(s(s(s(s(z))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[659, 11578, 3700])).
% 2.34/2.54 tff(11580,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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(11581,plain,
% 2.34/2.54 (((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(11582,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(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[11581])).
% 2.34/2.55 tff(11583,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(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[11582, 11580])).
% 2.34/2.55 tff(11584,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(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(11585,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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[11584, 11583])).
% 2.34/2.55 tff(11586,plain,
% 2.34/2.55 (~b(s(elem!1), s(s(elem!1)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11585, 453, 11579, 11480, 10539])).
% 2.34/2.55 tff(11587,plain,
% 2.34/2.55 (r(s(elem!1), s(s(elem!1)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[440, 11586, 10569])).
% 2.34/2.55 tff(11588,plain,
% 2.34/2.55 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[670, 11587, 11477])).
% 2.34/2.55 tff(11589,plain,
% 2.34/2.55 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[675, 11588, 10574])).
% 2.34/2.55 tff(11590,plain,
% 2.34/2.55 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9143, 11589, 10568])).
% 2.34/2.55 tff(11591,plain,
% 2.34/2.55 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[11590, 11466])).
% 2.34/2.55 tff(11592,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(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(11593,plain,
% 2.34/2.55 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(11594,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(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[11593])).
% 2.34/2.55 tff(11595,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(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[11594, 11592])).
% 2.34/2.55 tff(11596,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(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(11597,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(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[11596, 11595])).
% 2.34/2.55 tff(11598,plain,
% 2.34/2.55 ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11597, 453, 11223, 11537])).
% 2.34/2.55 tff(11599,plain,
% 2.34/2.55 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11598, 11591])).
% 2.34/2.55 tff(11600,plain,
% 2.34/2.55 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[11599, 11213])).
% 2.34/2.55 tff(11601,plain,
% 2.34/2.55 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2846, 11600, 11211])).
% 2.34/2.55 tff(11602,plain,
% 2.34/2.55 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[11601, 11209])).
% 2.34/2.55 tff(11603,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(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~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(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(11604,plain,
% 2.34/2.55 (((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(11605,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(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[11604])).
% 2.34/2.55 tff(11606,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(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[11605, 11603])).
% 2.34/2.55 tff(11607,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(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(11608,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(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[11607, 11606])).
% 2.34/2.55 tff(11609,plain,
% 2.34/2.55 (~b(s(s(elem!1)), s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11608, 453, 11579, 11480, 10539])).
% 2.34/2.55 tff(11610,plain,
% 2.34/2.55 ((s(s(elem!1)) = s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1874, 69, 11609])).
% 2.34/2.55 tff(11611,plain,
% 2.34/2.55 (r(s(s(elem!1)), s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11610, 10570])).
% 2.34/2.55 tff(11612,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(11613,plain,
% 2.34/2.55 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(11614,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[11613])).
% 2.34/2.55 tff(11615,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[11614, 11612])).
% 2.34/2.55 tff(11616,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(11617,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[11616, 11615])).
% 2.34/2.55 tff(11618,plain,
% 2.34/2.55 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11617, 268, 11611, 11529])).
% 2.34/2.55 tff(11619,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11618, 11602])).
% 2.34/2.55 tff(11620,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~(s(z) = elem!1)) | (s(elem!1) = s(s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(11621,plain,
% 2.34/2.55 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11620, 1071, 3700, 1055, 1764, 1779, 1121, 869, 629, 412, 1149])).
% 2.34/2.55 tff(11622,plain,
% 2.34/2.55 (b(s(s(s(s(z)))), s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2398, 11621, 8852])).
% 2.34/2.55 tff(11623,plain,
% 2.34/2.55 (b(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[11622, 11465])).
% 2.34/2.55 tff(11624,plain,
% 2.34/2.55 (b(s(elem!1), s(z))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[629, 3030])).
% 2.34/2.55 tff(11625,plain,
% 2.34/2.55 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 2.34/2.55 inference(monotonicity,[status(thm)],[1121])).
% 2.34/2.55 tff(11626,plain,
% 2.34/2.55 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 2.34/2.55 inference(symmetry,[status(thm)],[11625])).
% 2.34/2.55 tff(11627,plain,
% 2.34/2.55 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.34/2.55 inference(monotonicity,[status(thm)],[10571])).
% 2.34/2.55 tff(11628,plain,
% 2.34/2.55 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.34/2.55 inference(symmetry,[status(thm)],[11627])).
% 2.34/2.55 tff(11629,plain,
% 2.34/2.55 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 2.34/2.55 inference(transitivity,[status(thm)],[11628, 11626])).
% 2.34/2.55 tff(11630,plain,
% 2.34/2.55 (b(s(s(s(elem!1))), s(z))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[11223, 11629])).
% 2.34/2.55 tff(11631,plain,
% 2.34/2.55 (b(s(z), s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[8974, 1071, 10568])).
% 2.34/2.55 tff(11632,plain,
% 2.34/2.55 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7215, 11631, 11630, 11624])).
% 2.34/2.55 tff(11633,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11632, 11623])).
% 2.34/2.55 tff(11634,plain,((~b(elem!1, s(elem!1))) | (~(s(z) = elem!1)) | (s(s(s(s(z)))) = s(elem!1)) | (s(elem!1) = s(s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(11635,plain,
% 2.34/2.55 (~b(elem!1, s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11634, 11461, 8852, 3700, 1055, 1764, 1779, 11236, 1121, 11463, 1149])).
% 2.34/2.55 tff(11636,plain,
% 2.34/2.55 (~b(s(z), s(s(z)))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[11635, 11347])).
% 2.34/2.55 tff(11637,plain,
% 2.34/2.55 (r(s(z), s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3122, 11463, 10568])).
% 2.34/2.55 tff(11638,plain,
% 2.34/2.55 ((s(s(s(z))) = s(s(z))) <=> (s(s(s(z))) = s(elem!1))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[3164])).
% 2.34/2.55 tff(11639,plain,
% 2.34/2.55 ((s(s(s(z))) = s(s(z))) <=> (s(elem!1) = s(s(s(z))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[11638, 10378])).
% 2.34/2.55 tff(11640,plain,
% 2.34/2.55 ((s(s(s(z))) = s(s(z))) <=> (s(s(s(z))) = s(elem!1))),
% 2.34/2.55 inference(transitivity,[status(thm)],[11639, 10379])).
% 2.34/2.55 tff(11641,plain,
% 2.34/2.55 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[11640])).
% 2.34/2.55 tff(11642,plain,
% 2.34/2.55 (~(s(s(s(z))) = s(elem!1))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[160, 11641])).
% 2.34/2.55 tff(11643,plain,
% 2.34/2.55 (r(elem!1, s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1069, 11635, 11201])).
% 2.34/2.55 tff(11644,plain,
% 2.34/2.55 (~r(s(s(s(z))), s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9495, 11643, 1149])).
% 2.34/2.55 tff(11645,plain,
% 2.34/2.55 (b(s(s(s(z))), s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9480, 11644, 11642])).
% 2.34/2.55 tff(11646,plain,
% 2.34/2.55 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9415, 11463, 1149])).
% 2.34/2.55 tff(11647,plain,
% 2.34/2.55 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2570, 11646])).
% 2.34/2.55 tff(11648,plain,
% 2.34/2.55 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[10478])).
% 2.34/2.55 tff(11649,plain,
% 2.34/2.55 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.34/2.55 inference(symmetry,[status(thm)],[11648])).
% 2.34/2.55 tff(11650,plain,
% 2.34/2.55 (~r(s(s(s(z))), s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9495, 339, 1149])).
% 2.34/2.55 tff(11651,plain,
% 2.34/2.55 (b(s(s(s(z))), s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9480, 11650, 11642])).
% 2.34/2.55 tff(11652,plain,
% 2.34/2.55 (b(s(s(elem!1)), s(elem!1))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[11651, 11649])).
% 2.34/2.55 tff(11653,plain,
% 2.34/2.55 (r(s(z), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[1121])).
% 2.34/2.55 tff(11654,plain,
% 2.34/2.55 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 2.34/2.55 inference(symmetry,[status(thm)],[11653])).
% 2.34/2.55 tff(11655,plain,
% 2.34/2.55 (r(s(z), s(elem!1))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[339, 11654])).
% 2.34/2.55 tff(11656,plain,
% 2.34/2.55 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10504, 11655, 258])).
% 2.34/2.55 tff(11657,plain,
% 2.34/2.55 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2142, 11656, 4106])).
% 2.34/2.55 tff(11658,plain,
% 2.34/2.55 (~b(s(s(elem!1)), s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10494, 11657, 629, 10486])).
% 2.34/2.55 tff(11659,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11658, 11652])).
% 2.34/2.55 tff(11660,plain,((~r(elem!1, s(elem!1))) | (~(s(z) = elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(11661,plain,
% 2.34/2.55 (~r(s(s(s(s(s(z))))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11660, 11643, 1121, 10539, 11207, 11461, 1149])).
% 2.34/2.55 tff(11662,plain,
% 2.34/2.55 (b(s(s(s(s(s(z))))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[297, 11661])).
% 2.34/2.55 tff(11663,assumption,(b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 2.34/2.55 tff(11664,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(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(11665,plain,
% 2.34/2.55 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(11666,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(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[11665])).
% 2.34/2.55 tff(11667,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(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[11666, 11664])).
% 2.34/2.55 tff(11668,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(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(11669,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[11668, 11667])).
% 2.34/2.55 tff(11670,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11669, 453, 11663, 645, 374, 2611])).
% 2.34/2.55 tff(11671,plain,((~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(11672,plain,
% 2.34/2.55 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11671, 11662, 11647, 11645])).
% 2.34/2.55 tff(11673,plain,
% 2.34/2.55 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[659, 11672, 3700])).
% 2.34/2.55 tff(11674,plain,
% 2.34/2.55 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3228, 11673, 10568])).
% 2.34/2.55 tff(11675,plain,
% 2.34/2.55 (~r(s(z), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9047, 11674, 11637])).
% 2.34/2.55 tff(11676,plain,
% 2.34/2.55 (b(s(z), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[757, 11675])).
% 2.34/2.55 tff(11677,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11676, 11636])).
% 2.34/2.55 tff(11678,plain,((~b(s(elem!1), s(s(s(s(z)))))) | (~(s(z) = elem!1)) | (s(elem!1) = s(s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))) | (s(s(s(s(z)))) = s(elem!1)) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(11679,plain,
% 2.34/2.55 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11678, 1121, 3700, 1149, 8852, 1055, 11206, 11342, 1545, 637])).
% 2.34/2.55 tff(11680,plain,
% 2.34/2.55 (r(s(elem!1), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9382, 11679, 11231])).
% 2.34/2.55 tff(11681,plain,
% 2.34/2.55 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11381, 453, 11375, 11371, 10486])).
% 2.34/2.55 tff(11682,plain,
% 2.34/2.55 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[659, 11681, 3700])).
% 2.34/2.55 tff(11683,plain,
% 2.34/2.55 (r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[9650, 11320])).
% 2.34/2.55 tff(11684,plain,
% 2.34/2.55 (~r(elem!1, s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[6942, 11411, 11683])).
% 2.34/2.55 tff(11685,plain,
% 2.34/2.55 (b(elem!1, s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1087, 11684, 1055])).
% 2.34/2.55 tff(11686,plain,
% 2.34/2.55 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7898, 453, 11413, 11685, 299])).
% 2.34/2.55 tff(11687,plain,
% 2.34/2.55 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[328, 11686])).
% 2.34/2.55 tff(11688,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10607, 11687, 11682, 9650])).
% 2.34/2.55 tff(11689,plain,((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (elem!1 = s(s(s(s(z))))) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(s(s(z))), elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(11690,plain,
% 2.34/2.55 (~r(s(elem!1), elem!1)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11689, 11680, 3700, 11344, 11343, 1055, 637, 1545, 1121])).
% 2.34/2.55 tff(11691,plain,
% 2.34/2.55 (b(s(elem!1), elem!1)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2440, 11690, 10573])).
% 2.34/2.55 tff(11692,plain,
% 2.34/2.55 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[10565, 11680, 11342, 11206, 1121, 3700, 11691])).
% 2.34/2.55 tff(11693,plain,
% 2.34/2.55 (r(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[466, 11692, 8840])).
% 2.34/2.55 tff(11694,plain,
% 2.34/2.55 (~b(elem!1, s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11634, 11693, 8852, 3700, 1055, 11206, 11342, 11236, 1121, 11691, 1149])).
% 2.34/2.55 tff(11695,plain,
% 2.34/2.55 (r(elem!1, s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1069, 11694, 11201])).
% 2.34/2.55 tff(11696,plain,
% 2.34/2.55 (r(s(z), s(s(z)))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[11695, 11200])).
% 2.34/2.55 tff(11697,plain,
% 2.34/2.55 (r(s(z), s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3122, 11693, 10568])).
% 2.34/2.55 tff(11698,plain,
% 2.34/2.55 (~r(s(s(s(z))), s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9495, 11695, 1149])).
% 2.34/2.55 tff(11699,plain,
% 2.34/2.55 (b(s(s(s(z))), s(elem!1))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9480, 11698, 11642])).
% 2.34/2.55 tff(11700,plain,
% 2.34/2.55 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[9415, 11693, 1149])).
% 2.34/2.55 tff(11701,plain,
% 2.34/2.55 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2570, 11700])).
% 2.34/2.55 tff(11702,plain,
% 2.34/2.55 (~r(s(s(s(s(s(z))))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[11660, 11695, 1121, 11343, 11207, 11691, 1149])).
% 2.34/2.55 tff(11703,plain,
% 2.34/2.55 (b(s(s(s(s(s(z))))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[297, 11702])).
% 2.34/2.56 tff(11704,plain,
% 2.34/2.56 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[11671, 11703, 11701, 11699])).
% 2.34/2.56 tff(11705,plain,
% 2.34/2.56 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[659, 11704, 3700])).
% 2.34/2.56 tff(11706,plain,
% 2.34/2.56 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3228, 11705, 10568])).
% 2.34/2.56 tff(11707,plain,
% 2.34/2.56 (~r(s(z), s(s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9047, 11706, 11697])).
% 2.34/2.56 tff(11708,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[11707, 11696])).
% 2.34/2.56 tff(11709,plain,((~(s(z) = elem!1)) | (s(elem!1) = s(s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))) | (s(s(s(s(z)))) = s(elem!1)) | (elem!1 = s(s(s(s(z))))) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(s(s(z))), elem!1)) | b(s(z), s(s(s(z)))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(11710,plain,
% 2.34/2.56 (~(s(z) = elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[11709, 11198, 1149, 10371, 9, 11062, 11197, 221, 3448])).
% 2.34/2.56 tff(11711,plain,
% 2.34/2.56 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[547, 11710])).
% 2.34/2.56 tff(11712,plain,
% 2.34/2.56 (~(elem!1 = s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3026, 11711])).
% 2.34/2.56 tff(11713,plain,
% 2.34/2.56 (b(s(z), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[506, 11710, 4541])).
% 2.34/2.56 tff(11714,plain,
% 2.34/2.56 (~(s(s(s(z))) = elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2086, 128, 2076])).
% 2.34/2.56 tff(11715,plain,
% 2.34/2.56 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[11061, 3448, 228, 2076, 11714])).
% 2.34/2.56 tff(11716,plain,
% 2.34/2.56 (r(s(s(s(z))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[74, 58, 11714])).
% 2.34/2.56 tff(11717,plain,
% 2.34/2.56 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[5333, 6754, 228, 11715, 11716, 499])).
% 2.34/2.56 tff(11718,plain,
% 2.34/2.56 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[687, 11717])).
% 2.34/2.56 tff(11719,plain,
% 2.34/2.56 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[4119, 1099, 3448])).
% 2.34/2.56 tff(11720,plain,
% 2.34/2.56 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[518, 11719])).
% 2.34/2.56 tff(11721,plain,
% 2.34/2.56 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1788, 11720, 11718, 8000])).
% 2.34/2.56 tff(11722,plain,
% 2.34/2.56 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[328, 11721])).
% 2.34/2.56 tff(11723,plain,
% 2.34/2.56 (~r(s(s(s(s(z)))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[11146, 11722, 11715, 499, 6754, 1099])).
% 2.34/2.56 tff(11724,plain,
% 2.34/2.56 (b(s(s(s(s(z)))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[254, 11723, 3])).
% 2.34/2.56 tff(11725,plain,
% 2.34/2.56 (~b(s(s(z)), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[5574, 11724, 6754, 499, 1099])).
% 2.34/2.56 tff(11726,plain,
% 2.34/2.56 (~r(s(s(s(s(s(z))))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2414, 11722, 1099])).
% 2.34/2.56 tff(11727,plain,
% 2.34/2.56 (b(s(s(s(s(s(z))))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[297, 11726])).
% 2.34/2.56 tff(11728,plain,
% 2.34/2.56 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[5331, 11727, 6754, 499])).
% 2.34/2.56 tff(11729,plain,
% 2.34/2.56 (s(s(s(s(z)))) = elem!1),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2070, 76, 221, 2081, 3448])).
% 2.34/2.56 tff(11730,plain,
% 2.34/2.56 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[4469, 11729, 722])).
% 2.34/2.56 tff(11731,plain,
% 2.34/2.56 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1982, 4459, 11730])).
% 2.34/2.56 tff(11732,plain,
% 2.34/2.56 (~b(s(elem!1), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7006, 11729, 638])).
% 2.34/2.56 tff(11733,plain,
% 2.34/2.56 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[528, 11732, 76])).
% 2.34/2.56 tff(11734,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[518, 11733, 11731])).
% 2.34/2.56 tff(11735,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | b(s(s(s(s(s(z))))), elem!1) | b(s(z), s(s(s(z)))) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(11736,plain,
% 2.34/2.56 (~(s(s(s(z))) = elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[11735, 3457, 638, 221, 128])).
% 2.34/2.56 tff(11737,plain,
% 2.34/2.56 (r(s(s(s(z))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[74, 11736, 58])).
% 2.34/2.56 tff(11738,plain,
% 2.34/2.56 (~r(s(s(z)), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10463, 11737, 3457])).
% 2.34/2.56 tff(11739,plain,
% 2.34/2.56 (s(s(z)) = elem!1),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[782, 11738, 4])).
% 2.34/2.56 tff(11740,plain,
% 2.34/2.56 (s(s(s(z))) = s(elem!1)),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11739])).
% 2.34/2.56 tff(11741,plain,
% 2.34/2.56 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11740])).
% 2.34/2.56 tff(11742,plain,
% 2.34/2.56 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11740])).
% 2.34/2.56 tff(11743,plain,
% 2.34/2.56 ((s(elem!1) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.56 inference(symmetry,[status(thm)],[11742])).
% 2.34/2.56 tff(11744,plain,
% 2.34/2.56 ((s(elem!1) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[11743, 5661])).
% 2.34/2.56 tff(11745,plain,
% 2.34/2.56 ((~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))) <=> (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11744])).
% 2.34/2.56 tff(11746,plain,
% 2.34/2.56 (~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3814, 11739])).
% 2.34/2.56 tff(11747,plain,
% 2.34/2.56 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[11746, 11745])).
% 2.34/2.56 tff(11748,plain,
% 2.34/2.56 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11740])).
% 2.34/2.56 tff(11749,plain,
% 2.34/2.56 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.34/2.56 inference(symmetry,[status(thm)],[11748])).
% 2.34/2.56 tff(11750,plain,
% 2.34/2.56 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11749])).
% 2.34/2.56 tff(11751,plain,
% 2.34/2.56 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.34/2.56 inference(symmetry,[status(thm)],[11750])).
% 2.34/2.56 tff(11752,plain,
% 2.34/2.56 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11748])).
% 2.34/2.56 tff(11753,plain,
% 2.34/2.56 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.34/2.56 inference(symmetry,[status(thm)],[11752])).
% 2.34/2.56 tff(11754,plain,
% 2.34/2.56 ((~b(s(s(elem!1)), s(z))) <=> (~b(s(s(s(s(z)))), s(z)))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11753])).
% 2.34/2.56 tff(11755,plain,
% 2.34/2.56 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11749])).
% 2.34/2.56 tff(11756,plain,
% 2.34/2.56 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.34/2.56 inference(symmetry,[status(thm)],[11755])).
% 2.34/2.56 tff(11757,plain,
% 2.34/2.56 (~(s(s(s(z))) = elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[4472, 249, 221, 638, 722, 128])).
% 2.34/2.56 tff(11758,plain,
% 2.34/2.56 (r(s(s(s(z))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[74, 11757, 58])).
% 2.34/2.56 tff(11759,plain,
% 2.34/2.56 (~r(s(s(z)), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10463, 11758, 722])).
% 2.34/2.56 tff(11760,plain,
% 2.34/2.56 (s(s(z)) = elem!1),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[782, 11759, 4])).
% 2.34/2.56 tff(11761,plain,
% 2.34/2.56 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11760])).
% 2.34/2.56 tff(11762,plain,
% 2.34/2.56 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.34/2.56 inference(symmetry,[status(thm)],[11761])).
% 2.34/2.56 tff(11763,plain,
% 2.34/2.56 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[10455, 3553])).
% 2.34/2.56 tff(11764,plain,
% 2.34/2.56 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[3477])).
% 2.34/2.56 tff(11765,plain,
% 2.34/2.56 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[11764, 6536])).
% 2.34/2.56 tff(11766,plain,
% 2.34/2.56 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11765])).
% 2.34/2.56 tff(11767,plain,
% 2.34/2.56 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[557, 555])).
% 2.34/2.56 tff(11768,plain,
% 2.34/2.56 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[11767, 11766])).
% 2.34/2.56 tff(11769,plain,
% 2.34/2.56 (r(s(s(s(elem!1))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3576, 3468, 722])).
% 2.34/2.56 tff(11770,plain,
% 2.34/2.56 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[877, 3507, 11769])).
% 2.34/2.56 tff(11771,plain,
% 2.34/2.56 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[675, 11770, 11768])).
% 2.34/2.56 tff(11772,plain,
% 2.34/2.56 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[11771, 3545])).
% 2.34/2.56 tff(11773,plain,
% 2.34/2.56 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[3477])).
% 2.34/2.56 tff(11774,plain,
% 2.34/2.56 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[3469])).
% 2.34/2.56 tff(11775,plain,
% 2.34/2.56 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(elem!1)), s(elem!1))),
% 2.34/2.56 inference(transitivity,[status(thm)],[11774, 11773])).
% 2.34/2.56 tff(11776,plain,
% 2.34/2.56 (r(s(s(s(s(z)))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[254, 3490, 249])).
% 2.34/2.56 tff(11777,plain,
% 2.34/2.56 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[4961, 11776, 1545])).
% 2.34/2.56 tff(11778,plain,
% 2.34/2.56 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[518, 11777])).
% 2.34/2.56 tff(11779,plain,
% 2.34/2.56 (b(s(s(elem!1)), s(elem!1))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[11778, 11775])).
% 2.34/2.56 tff(11780,plain,
% 2.34/2.56 ((s(s(s(z))) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[3469])).
% 2.34/2.56 tff(11781,plain,
% 2.34/2.56 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11780])).
% 2.34/2.56 tff(11782,plain,
% 2.34/2.56 (~(s(elem!1) = s(s(elem!1)))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[555, 11781])).
% 2.34/2.56 tff(11783,plain,
% 2.34/2.56 (~r(s(elem!1), s(s(elem!1)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[11373, 3507, 5670])).
% 2.34/2.56 tff(11784,plain,
% 2.34/2.56 (b(s(elem!1), s(s(elem!1)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[440, 11783, 11782])).
% 2.34/2.56 tff(11785,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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(11786,plain,
% 2.34/2.56 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(11787,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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), 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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11786])).
% 2.34/2.56 tff(11788,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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), 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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[11787, 11785])).
% 2.34/2.56 tff(11789,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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(11790,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[11789, 11788])).
% 2.34/2.56 tff(11791,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[11790, 453, 11784, 11779, 11772, 11763])).
% 2.34/2.56 tff(11792,plain,((~(s(s(z)) = elem!1)) | (~r(s(s(s(z))), elem!1)) | b(s(s(s(s(z)))), elem!1) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(11793,plain,
% 2.34/2.56 (s(s(s(z))) = s(s(elem!1))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[11792, 11760, 249, 11758, 722])).
% 2.34/2.56 tff(11794,plain,
% 2.34/2.56 (s(z) = elem!1),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[547, 11793])).
% 2.34/2.56 tff(11795,plain,
% 2.34/2.56 (elem!1 = s(z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1125, 11794])).
% 2.34/2.56 tff(11796,plain,
% 2.34/2.56 (~r(s(s(s(s(z)))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9917, 11795, 722, 3448, 11758])).
% 2.34/2.56 tff(11797,plain,
% 2.34/2.56 (s(s(s(s(z)))) = elem!1),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[254, 11796, 249])).
% 2.34/2.56 tff(11798,plain,
% 2.34/2.56 (s(s(s(s(z)))) = s(s(z))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[11797, 11762])).
% 2.34/2.56 tff(11799,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[153, 11798])).
% 2.34/2.56 tff(11800,plain,(b(s(s(s(s(z)))), elem!1) | (~r(s(s(s(s(s(z))))), elem!1)) | b(s(s(z)), elem!1) | b(s(s(s(z))), elem!1) | b(s(z), s(s(s(z)))) | b(s(s(s(s(s(z))))), elem!1) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(11801,plain,
% 2.34/2.56 (b(s(s(s(s(z)))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[11800, 3457, 4, 58, 221, 638, 128])).
% 2.34/2.56 tff(11802,plain,
% 2.34/2.56 (b(s(s(elem!1)), elem!1)),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[11801, 11756])).
% 2.34/2.56 tff(11803,plain,
% 2.34/2.56 ((s(z) = s(s(z))) <=> (s(z) = elem!1)),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11739])).
% 2.34/2.56 tff(11804,plain,
% 2.34/2.56 ((s(z) = s(s(z))) <=> (elem!1 = s(z))),
% 2.34/2.56 inference(transitivity,[status(thm)],[11803, 1120])).
% 2.34/2.56 tff(11805,plain,
% 2.34/2.56 ((~(s(z) = s(s(z)))) <=> (~(elem!1 = s(z)))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11804])).
% 2.34/2.56 tff(11806,plain,
% 2.34/2.56 (~(elem!1 = s(z))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[752, 11805])).
% 2.34/2.56 tff(11807,plain,
% 2.34/2.56 (b(elem!1, s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1130, 11806, 2076])).
% 2.34/2.56 tff(11808,plain,
% 2.34/2.56 ((~(s(z) = s(s(z)))) <=> (~(s(z) = elem!1))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11803])).
% 2.34/2.56 tff(11809,plain,
% 2.34/2.56 (~(s(z) = elem!1)),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[752, 11808])).
% 2.34/2.56 tff(11810,plain,
% 2.34/2.56 (b(s(z), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[506, 11809, 4541])).
% 2.34/2.56 tff(11811,plain,
% 2.34/2.56 (~b(s(s(elem!1)), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[11014, 453, 11810, 11807, 11802])).
% 2.34/2.56 tff(11812,plain,
% 2.34/2.56 (~b(s(s(s(s(z)))), s(z))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[11811, 11754])).
% 2.34/2.56 tff(11813,assumption,(s(s(s(s(s(z))))) = s(s(s(elem!1)))), introduced(assumption)).
% 2.34/2.56 tff(11814,plain,
% 2.34/2.56 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.34/2.56 inference(symmetry,[status(thm)],[11813])).
% 2.34/2.56 tff(11815,plain,
% 2.34/2.56 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(z))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11814])).
% 2.34/2.56 tff(11816,plain,
% 2.34/2.56 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[846, 11815, 23])).
% 2.34/2.56 tff(11817,plain,
% 2.34/2.56 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11816])).
% 2.34/2.56 tff(11818,plain,
% 2.34/2.56 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.34/2.56 inference(symmetry,[status(thm)],[11817])).
% 2.34/2.56 tff(11819,plain,
% 2.34/2.56 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11818])).
% 2.34/2.56 tff(11820,plain,
% 2.34/2.56 (~b(s(s(elem!1)), s(z))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[1057, 11819])).
% 2.34/2.56 tff(11821,plain,
% 2.34/2.56 (r(s(s(elem!1)), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1047, 11820])).
% 2.34/2.56 tff(11822,plain,
% 2.34/2.56 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11816])).
% 2.34/2.56 tff(11823,plain,
% 2.34/2.56 (s(elem!1) = s(s(s(z)))),
% 2.34/2.56 inference(transitivity,[status(thm)],[195, 11822, 37])).
% 2.34/2.56 tff(11824,plain,
% 2.34/2.56 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(z))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11823])).
% 2.34/2.56 tff(11825,plain,
% 2.34/2.56 (r(s(z), s(s(s(z)))) <=> r(s(z), s(elem!1))),
% 2.34/2.56 inference(symmetry,[status(thm)],[11824])).
% 2.34/2.56 tff(11826,plain,
% 2.34/2.56 (r(s(z), s(elem!1))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[257, 11825])).
% 2.34/2.56 tff(11827,plain,
% 2.34/2.56 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11816])).
% 2.34/2.56 tff(11828,plain,
% 2.34/2.56 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.34/2.56 inference(symmetry,[status(thm)],[11827])).
% 2.34/2.56 tff(11829,plain,
% 2.34/2.56 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 2.34/2.56 inference(symmetry,[status(thm)],[11822])).
% 2.34/2.56 tff(11830,plain,
% 2.34/2.56 (s(s(s(z))) = s(elem!1)),
% 2.34/2.56 inference(transitivity,[status(thm)],[38, 11829, 194])).
% 2.34/2.56 tff(11831,plain,
% 2.34/2.56 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11830])).
% 2.34/2.56 tff(11832,plain,
% 2.34/2.56 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(elem!1))),
% 2.34/2.56 inference(transitivity,[status(thm)],[11831, 11828])).
% 2.34/2.56 tff(11833,plain,
% 2.34/2.56 (r(s(s(elem!1)), s(elem!1))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[11, 11832])).
% 2.34/2.56 tff(11834,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3414, 11833, 11826, 11821])).
% 2.34/2.56 tff(11835,plain,((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(11836,plain,
% 2.34/2.56 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[11835, 11812, 228, 11751])).
% 2.34/2.56 tff(11837,plain,
% 2.34/2.56 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[518, 11836])).
% 2.34/2.56 tff(11838,plain,
% 2.34/2.56 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1566, 11737, 3457])).
% 2.34/2.56 tff(11839,plain,
% 2.34/2.56 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[687, 11838])).
% 2.34/2.56 tff(11840,plain,
% 2.34/2.56 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7254, 11812, 4541, 11806])).
% 2.34/2.56 tff(11841,plain,
% 2.34/2.56 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1656, 11840])).
% 2.34/2.56 tff(11842,plain,
% 2.34/2.56 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[10102, 11841, 11839, 11837])).
% 2.34/2.56 tff(11843,plain,
% 2.34/2.56 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2846, 11842, 11747])).
% 2.34/2.56 tff(11844,plain,
% 2.34/2.56 (r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[11843, 11741])).
% 2.34/2.56 tff(11845,plain,
% 2.34/2.56 (~(s(s(s(s(s(s(s(s(z)))))))) = elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[5602, 11739])).
% 2.34/2.56 tff(11846,plain,
% 2.34/2.56 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11748])).
% 2.34/2.56 tff(11847,plain,
% 2.34/2.56 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.34/2.56 inference(symmetry,[status(thm)],[11846])).
% 2.34/2.56 tff(11848,plain,
% 2.34/2.56 (r(s(s(elem!1)), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1047, 11811])).
% 2.34/2.56 tff(11849,plain,
% 2.34/2.56 (r(s(s(s(s(z)))), s(z))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[11848, 11847])).
% 2.34/2.56 tff(11850,plain,
% 2.34/2.56 (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[9968, 11837, 3448, 11747, 11849])).
% 2.34/2.56 tff(11851,plain,
% 2.34/2.56 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2906, 69, 11850, 2886])).
% 2.34/2.56 tff(11852,plain,
% 2.34/2.56 (r(s(z), s(s(s(z)))) <=> r(s(z), s(elem!1))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11740])).
% 2.34/2.56 tff(11853,plain,
% 2.34/2.56 (r(s(z), s(elem!1))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[228, 11852])).
% 2.34/2.56 tff(11854,plain,
% 2.34/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(11855,plain,
% 2.34/2.56 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(11856,plain,
% 2.34/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11855])).
% 2.34/2.56 tff(11857,plain,
% 2.34/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[11856, 11854])).
% 2.34/2.56 tff(11858,plain,
% 2.34/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(11859,plain,
% 2.34/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[11858, 11857])).
% 2.34/2.56 tff(11860,plain,
% 2.34/2.56 (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[11859, 268, 11853, 11844])).
% 2.34/2.56 tff(11861,plain,
% 2.34/2.56 (b(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[6101, 69, 2884, 11860])).
% 2.34/2.56 tff(11862,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(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(11863,plain,
% 2.34/2.56 (((~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(11864,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(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11863])).
% 2.34/2.56 tff(11865,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(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.34/2.56 inference(transitivity,[status(thm)],[11864, 11862])).
% 2.34/2.56 tff(11866,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(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(11867,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(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[11866, 11865])).
% 2.34/2.56 tff(11868,plain,
% 2.34/2.56 (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[11867, 453, 11807, 11861, 11851])).
% 2.34/2.56 tff(11869,plain,
% 2.34/2.56 (r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[5649, 11868, 11845])).
% 2.34/2.56 tff(11870,plain,
% 2.34/2.56 (r(s(s(s(z))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11740])).
% 2.34/2.56 tff(11871,plain,
% 2.34/2.56 (r(s(elem!1), elem!1)),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[11737, 11870])).
% 2.34/2.56 tff(11872,plain,
% 2.34/2.56 (r(s(s(s(z))), s(z)) <=> r(s(elem!1), s(z))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[11740])).
% 2.34/2.56 tff(11873,plain,
% 2.34/2.56 (r(s(elem!1), s(z))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[3448, 11872])).
% 2.34/2.56 tff(11874,plain,
% 2.34/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(11875,plain,
% 2.34/2.56 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11876,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[11875])).
% 2.34/2.57 tff(11877,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.34/2.57 inference(transitivity,[status(thm)],[11876, 11874])).
% 2.34/2.57 tff(11878,plain,
% 2.34/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(11879,plain,
% 2.34/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[11878, 11877])).
% 2.34/2.57 tff(11880,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11879, 268, 11873, 11871, 11869, 11844])).
% 2.34/2.57 tff(11881,plain,(b(s(s(s(s(s(z))))), elem!1) | r(s(z), elem!1) | r(elem!1, s(z)) | b(s(s(z)), elem!1) | b(s(s(s(z))), elem!1) | b(s(z), s(s(s(z)))) | b(s(s(s(z))), s(z)) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(11882,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11881, 11728, 11725, 221, 128, 2076, 11715, 4541, 58])).
% 2.34/2.57 tff(11883,plain,(b(s(s(s(s(z)))), s(z)) | b(s(z), s(s(s(z)))) | b(s(s(s(z))), s(z)) | r(elem!1, s(z)) | r(s(z), elem!1) | b(s(s(s(z))), elem!1) | (~b(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(11884,plain,
% 2.34/2.57 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11883, 128, 221, 10664, 4541, 11196, 11713, 3, 11712])).
% 2.34/2.57 tff(11885,plain,
% 2.34/2.57 (b(elem!1, s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1130, 11712, 10664])).
% 2.34/2.57 tff(11886,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[5442, 453, 499, 2077, 1764, 530])).
% 2.34/2.57 tff(11887,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(11888,plain,
% 2.34/2.57 (~b(elem!1, s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11887, 11713, 11885, 11884])).
% 2.34/2.57 tff(11889,plain,
% 2.34/2.57 (r(elem!1, s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1087, 11888, 9])).
% 2.34/2.57 tff(11890,plain,
% 2.34/2.57 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[5333, 11885, 228, 11062, 11197, 11713])).
% 2.34/2.57 tff(11891,plain,
% 2.34/2.57 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[687, 11890])).
% 2.34/2.57 tff(11892,plain,
% 2.34/2.57 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[5432, 11889, 1149, 11197])).
% 2.34/2.57 tff(11893,plain,
% 2.34/2.57 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1656, 11892])).
% 2.34/2.57 tff(11894,plain,
% 2.34/2.57 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11895,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(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[11894])).
% 2.34/2.57 tff(11896,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(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[11895, 10973])).
% 2.34/2.57 tff(11897,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(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(11898,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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[11897, 11896])).
% 2.34/2.57 tff(11899,plain,
% 2.34/2.57 (~b(s(s(s(s(z)))), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11898, 453, 11713, 11885, 11884])).
% 2.34/2.57 tff(11900,plain,
% 2.34/2.57 (r(s(s(s(s(z)))), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[254, 11899, 3])).
% 2.34/2.57 tff(11901,plain,
% 2.34/2.57 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[8475, 11900, 1149])).
% 2.34/2.57 tff(11902,plain,
% 2.34/2.57 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[518, 11901])).
% 2.34/2.57 tff(11903,plain,
% 2.34/2.57 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[10120, 453, 11902, 11893, 11891])).
% 2.34/2.57 tff(11904,plain,
% 2.34/2.57 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[10556, 11903])).
% 2.34/2.57 tff(11905,plain,
% 2.34/2.57 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[427, 11904, 11889])).
% 2.34/2.57 tff(11906,plain,
% 2.34/2.57 (b(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[466, 11905, 11063])).
% 2.34/2.57 tff(11907,plain,
% 2.34/2.57 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[501, 11713, 221])).
% 2.34/2.57 tff(11908,plain,
% 2.34/2.57 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1788, 11902, 11891, 11893])).
% 2.34/2.57 tff(11909,plain,
% 2.34/2.57 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[328, 11908])).
% 2.34/2.57 tff(11910,plain,
% 2.34/2.57 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11156, 268, 11909, 11889])).
% 2.34/2.57 tff(11911,plain,
% 2.34/2.57 (b(s(s(s(s(s(z))))), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[643, 11910, 11062])).
% 2.34/2.57 tff(11912,plain,
% 2.34/2.57 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1788, 523, 1779, 1633])).
% 2.34/2.57 tff(11913,plain,
% 2.34/2.57 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[328, 11912])).
% 2.34/2.57 tff(11914,plain,
% 2.34/2.57 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[10556, 10121])).
% 2.34/2.57 tff(11915,plain,
% 2.34/2.57 (~b(s(z), s(s(s(s(s(z))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11166, 646, 2077, 499])).
% 2.34/2.57 tff(11916,plain,
% 2.34/2.57 (r(s(z), s(s(s(s(s(z))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[372, 11915])).
% 2.34/2.57 tff(11917,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11918,plain,
% 2.34/2.57 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11919,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[11918])).
% 2.34/2.57 tff(11920,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[11919, 11917])).
% 2.34/2.57 tff(11921,plain,
% 2.34/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(11922,plain,
% 2.34/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[11921, 11920])).
% 2.34/2.57 tff(11923,plain,
% 2.34/2.57 (~r(s(z), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11922, 268, 1159, 11916, 11914])).
% 2.34/2.57 tff(11924,plain,
% 2.34/2.57 (b(s(z), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1677, 69, 11923, 50])).
% 2.34/2.57 tff(11925,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(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11926,plain,
% 2.34/2.57 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11927,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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[11926])).
% 2.34/2.57 tff(11928,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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[11927, 11925])).
% 2.34/2.57 tff(11929,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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(11930,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(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[11929, 11928])).
% 2.34/2.57 tff(11931,plain,
% 2.34/2.57 (~b(s(s(s(z))), s(elem!1))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11930, 453, 523, 1633, 9384])).
% 2.34/2.57 tff(11932,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(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11933,plain,
% 2.34/2.57 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11934,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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[11933])).
% 2.34/2.57 tff(11935,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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[11934, 11932])).
% 2.34/2.57 tff(11936,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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(11937,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[11936, 11935])).
% 2.34/2.57 tff(11938,plain,
% 2.34/2.57 (~b(s(elem!1), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11937, 453, 523, 9384, 1974])).
% 2.34/2.57 tff(11939,plain,
% 2.34/2.57 (b(s(elem!1), s(z))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[2077, 4338])).
% 2.34/2.57 tff(11940,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1793, 11939])).
% 2.34/2.57 tff(11941,plain,((~(s(elem!1) = elem!1)) | b(s(elem!1), s(z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(11942,plain,
% 2.34/2.57 (~(s(elem!1) = elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11941, 11938, 2077])).
% 2.34/2.57 tff(11943,plain,
% 2.34/2.57 (r(s(elem!1), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[2440, 11942, 526])).
% 2.34/2.57 tff(11944,plain,
% 2.34/2.57 (~r(s(s(s(z))), s(elem!1))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7017, 11943, 1545])).
% 2.34/2.57 tff(11945,plain,
% 2.34/2.57 (s(s(s(z))) = s(elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9480, 11944, 11931])).
% 2.34/2.57 tff(11946,plain,
% 2.34/2.57 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[11945])).
% 2.34/2.57 tff(11947,plain,
% 2.34/2.57 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[10102, 523, 1779, 1633])).
% 2.34/2.57 tff(11948,plain,
% 2.34/2.57 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[11945])).
% 2.34/2.57 tff(11949,plain,
% 2.34/2.57 ((s(elem!1) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.57 inference(symmetry,[status(thm)],[11948])).
% 2.34/2.57 tff(11950,plain,
% 2.34/2.57 ((s(elem!1) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[11949, 5661])).
% 2.34/2.57 tff(11951,plain,
% 2.34/2.57 ((~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))) <=> (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[11950])).
% 2.34/2.57 tff(11952,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[4060, 9681])).
% 2.34/2.57 tff(11953,plain,((~(s(s(s(z))) = s(elem!1))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(11954,plain,
% 2.34/2.57 (s(s(z)) = elem!1),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11953, 11945])).
% 2.34/2.57 tff(11955,plain,
% 2.34/2.57 (~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[3814, 11954])).
% 2.34/2.57 tff(11956,plain,
% 2.34/2.57 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[11955, 11951])).
% 2.34/2.57 tff(11957,plain,
% 2.34/2.57 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[2846, 11956, 11947])).
% 2.34/2.57 tff(11958,plain,
% 2.34/2.57 (r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[11957, 11946])).
% 2.34/2.57 tff(11959,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(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11960,plain,
% 2.34/2.57 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11961,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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(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(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[11960])).
% 2.34/2.57 tff(11962,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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(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(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[11961, 11959])).
% 2.34/2.57 tff(11963,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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(11964,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(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[11963, 11962])).
% 2.34/2.57 tff(11965,plain,
% 2.34/2.57 (~b(s(z), s(elem!1))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[11964, 453, 523, 9384, 1974])).
% 2.34/2.57 tff(11966,plain,
% 2.34/2.57 (s(elem!1) = s(s(s(z)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9473, 11945])).
% 2.34/2.57 tff(11967,plain,
% 2.34/2.57 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9847, 11966])).
% 2.34/2.57 tff(11968,plain,
% 2.34/2.57 (~(s(z) = s(elem!1))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[9855, 11967])).
% 2.34/2.57 tff(11969,plain,
% 2.34/2.57 (r(s(z), s(elem!1))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[397, 11968, 11965])).
% 2.34/2.57 tff(11970,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11971,plain,
% 2.34/2.57 (((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(11972,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11971])).
% 2.34/2.58 tff(11973,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[11972, 11970])).
% 2.34/2.58 tff(11974,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(11975,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1)))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[11974, 11973])).
% 2.34/2.58 tff(11976,plain,
% 2.34/2.58 (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11975, 268, 11969, 11958])).
% 2.34/2.58 tff(11977,plain,
% 2.34/2.58 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[2906, 69, 11976, 2886])).
% 2.34/2.58 tff(11978,plain,
% 2.34/2.58 (~(s(s(s(s(s(s(s(s(z)))))))) = elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[5602, 11954])).
% 2.34/2.58 tff(11979,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(11980,plain,
% 2.34/2.58 (((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(11981,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11980])).
% 2.34/2.58 tff(11982,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[11981, 11979])).
% 2.34/2.58 tff(11983,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(elem!1))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(11984,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[11983, 11982])).
% 2.34/2.58 tff(11985,plain,
% 2.34/2.58 (~r(s(z), s(elem!1))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11984, 268, 2246, 3224])).
% 2.34/2.58 tff(11986,plain,
% 2.34/2.58 (s(z) = s(elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[397, 11985, 3641])).
% 2.34/2.58 tff(11987,plain,
% 2.34/2.58 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11986])).
% 2.34/2.58 tff(11988,plain,
% 2.34/2.58 (inj_0(s(elem!1)) = inj_0(s(z))),
% 2.34/2.58 inference(symmetry,[status(thm)],[11987])).
% 2.34/2.58 tff(11989,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(11990,plain,
% 2.34/2.58 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(11991,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11990])).
% 2.34/2.58 tff(11992,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[11991, 11989])).
% 2.34/2.58 tff(11993,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(11994,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[11993, 11992])).
% 2.34/2.58 tff(11995,plain,
% 2.34/2.58 (~r(s(elem!1), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11994, 268, 2246, 3224])).
% 2.34/2.58 tff(11996,plain,
% 2.34/2.58 (~(s(s(z)) = elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[3764, 11995, 233])).
% 2.34/2.58 tff(11997,plain,
% 2.34/2.58 (~(s(s(s(z))) = s(elem!1))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11953, 11996])).
% 2.34/2.58 tff(11998,plain,
% 2.34/2.58 (r(s(s(s(z))), s(elem!1))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9480, 11997, 6845])).
% 2.34/2.58 tff(11999,plain,
% 2.34/2.58 (~r(s(elem!1), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7017, 11998, 1545])).
% 2.34/2.58 tff(12000,plain,
% 2.34/2.58 (s(elem!1) = elem!1),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[2440, 11999, 526])).
% 2.34/2.58 tff(12001,plain,
% 2.34/2.58 (s(elem!1) = z),
% 2.34/2.58 inference(transitivity,[status(thm)],[12000, 86, 11988, 32])).
% 2.34/2.58 tff(12002,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[814, 12001])).
% 2.34/2.58 tff(12003,plain,((~r(s(elem!1), s(s(s(s(s(z))))))) | b(s(elem!1), elem!1) | (~r(s(s(s(z))), elem!1)) | b(s(s(s(z))), s(elem!1)) | (~r(s(s(s(z))), s(z))) | b(s(z), s(elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(12004,plain,
% 2.34/2.58 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12003, 11931, 1545, 526, 233, 11965, 2246])).
% 2.34/2.58 tff(12005,plain,
% 2.34/2.58 (b(s(elem!1), s(s(s(s(s(z))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[659, 12004, 3700])).
% 2.34/2.58 tff(12006,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(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12007,plain,
% 2.34/2.58 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12008,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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[12007])).
% 2.34/2.58 tff(12009,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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[12008, 12006])).
% 2.34/2.58 tff(12010,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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(12011,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[12010, 12009])).
% 2.34/2.58 tff(12012,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12011, 453, 1071, 923, 1779, 645])).
% 2.34/2.58 tff(12013,plain,((~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(12014,plain,
% 2.34/2.58 (~b(elem!1, s(elem!1))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12013, 12005, 1779, 923])).
% 2.34/2.58 tff(12015,plain,
% 2.34/2.58 (~(elem!1 = s(elem!1))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[8957, 11942])).
% 2.34/2.58 tff(12016,plain,
% 2.34/2.58 (r(elem!1, s(elem!1))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[1069, 12015, 12014])).
% 2.34/2.58 tff(12017,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12018,plain,
% 2.34/2.58 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12019,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[12018])).
% 2.34/2.58 tff(12020,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.34/2.58 inference(transitivity,[status(thm)],[12019, 12017])).
% 2.34/2.58 tff(12021,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(12022,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[12021, 12020])).
% 2.34/2.58 tff(12023,plain,
% 2.34/2.58 (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12022, 268, 12016, 11958])).
% 2.34/2.58 tff(12024,plain,
% 2.34/2.58 (b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[5649, 12023, 11978])).
% 2.34/2.58 tff(12025,plain,
% 2.34/2.58 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(z))) <=> (s(s(s(s(s(s(s(s(z)))))))) = elem!1)),
% 2.34/2.58 inference(monotonicity,[status(thm)],[11954])).
% 2.34/2.58 tff(12026,plain,
% 2.34/2.58 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(z))) <=> (elem!1 = s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[12025, 6008])).
% 2.34/2.58 tff(12027,plain,
% 2.34/2.58 ((~(s(s(s(s(s(s(s(s(z)))))))) = s(s(z)))) <=> (~(elem!1 = s(s(s(s(s(s(s(s(z))))))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[12026])).
% 2.34/2.58 tff(12028,assumption,(s(s(s(s(s(s(s(s(z)))))))) = s(s(z))), introduced(assumption)).
% 2.34/2.58 tff(12029,plain,
% 2.34/2.58 (inj_0(s(s(s(s(s(s(s(s(z))))))))) = inj_0(s(s(z)))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[12028])).
% 2.34/2.58 tff(12030,plain,
% 2.34/2.58 (s(s(s(s(s(s(s(z))))))) = s(z)),
% 2.34/2.58 inference(transitivity,[status(thm)],[2336, 12029, 28])).
% 2.34/2.58 tff(12031,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[2636, 12030])).
% 2.34/2.58 tff(12032,plain,(~(s(s(s(s(s(s(s(s(z)))))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(12033,plain,
% 2.34/2.58 (~(elem!1 = s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[12032, 12027])).
% 2.34/2.58 tff(12034,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12035,plain,
% 2.34/2.58 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12036,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(s(z))))))))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[12035])).
% 2.34/2.58 tff(12037,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[12036, 12034])).
% 2.34/2.58 tff(12038,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(12039,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(s(s(z))))))))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[12038, 12037])).
% 2.34/2.58 tff(12040,plain,
% 2.34/2.58 (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12039, 268, 12016, 11958])).
% 2.34/2.58 tff(12041,plain,
% 2.34/2.58 (b(elem!1, s(s(s(s(s(s(s(s(z)))))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[11518, 12040, 12033])).
% 2.34/2.58 tff(12042,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(z), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12043,plain,
% 2.34/2.58 (((~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12044,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(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(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(z), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[12043])).
% 2.34/2.58 tff(12045,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(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(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(z), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.34/2.58 inference(transitivity,[status(thm)],[12044, 12042])).
% 2.34/2.58 tff(12046,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(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(12047,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[12046, 12045])).
% 2.34/2.58 tff(12048,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12047, 453, 499, 12041, 12024, 11977])).
% 2.34/2.58 tff(12049,plain,((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | b(s(elem!1), elem!1) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (s(elem!1) = s(s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(12050,plain,
% 2.34/2.58 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12049, 526, 1545, 499, 2077, 1779, 923, 3700, 233, 11916, 523, 11924, 1633])).
% 2.34/2.58 tff(12051,plain,
% 2.34/2.58 (r(s(elem!1), s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[9382, 12050, 79])).
% 2.34/2.58 tff(12052,plain,
% 2.34/2.58 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[10607, 12051, 11913])).
% 2.34/2.58 tff(12053,plain,
% 2.34/2.58 (b(s(elem!1), s(s(s(s(s(z))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[659, 12052, 3700])).
% 2.34/2.58 tff(12054,plain,
% 2.34/2.58 (~b(elem!1, s(elem!1))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[12013, 12053, 1779, 923])).
% 2.34/2.58 tff(12055,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12056,plain,
% 2.34/2.58 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(12057,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[12056])).
% 2.34/2.59 tff(12058,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[12057, 12055])).
% 2.34/2.59 tff(12059,plain,
% 2.34/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(12060,plain,
% 2.34/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[12059, 12058])).
% 2.34/2.59 tff(12061,plain,
% 2.34/2.59 (~r(elem!1, s(elem!1))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12060, 268, 419, 12051])).
% 2.34/2.59 tff(12062,plain,
% 2.34/2.59 (elem!1 = s(elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1069, 12061, 12054])).
% 2.34/2.59 tff(12063,plain,
% 2.34/2.59 (s(elem!1) = elem!1),
% 2.34/2.59 inference(symmetry,[status(thm)],[12062])).
% 2.34/2.59 tff(12064,plain,
% 2.34/2.59 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), elem!1)),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12063])).
% 2.34/2.59 tff(12065,plain,
% 2.34/2.59 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(elem!1))),
% 2.34/2.59 inference(symmetry,[status(thm)],[12064])).
% 2.34/2.59 tff(12066,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12067,plain,
% 2.34/2.59 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12068,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12067])).
% 2.34/2.59 tff(12069,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[12068, 12066])).
% 2.34/2.59 tff(12070,plain,
% 2.34/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(12071,plain,
% 2.34/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[12070, 12069])).
% 2.34/2.59 tff(12072,plain,
% 2.34/2.59 (~r(s(elem!1), elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12071, 268, 419, 12051])).
% 2.34/2.59 tff(12073,plain,
% 2.34/2.59 (s(elem!1) = elem!1),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[2440, 12072, 526])).
% 2.34/2.59 tff(12074,plain,
% 2.34/2.59 (elem!1 = s(s(elem!1))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3351, 12073])).
% 2.34/2.59 tff(12075,plain,
% 2.34/2.59 (s(s(elem!1)) = elem!1),
% 2.34/2.59 inference(symmetry,[status(thm)],[12074])).
% 2.34/2.59 tff(12076,plain,
% 2.34/2.59 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = elem!1)),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12075])).
% 2.34/2.59 tff(12077,plain,
% 2.34/2.59 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(z)) = elem!1))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12076])).
% 2.34/2.59 tff(12078,plain,
% 2.34/2.59 (~b(s(s(s(s(s(z))))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[5331, 646, 2077, 499])).
% 2.34/2.59 tff(12079,plain,
% 2.34/2.59 (r(s(s(s(s(s(z))))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[297, 12078])).
% 2.34/2.59 tff(12080,plain,
% 2.34/2.59 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11276, 268, 11913, 12051])).
% 2.34/2.59 tff(12081,plain,
% 2.34/2.59 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[163])).
% 2.34/2.59 tff(12082,plain,
% 2.34/2.59 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(z))),
% 2.34/2.59 inference(symmetry,[status(thm)],[12081])).
% 2.34/2.59 tff(12083,plain,
% 2.34/2.59 ((~r(s(s(s(s(s(z))))), s(elem!1))) <=> (~r(s(s(s(s(s(z))))), s(z)))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12082])).
% 2.34/2.59 tff(12084,assumption,(~r(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 2.34/2.59 tff(12085,plain,
% 2.34/2.59 (~r(s(s(s(s(s(z))))), s(z))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[12084, 12083])).
% 2.34/2.59 tff(12086,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[258, 12085])).
% 2.34/2.59 tff(12087,plain,((~(s(z) = s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))) | r(s(s(s(s(s(z))))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(12088,plain,
% 2.34/2.59 (~(s(z) = s(elem!1))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12087, 12080, 12079])).
% 2.34/2.59 tff(12089,plain,
% 2.34/2.59 (~(s(elem!1) = s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[179, 12088])).
% 2.34/2.59 tff(12090,plain,
% 2.34/2.59 (~(s(s(z)) = s(s(elem!1)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1188, 12089])).
% 2.34/2.59 tff(12091,plain,
% 2.34/2.59 (~(s(s(z)) = elem!1)),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[12090, 12077])).
% 2.34/2.59 tff(12092,plain,
% 2.34/2.59 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(elem!1))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12062])).
% 2.34/2.59 tff(12093,plain,
% 2.34/2.59 (r(s(s(s(z))), s(elem!1))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[1545, 12092])).
% 2.34/2.59 tff(12094,plain,
% 2.34/2.59 (s(elem!1) = elem!1),
% 2.34/2.59 inference(symmetry,[status(thm)],[8954])).
% 2.34/2.59 tff(12095,plain,
% 2.34/2.59 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), elem!1)),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12094])).
% 2.34/2.59 tff(12096,plain,
% 2.34/2.59 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(elem!1))),
% 2.34/2.59 inference(symmetry,[status(thm)],[12095])).
% 2.34/2.59 tff(12097,plain,
% 2.34/2.59 (r(s(s(z)), s(elem!1))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[700, 12096])).
% 2.34/2.59 tff(12098,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(z)), s(elem!1))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12099,plain,
% 2.34/2.59 (((~r(s(s(z)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(z)), s(elem!1))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12100,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(z)), s(elem!1)))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12099])).
% 2.34/2.59 tff(12101,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(z)), s(elem!1))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[12100, 12098])).
% 2.34/2.59 tff(12102,plain,
% 2.34/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(12103,plain,
% 2.34/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(z)), s(elem!1)))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[12102, 12101])).
% 2.34/2.59 tff(12104,plain,
% 2.34/2.59 ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(elem!1)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12103, 268, 7009])).
% 2.34/2.59 tff(12105,plain,
% 2.34/2.59 (~r(s(s(s(z))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12104, 12097])).
% 2.34/2.59 tff(12106,plain,
% 2.34/2.59 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6942, 700, 419])).
% 2.34/2.59 tff(12107,plain,
% 2.34/2.59 (b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[2370, 69, 12106, 2359])).
% 2.34/2.59 tff(12108,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(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12109,plain,
% 2.34/2.59 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12110,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(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12109])).
% 2.34/2.59 tff(12111,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(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[12110, 12108])).
% 2.34/2.59 tff(12112,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(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(12113,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[12112, 12111])).
% 2.34/2.59 tff(12114,plain,
% 2.34/2.59 (~b(s(s(s(z))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12113, 453, 1633, 8417, 12107])).
% 2.34/2.59 tff(12115,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[2534, 69, 160, 12114, 12105])).
% 2.34/2.59 tff(12116,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))) | (~(elem!1 = s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(12117,plain,
% 2.34/2.59 (~r(s(s(z)), elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12116, 12093, 1633, 12062, 419, 1159])).
% 2.34/2.59 tff(12118,plain,
% 2.34/2.59 (b(s(s(z)), elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[782, 12117, 12091])).
% 2.34/2.59 tff(12119,plain,
% 2.34/2.59 (b(s(s(z)), s(elem!1))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[12118, 12065])).
% 2.34/2.59 tff(12120,plain,
% 2.34/2.59 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[4078, 12118, 923, 646])).
% 2.34/2.59 tff(12121,plain,
% 2.34/2.59 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[4081, 12120])).
% 2.34/2.59 tff(12122,plain,
% 2.34/2.59 (~r(s(z), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[2476, 12121, 12079])).
% 2.34/2.59 tff(12123,plain,
% 2.34/2.59 (b(s(z), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[757, 12122])).
% 2.34/2.59 tff(12124,plain,
% 2.34/2.59 (b(s(z), elem!1) <=> b(s(z), s(elem!1))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12062])).
% 2.34/2.59 tff(12125,plain,
% 2.34/2.59 (b(s(z), s(elem!1))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[499, 12124])).
% 2.34/2.59 tff(12126,plain,
% 2.34/2.59 (b(s(elem!1), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11941, 12073, 2077])).
% 2.34/2.59 tff(12127,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(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), 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(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(s(z), s(s(z)))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12128,plain,
% 2.34/2.59 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(s(z), s(s(z)))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12129,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(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), 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(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(s(z), s(s(z))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12128])).
% 2.34/2.59 tff(12130,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(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), 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(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(s(z), s(s(z)))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[12129, 12127])).
% 2.34/2.59 tff(12131,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(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(z), s(s(z)))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(12132,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(s(z), s(s(z))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[12131, 12130])).
% 2.34/2.59 tff(12133,plain,
% 2.34/2.59 (~b(s(s(z)), s(elem!1))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12132, 453, 12126, 12125, 12123])).
% 2.34/2.59 tff(12134,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12133, 12119])).
% 2.34/2.59 tff(12135,plain,(b(s(elem!1), elem!1) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (s(elem!1) = s(s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(12136,plain,
% 2.34/2.59 (b(s(elem!1), elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12135, 11906, 11911, 11893, 11889, 11900, 11197, 11713, 11885, 11891, 10371, 11907, 3448, 11902])).
% 2.34/2.59 tff(12137,plain,
% 2.34/2.59 (~b(s(z), s(elem!1))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[2152, 12136, 11713, 11906])).
% 2.34/2.59 tff(12138,plain,
% 2.34/2.59 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3132, 12136, 11911, 11906])).
% 2.34/2.59 tff(12139,plain,
% 2.34/2.59 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[659, 12138, 10371])).
% 2.34/2.59 tff(12140,plain,
% 2.34/2.59 (~b(s(z), s(s(s(s(s(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11166, 11911, 11885, 11713])).
% 2.34/2.59 tff(12141,plain,
% 2.34/2.59 (r(s(z), s(s(s(s(s(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[372, 12140])).
% 2.34/2.59 tff(12142,plain,
% 2.34/2.59 (~r(s(z), s(elem!1))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11984, 268, 12141, 12139])).
% 2.34/2.59 tff(12143,plain,
% 2.34/2.59 (s(z) = s(elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[397, 12142, 12137])).
% 2.34/2.59 tff(12144,plain,
% 2.34/2.59 (s(s(z)) = s(s(elem!1))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12143])).
% 2.34/2.59 tff(12145,plain,
% 2.34/2.59 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12144])).
% 2.34/2.59 tff(12146,plain,
% 2.34/2.59 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.59 inference(symmetry,[status(thm)],[12145])).
% 2.34/2.59 tff(12147,plain,
% 2.34/2.59 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), s(s(z))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12146])).
% 2.34/2.59 tff(12148,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(z))) | (~b(elem!1, s(z))) | (~b(s(z), 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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12149,plain,
% 2.34/2.59 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(12150,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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[12149])).
% 2.34/2.59 tff(12151,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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.34/2.59 inference(transitivity,[status(thm)],[12150, 12148])).
% 2.34/2.59 tff(12152,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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(12153,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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[12152, 12151])).
% 2.34/2.59 tff(12154,plain,
% 2.34/2.59 (~b(s(elem!1), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12153, 453, 11713, 11885, 12136])).
% 2.34/2.59 tff(12155,plain,
% 2.34/2.59 (~(s(elem!1) = elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11941, 12154, 11885])).
% 2.34/2.59 tff(12156,plain,
% 2.34/2.59 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[607, 12155])).
% 2.34/2.59 tff(12157,plain,
% 2.34/2.59 (~b(s(s(s(elem!1))), elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6839, 12143, 11196])).
% 2.34/2.59 tff(12158,plain,
% 2.34/2.59 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[10607, 12139, 11909])).
% 2.34/2.59 tff(12159,plain,
% 2.34/2.59 (b(s(elem!1), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[9382, 12158, 11907])).
% 2.34/2.59 tff(12160,plain,
% 2.34/2.59 (~b(s(s(s(z))), s(elem!1))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11930, 453, 11902, 11893, 12159])).
% 2.34/2.59 tff(12161,plain,
% 2.34/2.59 (~b(s(s(s(elem!1))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6847, 12143, 12160])).
% 2.34/2.59 tff(12162,plain,
% 2.34/2.59 (~(s(s(s(elem!1))) = elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6409, 12161, 11885])).
% 2.34/2.59 tff(12163,plain,
% 2.34/2.59 (r(s(s(s(elem!1))), elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[567, 12162, 12157])).
% 2.34/2.59 tff(12164,plain,
% 2.34/2.59 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 2.34/2.59 inference(monotonicity,[status(thm)],[1797])).
% 2.34/2.59 tff(12165,plain,
% 2.34/2.59 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.34/2.59 inference(symmetry,[status(thm)],[12164])).
% 2.34/2.59 tff(12166,plain,
% 2.34/2.59 (b(s(s(s(elem!1))), elem!1)),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[629, 12165])).
% 2.34/2.59 tff(12167,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3333, 12166])).
% 2.34/2.59 tff(12168,plain,((~(s(s(s(elem!1))) = s(elem!1))) | b(s(s(s(elem!1))), elem!1) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(12169,plain,
% 2.34/2.59 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[12168, 12157, 12136])).
% 2.34/2.59 tff(12170,plain,
% 2.34/2.59 (~(elem!1 = s(s(elem!1)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[4223, 12169])).
% 2.34/2.59 tff(12171,plain,
% 2.34/2.59 (~(s(s(elem!1)) = elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3359, 12170])).
% 2.34/2.59 tff(12172,plain,
% 2.34/2.59 (~(elem!1 = s(elem!1))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[8957, 12155])).
% 2.34/2.59 tff(12173,plain,
% 2.34/2.59 (~r(s(elem!1), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11994, 268, 12141, 12139])).
% 2.34/2.59 tff(12174,plain,
% 2.34/2.59 (~(s(s(z)) = elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3764, 12173, 3448])).
% 2.34/2.59 tff(12175,plain,
% 2.34/2.59 (~(s(s(s(z))) = s(elem!1))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[11953, 12174])).
% 2.34/2.59 tff(12176,plain,
% 2.34/2.59 (r(s(s(s(z))), s(elem!1))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[9480, 12175, 12160])).
% 2.34/2.60 tff(12177,plain,
% 2.34/2.60 (~r(elem!1, s(elem!1))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[9495, 12176, 1149])).
% 2.34/2.60 tff(12178,plain,
% 2.34/2.60 (b(elem!1, s(elem!1))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[1069, 12177, 12172])).
% 2.34/2.60 tff(12179,plain,
% 2.34/2.60 (~(s(elem!1) = s(s(elem!1)))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[1861, 12170])).
% 2.34/2.60 tff(12180,plain,
% 2.34/2.60 (~b(s(s(s(s(s(z))))), s(z))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[5331, 11911, 11885, 11713])).
% 2.34/2.60 tff(12181,plain,
% 2.34/2.60 (r(s(s(s(s(s(z))))), s(z))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[297, 12180])).
% 2.34/2.60 tff(12182,plain,
% 2.34/2.60 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 2.34/2.60 inference(monotonicity,[status(thm)],[4981])).
% 2.34/2.60 tff(12183,plain,
% 2.34/2.60 (b(s(s(z)), elem!1)),
% 2.34/2.60 inference(modus_ponens,[status(thm)],[909, 12182])).
% 2.34/2.60 tff(12184,plain,
% 2.34/2.60 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[4078, 12183, 923, 646])).
% 2.34/2.60 tff(12185,plain,
% 2.34/2.60 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.34/2.60 inference(monotonicity,[status(thm)],[163, 4980])).
% 2.34/2.60 tff(12186,plain,
% 2.34/2.60 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 2.34/2.60 inference(symmetry,[status(thm)],[12185])).
% 2.34/2.60 tff(12187,plain,
% 2.34/2.60 (~b(s(elem!1), s(s(elem!1)))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[1079, 909, 629, 1071])).
% 2.34/2.60 tff(12188,plain,
% 2.34/2.60 (r(s(elem!1), s(s(elem!1)))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[440, 12187, 1997])).
% 2.34/2.60 tff(12189,plain,
% 2.34/2.60 (r(s(z), s(s(z)))),
% 2.34/2.60 inference(modus_ponens,[status(thm)],[12188, 12186])).
% 2.34/2.60 tff(12190,plain,
% 2.34/2.60 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[2476, 12189, 258])).
% 2.34/2.60 tff(12191,plain,
% 2.34/2.60 ($false),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[4081, 12190, 12184])).
% 2.34/2.60 tff(12192,plain,((~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~(s(z) = s(elem!1))) | (s(elem!1) = s(s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.60 tff(12193,plain,
% 2.34/2.60 (~b(s(s(elem!1)), elem!1)),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[12192, 12181, 11906, 11911, 12143, 12179, 12136, 12178])).
% 2.34/2.60 tff(12194,plain,
% 2.34/2.60 (r(s(s(elem!1)), elem!1)),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[2240, 12193, 12171])).
% 2.34/2.60 tff(12195,plain,
% 2.34/2.60 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[877, 12194, 12163])).
% 2.34/2.60 tff(12196,plain,
% 2.34/2.60 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[675, 12195, 12156])).
% 2.34/2.60 tff(12197,plain,
% 2.34/2.60 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.34/2.60 inference(monotonicity,[status(thm)],[4982])).
% 2.34/2.60 tff(12198,plain,
% 2.34/2.60 (b(s(s(elem!1)), s(s(s(z))))),
% 2.34/2.60 inference(modus_ponens,[status(thm)],[3365, 12197])).
% 2.34/2.60 tff(12199,assumption,(~b(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 2.34/2.60 tff(12200,plain,
% 2.34/2.60 ($false),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[12199, 12198])).
% 2.34/2.60 tff(12201,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(z)))) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.60 tff(12202,plain,
% 2.34/2.60 (b(s(s(elem!1)), s(s(s(z))))),
% 2.34/2.60 inference(unit_resolution,[status(thm)],[12201, 12196, 12143])).
% 2.34/2.60 tff(12203,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(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.34/2.60 inference(rewrite,[status(thm)],[])).
% 2.34/2.60 tff(12204,plain,
% 2.34/2.60 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(12205,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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12204])).
% 2.44/2.60 tff(12206,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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[12205, 12203])).
% 2.44/2.60 tff(12207,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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(12208,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(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12207, 12206])).
% 2.44/2.60 tff(12209,plain,
% 2.44/2.60 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12208, 453, 11902, 12202, 11893])).
% 2.44/2.60 tff(12210,plain,
% 2.44/2.60 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12209, 12147])).
% 2.44/2.60 tff(12211,plain,
% 2.44/2.60 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12144])).
% 2.44/2.60 tff(12212,plain,
% 2.44/2.60 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 2.44/2.60 inference(symmetry,[status(thm)],[12211])).
% 2.44/2.60 tff(12213,plain,
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% 2.44/2.60 inference(modus_ponens,[status(thm)],[12194, 12212])).
% 2.44/2.60 tff(12214,plain,
% 2.44/2.60 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4297, 12213, 11900])).
% 2.44/2.60 tff(12215,plain,
% 2.44/2.60 (b(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4293, 12214])).
% 2.44/2.60 tff(12216,plain,
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[12215, 12210])).
% 2.44/2.60 tff(12217,plain,(b(s(s(s(z))), s(z)) | (~r(elem!1, s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | b(s(z), s(s(s(z)))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(12218,plain,
% 2.44/2.60 (b(s(s(s(z))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12217, 3, 1149, 221, 4541])).
% 2.44/2.60 tff(12219,plain,
% 2.44/2.60 (b(s(s(s(z))), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[5444, 12218, 221, 3])).
% 2.44/2.60 tff(12220,plain,
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[3026, 548])).
% 2.44/2.60 tff(12221,plain,
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[1130, 12220, 2076])).
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% 2.44/2.60 tff(12223,plain,((s(z) = elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | r(elem!1, s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(12224,plain,
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[12223, 12219, 12218, 10664, 4541])).
% 2.44/2.60 tff(12225,plain,
% 2.44/2.60 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12224])).
% 2.44/2.60 tff(12226,plain,
% 2.44/2.60 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.44/2.60 inference(transitivity,[status(thm)],[12225, 56])).
% 2.44/2.60 tff(12227,plain,
% 2.44/2.60 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12226])).
% 2.44/2.60 tff(12228,plain,
% 2.44/2.60 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[289, 12227])).
% 2.44/2.60 tff(12229,plain,
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[1125, 12224])).
% 2.44/2.60 tff(12230,plain,
% 2.44/2.60 (s(s(z)) = s(elem!1)),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12224])).
% 2.44/2.60 tff(12231,plain,
% 2.44/2.60 (s(s(s(z))) = s(s(elem!1))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12230])).
% 2.44/2.60 tff(12232,plain,
% 2.44/2.60 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12231])).
% 2.44/2.60 tff(12233,plain,
% 2.44/2.60 (b(s(s(elem!1)), elem!1)),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12219, 12232])).
% 2.44/2.60 tff(12234,plain,
% 2.44/2.60 (~(s(s(s(z))) = elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4868, 12218, 221, 3])).
% 2.44/2.60 tff(12235,plain,
% 2.44/2.60 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4144, 12234])).
% 2.44/2.60 tff(12236,plain,
% 2.44/2.60 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12225])).
% 2.44/2.60 tff(12237,plain,
% 2.44/2.60 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[289, 12236])).
% 2.44/2.60 tff(12238,plain,
% 2.44/2.60 (~b(s(s(s(s(z)))), elem!1)),
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% 2.44/2.60 tff(12239,plain,
% 2.44/2.60 (~b(s(s(s(s(z)))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[10531, 12238, 12224])).
% 2.44/2.60 tff(12240,plain,
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[1098, 12239])).
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% 2.44/2.60 (~r(s(s(s(s(s(z))))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2921, 12240, 12219, 12229, 12218, 12233])).
% 2.44/2.60 tff(12242,plain,
% 2.44/2.60 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[9207, 12241, 12229])).
% 2.44/2.60 tff(12243,plain,
% 2.44/2.60 (r(s(s(s(s(z)))), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[254, 12238, 3])).
% 2.44/2.60 tff(12244,plain,
% 2.44/2.60 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[8475, 12243, 1149])).
% 2.44/2.60 tff(12245,plain,
% 2.44/2.60 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[518, 12244])).
% 2.44/2.60 tff(12246,plain,
% 2.44/2.60 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12224])).
% 2.44/2.60 tff(12247,plain,
% 2.44/2.60 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 2.44/2.60 inference(symmetry,[status(thm)],[12246])).
% 2.44/2.60 tff(12248,plain,
% 2.44/2.60 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), s(z))),
% 2.44/2.60 inference(transitivity,[status(thm)],[12232, 12247])).
% 2.44/2.60 tff(12249,plain,
% 2.44/2.60 (b(s(s(elem!1)), s(z))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12219, 12248])).
% 2.44/2.60 tff(12250,plain,
% 2.44/2.60 (b(s(s(s(s(s(z))))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[297, 12241])).
% 2.44/2.60 tff(12251,plain,
% 2.44/2.60 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[3198, 12250, 12229, 12249, 12240, 12218, 12237, 12245, 12219])).
% 2.44/2.60 tff(12252,plain,
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[643, 12251, 12242, 12228])).
% 2.44/2.60 tff(12253,plain,((s(s(s(s(z)))) = elem!1) | (~r(elem!1, s(s(s(z))))) | r(s(z), elem!1) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(12254,plain,
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[12253, 10663, 4541, 221])).
% 2.44/2.60 tff(12255,plain,
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[4108, 12254])).
% 2.44/2.60 tff(12256,plain,
% 2.44/2.60 (s(elem!1) = s(s(s(s(s(z)))))),
% 2.44/2.60 inference(symmetry,[status(thm)],[12255])).
% 2.44/2.60 tff(12257,plain,
% 2.44/2.60 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12256])).
% 2.44/2.60 tff(12258,plain,
% 2.44/2.60 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 2.44/2.60 inference(symmetry,[status(thm)],[12257])).
% 2.44/2.60 tff(12259,plain,
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[9368, 12255])).
% 2.44/2.60 tff(12260,plain,
% 2.44/2.60 (~r(elem!1, s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1157, 10663, 228])).
% 2.44/2.60 tff(12261,plain,
% 2.44/2.60 (~r(s(s(s(s(z)))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4551, 12254, 12260])).
% 2.44/2.60 tff(12262,plain,
% 2.44/2.60 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1098, 12261])).
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[10531, 12262, 12259])).
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[506, 12263, 4541])).
% 2.44/2.60 tff(12265,plain,
% 2.44/2.60 (s(elem!1) = s(s(s(s(s(z)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4499, 12255])).
% 2.44/2.60 tff(12266,plain,
% 2.44/2.60 (b(elem!1, s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4309, 12265, 12262])).
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% 2.44/2.60 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[1170])).
% 2.44/2.60 tff(12268,plain,
% 2.44/2.60 (b(elem!1, s(s(s(z))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[523, 12267])).
% 2.44/2.60 tff(12269,plain,
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[4490, 12268])).
% 2.44/2.60 tff(12270,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | b(elem!1, s(s(s(z)))) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[12270, 12254, 4490])).
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[518, 12271])).
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[12253, 1149, 4541, 221])).
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[4108, 12273])).
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% 2.44/2.60 inference(monotonicity,[status(thm)],[12274])).
% 2.44/2.60 tff(12276,plain,
% 2.44/2.60 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 2.44/2.60 inference(symmetry,[status(thm)],[12275])).
% 2.44/2.60 tff(12277,plain,
% 2.44/2.60 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12276])).
% 2.44/2.60 tff(12278,plain,
% 2.44/2.60 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12277])).
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% 2.44/2.60 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[12278, 1307])).
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% 2.44/2.60 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(elem!1))),
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% 2.44/2.60 tff(12281,plain,
% 2.44/2.60 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12280])).
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% 2.44/2.60 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1273, 12273])).
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[1436, 12282])).
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% 2.44/2.60 inference(modus_ponens,[status(thm)],[12283, 12281])).
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[4223, 12284])).
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[11368, 12286])).
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% 2.44/2.60 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12274])).
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% 2.44/2.60 ((s(z) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(z))),
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% 2.44/2.60 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(z) = s(elem!1)))),
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% 2.44/2.60 (~b(s(s(s(s(s(z))))), elem!1)),
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% 2.44/2.60 ((s(elem!1) = s(s(s(s(z))))) <=> (s(elem!1) = elem!1)),
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% 2.44/2.60 tff(12295,plain,
% 2.44/2.60 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(elem!1) = elem!1))),
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[512, 12296, 11])).
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[9368, 12274])).
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% 2.44/2.60 inference(unit_resolution,[status(thm)],[506, 12304, 4541])).
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% 2.44/2.60 inference(monotonicity,[status(thm)],[12275])).
% 2.44/2.60 tff(12307,plain,
% 2.44/2.60 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(z)) = s(s(elem!1))))),
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% 2.44/2.60 (s(elem!1) = s(s(s(s(s(z)))))),
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% 2.44/2.60 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12273])).
% 2.44/2.60 tff(12312,plain,
% 2.44/2.60 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[12311, 55])).
% 2.44/2.60 tff(12313,plain,
% 2.44/2.60 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.44/2.60 inference(transitivity,[status(thm)],[12312, 56])).
% 2.44/2.60 tff(12314,plain,
% 2.44/2.60 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12313])).
% 2.44/2.60 tff(12315,plain,
% 2.44/2.60 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[319, 12314])).
% 2.44/2.60 tff(12316,plain,
% 2.44/2.60 (r(s(s(s(s(s(z))))), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[643, 638, 12315])).
% 2.44/2.60 tff(12317,plain,
% 2.44/2.60 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4469, 12316, 12273])).
% 2.44/2.60 tff(12318,plain,
% 2.44/2.60 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1982, 12317, 11])).
% 2.44/2.60 tff(12319,plain,
% 2.44/2.60 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[687, 12318])).
% 2.44/2.60 tff(12320,plain,
% 2.44/2.60 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4526, 443, 12319, 12303])).
% 2.44/2.60 tff(12321,plain,
% 2.44/2.60 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[10556, 12320])).
% 2.44/2.60 tff(12322,plain,
% 2.44/2.60 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[8666, 12321, 11])).
% 2.44/2.60 tff(12323,plain,
% 2.44/2.60 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2570, 12322])).
% 2.44/2.60 tff(12324,plain,
% 2.44/2.60 (~b(s(s(s(z))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2619, 12323, 443, 12319])).
% 2.44/2.60 tff(12325,plain,
% 2.44/2.60 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(elem!1))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12274])).
% 2.44/2.60 tff(12326,plain,
% 2.44/2.60 (b(s(s(s(z))), s(elem!1))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12323, 12325])).
% 2.44/2.60 tff(12327,plain,
% 2.44/2.60 ((s(elem!1) = s(s(s(s(z))))) <=> (s(elem!1) = elem!1)),
% 2.44/2.60 inference(monotonicity,[status(thm)],[1170])).
% 2.44/2.60 tff(12328,plain,
% 2.44/2.60 ((s(elem!1) = s(s(s(s(z))))) <=> (elem!1 = s(elem!1))),
% 2.44/2.60 inference(transitivity,[status(thm)],[12327, 1028])).
% 2.44/2.60 tff(12329,plain,
% 2.44/2.60 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(elem!1 = s(elem!1)))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12328])).
% 2.44/2.60 tff(12330,plain,
% 2.44/2.60 (~(elem!1 = s(elem!1))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12297, 12329])).
% 2.44/2.60 tff(12331,plain,
% 2.44/2.60 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4469, 6999, 1170])).
% 2.44/2.60 tff(12332,plain,
% 2.44/2.60 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1982, 12331, 11])).
% 2.44/2.60 tff(12333,plain,
% 2.44/2.60 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[687, 12332])).
% 2.44/2.60 tff(12334,plain,
% 2.44/2.60 (b(s(elem!1), s(s(s(z))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12333, 8645])).
% 2.44/2.60 tff(12335,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(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(12336,plain,
% 2.44/2.60 (((~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(12337,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(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12336])).
% 2.44/2.60 tff(12338,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(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.44/2.60 inference(transitivity,[status(thm)],[12337, 12335])).
% 2.44/2.60 tff(12339,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(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(12340,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12339, 12338])).
% 2.44/2.60 tff(12341,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12340, 453, 1071, 11663, 1291, 8937])).
% 2.44/2.60 tff(12342,plain,((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(12343,plain,
% 2.44/2.60 (~b(elem!1, s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[12342, 1291, 12334, 11663])).
% 2.44/2.60 tff(12344,plain,
% 2.44/2.60 (r(elem!1, s(elem!1))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1069, 12343, 12330])).
% 2.44/2.60 tff(12345,plain,
% 2.44/2.60 (elem!1 = s(s(s(s(z))))),
% 2.44/2.60 inference(symmetry,[status(thm)],[1170])).
% 2.44/2.60 tff(12346,plain,
% 2.44/2.60 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12345])).
% 2.44/2.60 tff(12347,plain,
% 2.44/2.60 ((s(s(z)) = elem!1) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.44/2.60 inference(transitivity,[status(thm)],[12346, 1])).
% 2.44/2.60 tff(12348,plain,
% 2.44/2.60 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.44/2.60 inference(symmetry,[status(thm)],[12347])).
% 2.44/2.60 tff(12349,plain,
% 2.44/2.60 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12348])).
% 2.44/2.60 tff(12350,plain,
% 2.44/2.60 (~(s(s(z)) = elem!1)),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[153, 12349])).
% 2.44/2.60 tff(12351,plain,
% 2.44/2.60 (~b(s(s(z)), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[11083, 1291, 128, 4541, 2076])).
% 2.44/2.60 tff(12352,plain,
% 2.44/2.60 (r(s(s(z)), elem!1)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[782, 12351, 12350])).
% 2.44/2.60 tff(12353,assumption,(s(s(z)) = s(s(s(z)))), introduced(assumption)).
% 2.44/2.60 tff(12354,plain,
% 2.44/2.60 (s(s(s(z))) = s(s(z))),
% 2.44/2.60 inference(symmetry,[status(thm)],[12353])).
% 2.44/2.60 tff(12355,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[160, 12354])).
% 2.44/2.60 tff(12356,plain,(~(s(s(z)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(12357,plain,
% 2.44/2.60 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[8385])).
% 2.44/2.60 tff(12358,plain,
% 2.44/2.60 ((~b(s(elem!1), s(s(z)))) <=> (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12357])).
% 2.44/2.60 tff(12359,plain,
% 2.44/2.60 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4469, 3457, 1170])).
% 2.44/2.60 tff(12360,plain,
% 2.44/2.60 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[1982, 12359, 11])).
% 2.44/2.60 tff(12361,plain,
% 2.44/2.60 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[687, 12360])).
% 2.44/2.60 tff(12362,plain,
% 2.44/2.60 (b(s(elem!1), s(s(s(z))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[12361, 8645])).
% 2.44/2.60 tff(12363,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(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(12364,plain,
% 2.44/2.60 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(12365,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(z))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z))))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[12364])).
% 2.44/2.61 tff(12366,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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[12365, 12363])).
% 2.44/2.61 tff(12367,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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(12368,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[12367, 12366])).
% 2.44/2.61 tff(12369,plain,
% 2.44/2.61 (~b(s(elem!1), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12368, 453, 11663, 12362, 2957])).
% 2.44/2.61 tff(12370,plain,
% 2.44/2.61 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[12369, 12358])).
% 2.44/2.61 tff(12371,plain,
% 2.44/2.61 (r(s(elem!1), s(s(z))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[8385])).
% 2.44/2.61 tff(12372,plain,
% 2.44/2.61 ((~r(s(elem!1), s(s(z)))) <=> (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[12371])).
% 2.44/2.61 tff(12373,plain,
% 2.44/2.61 ((~(elem!1 = s(s(s(s(s(z))))))) <=> (~(s(elem!1) = elem!1))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[8641])).
% 2.44/2.61 tff(12374,plain,
% 2.44/2.61 (~(s(elem!1) = elem!1)),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[8840, 12373])).
% 2.44/2.61 tff(12375,plain,
% 2.44/2.61 (r(s(elem!1), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2440, 7007, 12374])).
% 2.44/2.61 tff(12376,plain,
% 2.44/2.61 (~r(s(elem!1), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[7078, 268, 12375, 700])).
% 2.44/2.61 tff(12377,plain,
% 2.44/2.61 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[12376, 12372])).
% 2.44/2.61 tff(12378,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[4081, 12377, 12370])).
% 2.44/2.61 tff(12379,plain,(b(s(s(s(s(s(z))))), elem!1) | (~r(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~(s(s(s(s(z)))) = elem!1)) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(12380,plain,
% 2.44/2.61 (~b(s(s(z)), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12379, 700, 638, 11, 11663, 1170, 1544])).
% 2.44/2.61 tff(12381,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12382,plain,
% 2.44/2.61 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12383,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[12382])).
% 2.44/2.61 tff(12384,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[12383, 12381])).
% 2.44/2.61 tff(12385,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(12386,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z)))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[12385, 12384])).
% 2.44/2.61 tff(12387,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12386, 268, 339, 700, 1149, 2580])).
% 2.44/2.61 tff(12388,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(12389,plain,
% 2.44/2.61 (~r(s(s(z)), s(s(s(z))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12388, 700, 339, 1149])).
% 2.44/2.61 tff(12390,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1350, 69, 12389, 12380, 12356])).
% 2.44/2.61 tff(12391,plain,((~r(s(s(z)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(z))))) | b(s(s(s(s(s(z))))), elem!1) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(12392,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12391, 12352, 12344, 1149, 638, 11, 11663, 1170])).
% 2.44/2.61 tff(12393,plain,((~b(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | b(s(s(s(s(s(z))))), elem!1) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~(s(s(s(s(z)))) = elem!1)) | b(s(s(s(z))), s(z)) | r(s(z), elem!1) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(12394,plain,
% 2.44/2.61 (~b(s(s(s(z))), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12393, 12326, 638, 11, 1149, 12273, 12324, 4541, 10664])).
% 2.44/2.61 tff(12395,plain,
% 2.44/2.61 (b(s(s(z)), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11881, 12394, 221, 638, 10664, 12315, 4541, 12324])).
% 2.44/2.61 tff(12396,plain,
% 2.44/2.61 (~b(s(s(z)), s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[10930, 453, 2077, 909, 922])).
% 2.44/2.61 tff(12397,plain,
% 2.44/2.61 (r(s(s(z)), s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[4239, 69, 4227, 12396])).
% 2.44/2.61 tff(12398,plain,
% 2.44/2.61 (~b(s(s(elem!1)), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11014, 453, 499, 2077, 909])).
% 2.44/2.61 tff(12399,plain,
% 2.44/2.61 (r(s(s(elem!1)), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1047, 12398])).
% 2.44/2.61 tff(12400,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[7068, 268, 12399, 5572, 12397])).
% 2.44/2.61 tff(12401,plain,((~b(s(s(elem!1)), elem!1)) | (s(s(z)) = s(s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(12402,plain,
% 2.44/2.61 (~b(s(s(elem!1)), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12401, 12395, 12310, 12308, 12305])).
% 2.44/2.61 tff(12403,plain,
% 2.44/2.61 (r(s(s(elem!1)), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2240, 12402, 12300])).
% 2.44/2.61 tff(12404,plain,
% 2.44/2.61 (~(s(s(elem!1)) = s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11368, 8134])).
% 2.44/2.61 tff(12405,plain,
% 2.44/2.61 (~b(s(s(s(s(z)))), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[9368, 8112])).
% 2.44/2.61 tff(12406,plain,
% 2.44/2.61 (~r(s(s(s(s(z)))), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[4551, 1170, 2076])).
% 2.44/2.61 tff(12407,plain,
% 2.44/2.61 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1098, 12406])).
% 2.44/2.61 tff(12408,plain,
% 2.44/2.61 (~(s(z) = elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[10531, 12407, 12405])).
% 2.44/2.61 tff(12409,plain,
% 2.44/2.61 (b(s(z), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[506, 12408, 4541])).
% 2.44/2.61 tff(12410,plain,
% 2.44/2.61 (s(elem!1) = s(s(s(s(s(z)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[4499, 8112])).
% 2.44/2.61 tff(12411,plain,
% 2.44/2.61 (b(elem!1, s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[4309, 12410, 12407])).
% 2.44/2.61 tff(12412,plain,
% 2.44/2.61 (r(s(s(s(s(z)))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[1170])).
% 2.44/2.61 tff(12413,plain,
% 2.44/2.61 (~(s(s(s(z))) = elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[81, 12297])).
% 2.44/2.61 tff(12414,plain,
% 2.44/2.61 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[4144, 12413])).
% 2.44/2.61 tff(12415,plain,
% 2.44/2.61 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 2.44/2.61 inference(transitivity,[status(thm)],[8711, 174])).
% 2.44/2.61 tff(12416,plain,
% 2.44/2.61 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(z) = s(elem!1)))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[12415])).
% 2.44/2.61 tff(12417,plain,
% 2.44/2.61 (~(s(z) = s(elem!1))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[289, 12416])).
% 2.44/2.61 tff(12418,plain,
% 2.44/2.61 (~(s(elem!1) = s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[179, 177])).
% 2.44/2.61 tff(12419,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(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), 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(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12420,plain,
% 2.44/2.61 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12421,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[12420])).
% 2.44/2.61 tff(12422,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[12421, 12419])).
% 2.44/2.61 tff(12423,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(12424,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[12423, 12422])).
% 2.44/2.61 tff(12425,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12424, 453, 1059, 499, 1764, 2401])).
% 2.44/2.61 tff(12426,plain,((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(12427,plain,
% 2.44/2.61 (~b(s(z), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12426, 1059, 1764, 2401])).
% 2.44/2.61 tff(12428,plain,
% 2.44/2.61 (r(s(z), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[506, 12427, 492])).
% 2.44/2.61 tff(12429,plain,
% 2.44/2.61 (~r(s(z), s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1912, 12428, 1892])).
% 2.44/2.61 tff(12430,plain,
% 2.44/2.61 (b(s(z), s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[397, 12429, 177])).
% 2.44/2.61 tff(12431,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), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), 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), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12432,plain,
% 2.44/2.61 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12433,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(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), 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), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[12432])).
% 2.44/2.61 tff(12434,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(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), 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), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[12433, 12431])).
% 2.44/2.61 tff(12435,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(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(12436,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[12435, 12434])).
% 2.44/2.61 tff(12437,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12436, 453, 1059, 12430, 1764, 2401])).
% 2.44/2.61 tff(12438,plain,((~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))) | (s(z) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(12439,plain,
% 2.44/2.61 (~b(s(elem!1), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12438, 177, 2401, 1764, 1892, 492])).
% 2.44/2.61 tff(12440,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[353, 12439, 12418, 3761])).
% 2.44/2.61 tff(12441,plain,((s(z) = s(elem!1)) | r(s(elem!1), s(z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(12442,plain,
% 2.44/2.61 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12441, 3761, 12408, 12417, 1892, 12407])).
% 2.44/2.61 tff(12443,plain,
% 2.44/2.61 (r(s(s(s(s(z)))), s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2398, 12442, 12414])).
% 2.44/2.61 tff(12444,plain,
% 2.44/2.61 (r(elem!1, s(elem!1))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[12443, 12412])).
% 2.44/2.61 tff(12445,plain,
% 2.44/2.61 (~r(s(s(z)), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12391, 12444, 1149, 638, 11, 11663, 1170])).
% 2.44/2.61 tff(12446,plain,
% 2.44/2.61 (b(s(s(z)), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[782, 12445, 12350])).
% 2.44/2.61 tff(12447,plain,
% 2.44/2.61 (~b(s(s(elem!1)), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12401, 12446, 12411, 8699, 12409])).
% 2.44/2.61 tff(12448,plain,
% 2.44/2.61 (r(s(s(elem!1)), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[2240, 12447, 8693])).
% 2.44/2.61 tff(12449,plain,
% 2.44/2.61 (~r(s(s(elem!1)), s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11304, 268, 1892, 12448])).
% 2.44/2.61 tff(12450,plain,
% 2.44/2.61 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[1874, 69, 12449, 12404])).
% 2.44/2.61 tff(12451,plain,
% 2.44/2.61 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[547, 12408])).
% 2.44/2.61 tff(12452,plain,
% 2.44/2.61 (~b(s(s(s(z))), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[11083, 12446, 128, 4541, 2076])).
% 2.44/2.61 tff(12453,plain,
% 2.44/2.61 (r(s(s(s(z))), elem!1)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[74, 12452, 12413])).
% 2.44/2.61 tff(12454,plain,
% 2.44/2.61 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[5213, 12448, 12453])).
% 2.44/2.61 tff(12455,plain,
% 2.44/2.61 (b(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[5203, 12454, 12451])).
% 2.44/2.61 tff(12456,plain,
% 2.44/2.61 (b(s(elem!1), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[353, 3761, 8713])).
% 2.44/2.61 tff(12457,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(elem!1), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), 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(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12458,plain,
% 2.44/2.61 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12459,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(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[12458])).
% 2.44/2.61 tff(12460,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(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[12459, 12457])).
% 2.44/2.61 tff(12461,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(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(12462,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[12461, 12460])).
% 2.44/2.61 tff(12463,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12462, 453, 12456, 11663, 12455, 12450])).
% 2.44/2.61 tff(12464,plain,(r(s(elem!1), s(z)) | (~b(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), elem!1)) | b(s(s(s(z))), s(z)) | r(s(z), elem!1) | r(elem!1, s(z)) | (~r(elem!1, s(s(s(z))))) | b(s(s(s(s(s(z))))), elem!1) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(12465,plain,
% 2.44/2.61 (r(s(elem!1), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12464, 12326, 1892, 12324, 4541, 10664, 1149, 638, 11, 12273])).
% 2.44/2.61 tff(12466,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12467,plain,
% 2.44/2.61 (((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(12468,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[12467])).
% 2.44/2.61 tff(12469,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 2.44/2.61 inference(transitivity,[status(thm)],[12468, 12466])).
% 2.44/2.61 tff(12470,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(12471,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[12470, 12469])).
% 2.44/2.61 tff(12472,plain,
% 2.44/2.61 (~r(s(s(elem!1)), s(elem!1))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[12471, 268, 12465, 1892, 12403])).
% 2.44/2.61 tff(12473,plain,
% 2.44/2.61 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1874, 69, 12472, 12287])).
% 2.44/2.62 tff(12474,plain,
% 2.44/2.62 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[547, 12304])).
% 2.44/2.62 tff(12475,plain,
% 2.44/2.62 (r(s(s(s(z))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[74, 12394, 12413])).
% 2.44/2.62 tff(12476,plain,
% 2.44/2.62 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[5213, 12403, 12475])).
% 2.44/2.62 tff(12477,plain,
% 2.44/2.62 (b(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[5203, 12476, 12474])).
% 2.44/2.62 tff(12478,plain,
% 2.44/2.62 (~r(s(elem!1), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11373, 12403, 1892])).
% 2.44/2.62 tff(12479,plain,
% 2.44/2.62 (b(s(elem!1), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[440, 12478, 12286])).
% 2.44/2.62 tff(12480,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(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(12481,plain,
% 2.44/2.62 (((~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(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(12482,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(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(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12481])).
% 2.44/2.62 tff(12483,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(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(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[12482, 12480])).
% 2.44/2.62 tff(12484,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(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(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(12485,plain,
% 2.44/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12484, 12483])).
% 2.44/2.62 tff(12486,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12485, 453, 12479, 12326, 12477, 12473])).
% 2.44/2.62 tff(12487,plain,((~b(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), elem!1)) | b(s(z), s(s(s(z)))) | b(s(s(s(s(s(z))))), elem!1) | r(s(z), elem!1) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(12488,plain,
% 2.44/2.62 (~b(s(z), s(s(s(s(s(z))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12487, 12299, 221, 12293, 4541, 11, 1149])).
% 2.44/2.62 tff(12489,plain,
% 2.44/2.62 (~b(s(z), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[7032, 12488, 12273])).
% 2.44/2.62 tff(12490,plain,
% 2.44/2.62 (r(s(z), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[397, 12489, 12292])).
% 2.44/2.62 tff(12491,plain,
% 2.44/2.62 (~b(s(z), s(s(s(s(s(z))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12487, 1892, 221, 638, 4541, 11, 1149])).
% 2.44/2.62 tff(12492,plain,
% 2.44/2.62 (r(s(z), s(s(s(s(s(z))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[372, 12491])).
% 2.44/2.62 tff(12493,plain,
% 2.44/2.62 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[9017, 12492, 228])).
% 2.44/2.62 tff(12494,plain,
% 2.44/2.62 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2570, 12493])).
% 2.44/2.62 tff(12495,plain,
% 2.44/2.62 (b(s(s(s(z))), s(elem!1))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12494, 12325])).
% 2.44/2.62 tff(12496,plain,
% 2.44/2.62 (~b(s(s(s(z))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12393, 128, 638, 11, 1149, 12273, 12495, 4541, 10664])).
% 2.44/2.62 tff(12497,plain,
% 2.44/2.62 (b(s(s(z)), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11881, 12496, 221, 638, 10664, 12315, 4541, 128])).
% 2.44/2.62 tff(12498,plain,
% 2.44/2.62 (~b(s(s(elem!1)), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12401, 12497, 12310, 12308, 12305])).
% 2.44/2.62 tff(12499,plain,
% 2.44/2.62 (r(s(s(elem!1)), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2240, 12498, 12300])).
% 2.44/2.62 tff(12500,plain,
% 2.44/2.62 (r(s(elem!1), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12464, 128, 1892, 12495, 4541, 10664, 1149, 638, 11, 12273])).
% 2.44/2.62 tff(12501,plain,
% 2.44/2.62 (~r(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12471, 268, 12500, 1892, 12499])).
% 2.44/2.62 tff(12502,plain,
% 2.44/2.62 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1874, 69, 12501, 12287])).
% 2.44/2.62 tff(12503,plain,
% 2.44/2.62 (r(s(s(s(z))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[74, 12496, 12413])).
% 2.44/2.62 tff(12504,plain,
% 2.44/2.62 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[5213, 12499, 12503])).
% 2.44/2.62 tff(12505,plain,
% 2.44/2.62 (b(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[5203, 12504, 12474])).
% 2.44/2.62 tff(12506,plain,
% 2.44/2.62 (~r(s(elem!1), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11373, 12499, 1892])).
% 2.44/2.62 tff(12507,plain,
% 2.44/2.62 (b(s(elem!1), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[440, 12506, 12286])).
% 2.44/2.62 tff(12508,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12485, 453, 12507, 12495, 12505, 12502])).
% 2.44/2.62 tff(12509,plain,(b(s(s(s(z))), s(z)) | (~r(s(elem!1), elem!1)) | b(s(z), s(s(s(z)))) | b(s(s(s(s(s(z))))), elem!1) | r(s(z), elem!1) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(12510,plain,
% 2.44/2.62 (b(s(s(s(z))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12509, 12299, 221, 12293, 4541, 11, 1149])).
% 2.44/2.62 tff(12511,plain,
% 2.44/2.62 (~b(s(s(s(z))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12223, 12510, 12304, 10664, 4541])).
% 2.44/2.62 tff(12512,plain,
% 2.44/2.62 (r(s(s(s(z))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[74, 12511, 12413])).
% 2.44/2.62 tff(12513,plain,
% 2.44/2.62 (~b(s(s(elem!1)), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[5215, 12512, 12474, 12300, 12310, 12510, 12305])).
% 2.44/2.62 tff(12514,plain,
% 2.44/2.62 (r(s(s(elem!1)), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1047, 12513])).
% 2.44/2.62 tff(12515,plain,
% 2.44/2.62 (~r(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[3414, 12514, 12490])).
% 2.44/2.62 tff(12516,plain,
% 2.44/2.62 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1874, 69, 12515, 12287])).
% 2.44/2.62 tff(12517,plain,
% 2.44/2.62 (elem!1 = s(s(s(s(z))))),
% 2.44/2.62 inference(symmetry,[status(thm)],[12273])).
% 2.44/2.62 tff(12518,plain,
% 2.44/2.62 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12517])).
% 2.44/2.62 tff(12519,plain,
% 2.44/2.62 ((s(s(z)) = elem!1) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.44/2.62 inference(transitivity,[status(thm)],[12518, 1])).
% 2.44/2.62 tff(12520,plain,
% 2.44/2.62 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.44/2.62 inference(symmetry,[status(thm)],[12519])).
% 2.44/2.62 tff(12521,plain,
% 2.44/2.62 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12520])).
% 2.44/2.62 tff(12522,plain,
% 2.44/2.62 (~(s(s(z)) = elem!1)),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[153, 12521])).
% 2.44/2.62 tff(12523,plain,
% 2.44/2.62 (r(s(s(s(s(s(z))))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[643, 12293, 12315])).
% 2.44/2.62 tff(12524,plain,
% 2.44/2.62 (~r(s(s(z)), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[10463, 12512, 12523])).
% 2.44/2.62 tff(12525,plain,
% 2.44/2.62 (b(s(s(z)), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[782, 12524, 12522])).
% 2.44/2.62 tff(12526,plain,
% 2.44/2.62 (~b(s(s(elem!1)), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12401, 12525, 12310, 12308, 12305])).
% 2.44/2.62 tff(12527,plain,
% 2.44/2.62 (r(s(s(elem!1)), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2240, 12526, 12300])).
% 2.44/2.62 tff(12528,plain,
% 2.44/2.62 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[5213, 12527, 12512])).
% 2.44/2.62 tff(12529,plain,
% 2.44/2.62 (b(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[5203, 12528, 12474])).
% 2.44/2.62 tff(12530,plain,
% 2.44/2.62 (r(s(z), s(s(s(s(s(z))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[372, 12488])).
% 2.44/2.62 tff(12531,plain,
% 2.44/2.62 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[9017, 12530, 228])).
% 2.44/2.62 tff(12532,plain,
% 2.44/2.62 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2570, 12531])).
% 2.44/2.62 tff(12533,plain,
% 2.44/2.62 (b(s(s(s(z))), s(elem!1))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12532, 12325])).
% 2.44/2.62 tff(12534,plain,
% 2.44/2.62 (~r(s(elem!1), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11373, 12527, 12299])).
% 2.44/2.62 tff(12535,plain,
% 2.44/2.62 (b(s(elem!1), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[440, 12534, 12286])).
% 2.44/2.62 tff(12536,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12485, 453, 12535, 12533, 12529, 12516])).
% 2.44/2.62 tff(12537,plain,(b(s(elem!1), elem!1) | r(s(z), elem!1) | b(s(z), s(s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(12538,plain,
% 2.44/2.62 (b(s(elem!1), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12537, 4541, 221, 12272, 10663])).
% 2.44/2.62 tff(12539,plain,
% 2.44/2.62 (b(s(s(s(s(s(z))))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[7006, 12538, 12254])).
% 2.44/2.62 tff(12540,plain,
% 2.44/2.62 (~b(s(s(s(s(s(z))))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[5331, 12539, 12266, 12264])).
% 2.44/2.62 tff(12541,plain,
% 2.44/2.62 (r(s(s(s(s(s(z))))), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[297, 12540])).
% 2.44/2.62 tff(12542,plain,
% 2.44/2.62 (elem!1 = s(s(s(s(z))))),
% 2.44/2.62 inference(symmetry,[status(thm)],[12254])).
% 2.44/2.62 tff(12543,plain,
% 2.44/2.62 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12542])).
% 2.44/2.62 tff(12544,plain,
% 2.44/2.62 ((s(s(z)) = elem!1) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.44/2.62 inference(transitivity,[status(thm)],[12543, 1])).
% 2.44/2.62 tff(12545,plain,
% 2.44/2.62 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.44/2.62 inference(symmetry,[status(thm)],[12544])).
% 2.44/2.62 tff(12546,plain,
% 2.44/2.62 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12545])).
% 2.44/2.62 tff(12547,plain,
% 2.44/2.62 (~(s(s(z)) = elem!1)),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[153, 12546])).
% 2.44/2.62 tff(12548,plain,
% 2.44/2.62 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12255])).
% 2.44/2.62 tff(12549,plain,
% 2.44/2.62 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12548])).
% 2.44/2.62 tff(12550,plain,
% 2.44/2.62 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12549])).
% 2.44/2.62 tff(12551,plain,
% 2.44/2.62 (~(s(s(z)) = s(s(elem!1)))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[2661, 12550])).
% 2.44/2.62 tff(12552,plain,
% 2.44/2.62 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 2.44/2.62 inference(symmetry,[status(thm)],[12548])).
% 2.44/2.62 tff(12553,plain,
% 2.44/2.62 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12552])).
% 2.44/2.62 tff(12554,plain,
% 2.44/2.62 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12553])).
% 2.44/2.62 tff(12555,plain,
% 2.44/2.62 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[12554, 1307])).
% 2.44/2.62 tff(12556,plain,
% 2.44/2.62 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.44/2.62 inference(symmetry,[status(thm)],[12555])).
% 2.44/2.62 tff(12557,plain,
% 2.44/2.62 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12556])).
% 2.44/2.62 tff(12558,plain,
% 2.44/2.62 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1273, 12254])).
% 2.44/2.62 tff(12559,plain,
% 2.44/2.62 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1436, 12558])).
% 2.44/2.62 tff(12560,plain,
% 2.44/2.62 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12559, 12557])).
% 2.44/2.62 tff(12561,plain,
% 2.44/2.62 (~(elem!1 = s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[4223, 12560])).
% 2.44/2.62 tff(12562,plain,
% 2.44/2.62 (~(s(s(elem!1)) = elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[3359, 12561])).
% 2.44/2.62 tff(12563,plain,
% 2.44/2.62 (~r(s(s(s(s(z)))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[8475, 12272, 10663])).
% 2.44/2.62 tff(12564,plain,
% 2.44/2.62 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[512, 12563, 12272])).
% 2.44/2.62 tff(12565,plain,
% 2.44/2.62 (~(s(s(s(z))) = elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[81, 12564])).
% 2.44/2.62 tff(12566,plain,
% 2.44/2.62 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[3160, 11916, 257])).
% 2.44/2.62 tff(12567,plain,
% 2.44/2.62 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[687, 12566])).
% 2.44/2.62 tff(12568,plain,
% 2.44/2.62 (b(s(elem!1), s(s(s(z))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12567, 8645])).
% 2.44/2.62 tff(12569,plain,
% 2.44/2.62 (b(s(elem!1), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1336, 646, 1170])).
% 2.44/2.62 tff(12570,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(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(12571,plain,
% 2.44/2.62 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(12572,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12571])).
% 2.44/2.62 tff(12573,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.44/2.62 inference(transitivity,[status(thm)],[12572, 12570])).
% 2.44/2.62 tff(12574,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(12575,plain,
% 2.44/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12574, 12573])).
% 2.44/2.62 tff(12576,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12575, 453, 2077, 12569, 1291, 12568])).
% 2.44/2.62 tff(12577,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~(s(s(s(s(z)))) = elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(12578,plain,
% 2.44/2.62 (~b(s(s(s(z))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12577, 12539, 12254, 228, 12266, 12264])).
% 2.44/2.62 tff(12579,plain,
% 2.44/2.62 (r(s(s(s(z))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[74, 12578, 12565])).
% 2.44/2.62 tff(12580,plain,
% 2.44/2.62 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[547, 12263])).
% 2.44/2.62 tff(12581,plain,
% 2.44/2.62 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12255])).
% 2.44/2.62 tff(12582,plain,
% 2.44/2.62 ((s(z) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(z))),
% 2.44/2.62 inference(transitivity,[status(thm)],[12581, 173])).
% 2.44/2.62 tff(12583,plain,
% 2.44/2.62 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 2.44/2.62 inference(transitivity,[status(thm)],[12582, 174])).
% 2.44/2.62 tff(12584,plain,
% 2.44/2.62 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(z) = s(elem!1)))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12583])).
% 2.44/2.62 tff(12585,plain,
% 2.44/2.62 (~(s(z) = s(elem!1))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[289, 12584])).
% 2.44/2.62 tff(12586,plain,
% 2.44/2.62 (~(elem!1 = s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[3026, 12580])).
% 2.44/2.62 tff(12587,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[3403, 9870, 6754, 629, 1549])).
% 2.44/2.62 tff(12588,plain,((elem!1 = s(z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | r(s(z), elem!1) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(12589,plain,
% 2.44/2.62 (~b(s(z), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12588, 12538, 4541, 12260, 12586])).
% 2.44/2.62 tff(12590,plain,
% 2.44/2.62 (r(s(z), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[397, 12589, 12585])).
% 2.44/2.62 tff(12591,plain,
% 2.44/2.62 (~(s(elem!1) = s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1861, 12561])).
% 2.44/2.62 tff(12592,plain,
% 2.44/2.62 (~(s(s(elem!1)) = s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11368, 12591])).
% 2.44/2.62 tff(12593,plain,
% 2.44/2.62 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(elem!1))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12255])).
% 2.44/2.62 tff(12594,plain,
% 2.44/2.62 (~b(s(z), s(s(s(s(s(z))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11166, 12539, 12266, 12264])).
% 2.44/2.62 tff(12595,plain,
% 2.44/2.62 (r(s(z), s(s(s(s(s(z))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[372, 12594])).
% 2.44/2.62 tff(12596,plain,
% 2.44/2.62 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[9017, 12595, 228])).
% 2.44/2.62 tff(12597,plain,
% 2.44/2.62 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2570, 12596])).
% 2.44/2.62 tff(12598,plain,
% 2.44/2.62 (b(s(s(s(z))), s(elem!1))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12597, 12593])).
% 2.44/2.62 tff(12599,plain,
% 2.44/2.62 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.44/2.62 inference(monotonicity,[status(thm)],[7962])).
% 2.44/2.62 tff(12600,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(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(12601,plain,
% 2.44/2.62 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(12602,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12601])).
% 2.44/2.62 tff(12603,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[12602, 12600])).
% 2.44/2.62 tff(12604,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(12605,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(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12604, 12603])).
% 2.44/2.62 tff(12606,plain,
% 2.44/2.62 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12605, 453, 629, 11663, 6555])).
% 2.44/2.62 tff(12607,plain,
% 2.44/2.62 (r(s(s(s(z))), s(s(elem!1)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[5203, 12606, 555])).
% 2.44/2.62 tff(12608,plain,
% 2.44/2.62 (~r(s(s(elem!1)), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[5213, 12607, 1545])).
% 2.44/2.62 tff(12609,plain,
% 2.44/2.62 (b(s(s(elem!1)), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2240, 12608, 5181])).
% 2.44/2.62 tff(12610,plain,
% 2.44/2.62 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12609, 12599])).
% 2.44/2.62 tff(12611,plain,
% 2.44/2.62 (b(s(s(s(s(s(s(z)))))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[7961])).
% 2.44/2.62 tff(12612,plain,
% 2.44/2.62 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.44/2.62 inference(symmetry,[status(thm)],[12611])).
% 2.44/2.62 tff(12613,plain,
% 2.44/2.62 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[6555, 12612])).
% 2.44/2.62 tff(12614,assumption,(b(s(s(s(s(s(s(z)))))), s(elem!1))), introduced(assumption)).
% 2.44/2.62 tff(12615,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(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(12616,plain,
% 2.44/2.62 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(12617,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[12616])).
% 2.44/2.62 tff(12618,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.44/2.62 inference(transitivity,[status(thm)],[12617, 12615])).
% 2.44/2.62 tff(12619,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(12620,plain,
% 2.44/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[12619, 12618])).
% 2.44/2.62 tff(12621,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12620, 453, 2077, 629, 12614, 963])).
% 2.44/2.62 tff(12622,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(12623,plain,
% 2.44/2.62 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12622, 12613, 2077, 629])).
% 2.44/2.62 tff(12624,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12623, 12610])).
% 2.44/2.62 tff(12625,plain,((~b(s(s(elem!1)), s(elem!1))) | (~(s(s(s(s(s(z))))) = s(elem!1))) | (s(s(elem!1)) = elem!1) | (~r(s(s(s(z))), elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(12626,plain,
% 2.44/2.62 (~b(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[12625, 12255, 12562, 12579, 12580, 12266, 12538, 12598])).
% 2.44/2.62 tff(12627,plain,
% 2.44/2.62 (r(s(s(elem!1)), s(elem!1))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1874, 69, 12626, 12592])).
% 2.44/2.62 tff(12628,plain,
% 2.44/2.62 (~r(s(s(elem!1)), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[3414, 12627, 12590])).
% 2.44/2.62 tff(12629,plain,
% 2.44/2.62 (b(s(s(elem!1)), s(z))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1047, 12628])).
% 2.44/2.62 tff(12630,plain,
% 2.44/2.62 (~r(s(s(z)), elem!1)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[11032, 12629, 12580, 12579, 12562, 12551, 12264, 12266])).
% 2.44/2.63 tff(12631,plain,
% 2.44/2.63 (b(s(s(z)), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[782, 12630, 12547])).
% 2.44/2.63 tff(12632,plain,
% 2.44/2.63 (~b(s(z), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[6633, 453, 12264, 12266, 12631])).
% 2.44/2.63 tff(12633,plain,
% 2.44/2.63 (r(s(z), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[757, 12632])).
% 2.44/2.63 tff(12634,plain,
% 2.44/2.63 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2476, 12633, 12541])).
% 2.44/2.63 tff(12635,plain,
% 2.44/2.63 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4081, 12634])).
% 2.44/2.63 tff(12636,plain,
% 2.44/2.63 (b(s(elem!1), s(s(z)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[12635, 12258])).
% 2.44/2.63 tff(12637,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(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(12638,plain,
% 2.44/2.63 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(12639,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12638])).
% 2.44/2.63 tff(12640,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.44/2.63 inference(transitivity,[status(thm)],[12639, 12637])).
% 2.44/2.63 tff(12641,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(12642,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[12641, 12640])).
% 2.44/2.63 tff(12643,plain,
% 2.44/2.63 (~b(s(elem!1), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12642, 453, 12266, 12538, 12631])).
% 2.44/2.63 tff(12644,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12643, 12636])).
% 2.44/2.63 tff(12645,plain,(r(s(z), elem!1) | b(s(z), s(s(s(z)))) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(12646,plain,
% 2.44/2.63 (r(s(z), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12645, 4490, 221])).
% 2.44/2.63 tff(12647,plain,
% 2.44/2.63 (~r(s(s(s(z))), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4885, 12646, 228])).
% 2.44/2.63 tff(12648,plain,
% 2.44/2.63 (~r(s(s(s(s(z)))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4119, 3448, 11])).
% 2.44/2.63 tff(12649,plain,
% 2.44/2.63 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1098, 12648])).
% 2.44/2.63 tff(12650,plain,
% 2.44/2.63 (~r(s(z), s(s(s(s(z)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1692, 268, 11, 228])).
% 2.44/2.63 tff(12651,plain,
% 2.44/2.63 (r(s(z), s(s(s(s(z))))) <=> r(s(z), elem!1)),
% 2.44/2.63 inference(monotonicity,[status(thm)],[4148])).
% 2.44/2.63 tff(12652,plain,
% 2.44/2.63 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(z)))))),
% 2.44/2.63 inference(symmetry,[status(thm)],[12651])).
% 2.44/2.63 tff(12653,plain,
% 2.44/2.63 (r(s(z), s(s(s(s(z)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[701, 12652])).
% 2.44/2.63 tff(12654,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[390, 12653])).
% 2.44/2.63 tff(12655,plain,((~(s(s(s(s(s(z))))) = s(elem!1))) | r(s(z), s(s(s(s(z))))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(12656,plain,
% 2.44/2.63 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12655, 12650, 701])).
% 2.44/2.63 tff(12657,plain,
% 2.44/2.63 (~(s(s(s(s(z)))) = elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4108, 12656])).
% 2.44/2.63 tff(12658,plain,
% 2.44/2.63 (~(elem!1 = s(s(s(s(z)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[8, 12657])).
% 2.44/2.63 tff(12659,plain,
% 2.44/2.63 (~(s(s(s(z))) = elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[9990, 12657, 221, 128])).
% 2.44/2.63 tff(12660,plain,
% 2.44/2.63 (b(s(s(s(z))), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[74, 12659, 2])).
% 2.44/2.63 tff(12661,plain,
% 2.44/2.63 (~(elem!1 = s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[8856, 12660, 128])).
% 2.44/2.63 tff(12662,plain,
% 2.44/2.63 (~(elem!1 = s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4487, 12659])).
% 2.44/2.63 tff(12663,plain,
% 2.44/2.63 (r(elem!1, s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4492, 12662, 4490])).
% 2.44/2.63 tff(12664,plain,
% 2.44/2.63 (~r(elem!1, s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1157, 12663, 228])).
% 2.44/2.63 tff(12665,plain,
% 2.44/2.63 (b(elem!1, s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1130, 12664, 12661])).
% 2.44/2.63 tff(12666,plain,
% 2.44/2.63 (~r(s(s(z)), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[10897, 12665, 701, 12658, 12649])).
% 2.44/2.63 tff(12667,plain,
% 2.44/2.63 (~r(s(s(s(s(z)))), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[8475, 12663, 11])).
% 2.44/2.63 tff(12668,plain,
% 2.44/2.63 (b(s(s(s(s(z)))), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[254, 12667, 12657])).
% 2.44/2.63 tff(12669,plain,
% 2.44/2.63 (~b(s(s(z)), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[7330, 12668, 12660, 12665])).
% 2.44/2.63 tff(12670,plain,
% 2.44/2.63 (s(s(z)) = elem!1),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[782, 12669, 12666])).
% 2.44/2.63 tff(12671,plain,
% 2.44/2.63 (s(s(s(z))) = s(elem!1)),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12670])).
% 2.44/2.63 tff(12672,plain,
% 2.44/2.63 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12671])).
% 2.44/2.63 tff(12673,plain,
% 2.44/2.63 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(elem!1)))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12672])).
% 2.44/2.63 tff(12674,plain,
% 2.44/2.63 (b(s(z), s(s(s(s(z)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1677, 69, 12650, 50])).
% 2.44/2.63 tff(12675,plain,
% 2.44/2.63 (b(s(z), s(s(elem!1)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[12674, 12673])).
% 2.44/2.63 tff(12676,plain,
% 2.44/2.63 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.44/2.63 inference(symmetry,[status(thm)],[12672])).
% 2.44/2.63 tff(12677,plain,
% 2.44/2.63 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12676])).
% 2.44/2.63 tff(12678,plain,
% 2.44/2.63 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.44/2.63 inference(symmetry,[status(thm)],[12677])).
% 2.44/2.63 tff(12679,plain,
% 2.44/2.63 (b(s(s(elem!1)), elem!1)),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[12668, 12678])).
% 2.44/2.63 tff(12680,plain,
% 2.44/2.63 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12672])).
% 2.44/2.63 tff(12681,plain,
% 2.44/2.63 (b(s(s(elem!1)), s(z))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[12649, 12680])).
% 2.44/2.63 tff(12682,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(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(12683,plain,
% 2.44/2.63 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(12684,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(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12683])).
% 2.44/2.63 tff(12685,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(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 2.44/2.63 inference(transitivity,[status(thm)],[12684, 12682])).
% 2.44/2.63 tff(12686,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(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(12687,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[12686, 12685])).
% 2.44/2.63 tff(12688,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12687, 453, 12665, 12681, 12679, 12675])).
% 2.44/2.63 tff(12689,plain,((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(s(z))), s(z)) | b(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(12690,plain,
% 2.44/2.63 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12689, 123, 12646, 4490, 12647, 221])).
% 2.44/2.63 tff(12691,plain,
% 2.44/2.63 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[518, 12690])).
% 2.44/2.63 tff(12692,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12270, 12691, 10655, 4490])).
% 2.44/2.63 tff(12693,plain,((~(s(s(s(z))) = elem!1)) | b(elem!1, s(s(s(z)))) | b(s(z), s(s(s(z)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(12694,plain,
% 2.44/2.63 (~(s(s(s(z))) = elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12693, 10, 221, 4490])).
% 2.44/2.63 tff(12695,plain,
% 2.44/2.63 (~(elem!1 = s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4487, 12694])).
% 2.44/2.63 tff(12696,plain,
% 2.44/2.63 (r(s(z), elem!1) <=> r(s(z), s(z))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[1100])).
% 2.44/2.63 tff(12697,plain,
% 2.44/2.63 (r(s(z), s(z)) <=> r(s(z), elem!1)),
% 2.44/2.63 inference(symmetry,[status(thm)],[12696])).
% 2.44/2.63 tff(12698,plain,
% 2.44/2.63 ((~r(s(z), s(z))) <=> (~r(s(z), elem!1))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12697])).
% 2.44/2.63 tff(12699,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(z))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(z))) | (~r(s(z), elem!1)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(12700,plain,
% 2.44/2.63 (((~r(s(z), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(z)))) <=> ((~r(s(z), s(z))) | (~r(s(z), elem!1)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(12701,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(z))) | (~r(s(z), elem!1))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12700])).
% 2.44/2.63 tff(12702,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(z))) | (~r(s(z), elem!1)))),
% 2.44/2.63 inference(transitivity,[status(thm)],[12701, 12699])).
% 2.44/2.63 tff(12703,plain,
% 2.44/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(z))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(12704,plain,
% 2.44/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(z))) | (~r(s(z), elem!1))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[12703, 12702])).
% 2.44/2.63 tff(12705,plain,
% 2.44/2.63 (~r(s(z), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12704, 268, 701])).
% 2.44/2.63 tff(12706,plain,
% 2.44/2.63 (~r(s(z), elem!1)),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[12705, 12698])).
% 2.44/2.63 tff(12707,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[701, 12706])).
% 2.44/2.63 tff(12708,plain,((~(elem!1 = s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(12709,plain,
% 2.44/2.63 (~(elem!1 = s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12708, 12646])).
% 2.44/2.63 tff(12710,plain,
% 2.44/2.63 (r(elem!1, s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1130, 10, 12709])).
% 2.44/2.63 tff(12711,plain,
% 2.44/2.63 (~r(elem!1, s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1157, 12710, 228])).
% 2.44/2.63 tff(12712,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4492, 12711, 12695, 4490])).
% 2.44/2.63 tff(12713,plain,(b(elem!1, s(z)) | b(elem!1, s(s(s(z)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(12714,plain,
% 2.44/2.63 (b(elem!1, s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12713, 4490, 221])).
% 2.44/2.63 tff(12715,plain,
% 2.44/2.63 (b(s(s(s(z))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2080, 76, 2077])).
% 2.44/2.63 tff(12716,plain,
% 2.44/2.63 (s(s(s(s(z)))) = elem!1),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4868, 12715, 221, 76])).
% 2.44/2.63 tff(12717,plain,
% 2.44/2.63 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4108, 12716])).
% 2.44/2.63 tff(12718,plain,
% 2.44/2.63 (s(s(s(s(s(z))))) = s(s(s(s(z))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[12717, 162])).
% 2.44/2.63 tff(12719,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[319, 12718])).
% 2.44/2.63 tff(12720,plain,((~(s(s(s(z))) = elem!1)) | b(s(z), s(s(s(z)))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(12721,plain,
% 2.44/2.63 (~(s(s(s(z))) = elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12720, 12714, 221])).
% 2.44/2.63 tff(12722,plain,
% 2.44/2.63 (~(elem!1 = s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4487, 12721])).
% 2.44/2.63 tff(12723,plain,
% 2.44/2.63 (r(elem!1, s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4492, 12722, 4490])).
% 2.44/2.63 tff(12724,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(12725,plain,
% 2.44/2.63 (((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(12726,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12725])).
% 2.44/2.63 tff(12727,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[12726, 12724])).
% 2.44/2.63 tff(12728,plain,
% 2.44/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(12729,plain,
% 2.44/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[12728, 12727])).
% 2.44/2.63 tff(12730,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12729, 268, 12646, 12723, 228])).
% 2.44/2.63 tff(12731,plain,(b(elem!1, s(s(s(z)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(12732,plain,
% 2.44/2.63 (b(elem!1, s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12731, 221])).
% 2.44/2.63 tff(12733,plain,
% 2.44/2.63 (~b(s(s(s(s(z)))), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[5423, 12732, 1764, 10654])).
% 2.44/2.63 tff(12734,plain,
% 2.44/2.63 (s(s(s(s(s(z))))) = elem!1),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[8833, 12733, 10, 2])).
% 2.44/2.63 tff(12735,plain,
% 2.44/2.63 (elem!1 = s(s(s(s(s(z)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[5538, 12734])).
% 2.44/2.63 tff(12736,plain,
% 2.44/2.63 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12735])).
% 2.44/2.63 tff(12737,plain,
% 2.44/2.63 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[1291, 12736])).
% 2.44/2.63 tff(12738,plain,
% 2.44/2.63 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12735])).
% 2.44/2.63 tff(12739,plain,
% 2.44/2.63 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[12732, 12738])).
% 2.44/2.63 tff(12740,plain,
% 2.44/2.63 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12735])).
% 2.44/2.63 tff(12741,plain,
% 2.44/2.63 ((s(s(z)) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.44/2.63 inference(transitivity,[status(thm)],[12740, 4133])).
% 2.44/2.63 tff(12742,plain,
% 2.44/2.63 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.44/2.63 inference(symmetry,[status(thm)],[12741])).
% 2.44/2.63 tff(12743,plain,
% 2.44/2.63 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12742])).
% 2.44/2.63 tff(12744,plain,
% 2.44/2.63 (~(s(s(z)) = elem!1)),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[52, 12743])).
% 2.44/2.63 tff(12745,plain,
% 2.44/2.63 (~(s(elem!1) = s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[5852, 12734])).
% 2.44/2.63 tff(12746,plain,
% 2.44/2.63 (~(s(s(z)) = s(s(elem!1)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1188, 12745])).
% 2.44/2.63 tff(12747,plain,
% 2.44/2.63 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12735])).
% 2.44/2.63 tff(12748,plain,
% 2.44/2.63 ((s(elem!1) = elem!1) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 2.44/2.63 inference(transitivity,[status(thm)],[12747, 623])).
% 2.44/2.63 tff(12749,plain,
% 2.44/2.63 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 2.44/2.63 inference(symmetry,[status(thm)],[12748])).
% 2.44/2.63 tff(12750,plain,
% 2.44/2.63 ((~(s(s(s(s(s(z))))) = s(elem!1))) <=> (~(s(elem!1) = elem!1))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12749])).
% 2.44/2.63 tff(12751,plain,
% 2.44/2.63 (~(s(elem!1) = elem!1)),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[10372, 12750])).
% 2.44/2.63 tff(12752,plain,
% 2.44/2.63 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[5786])).
% 2.44/2.63 tff(12753,plain,
% 2.44/2.63 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[5529])).
% 2.44/2.63 tff(12754,plain,
% 2.44/2.63 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[12753, 12752])).
% 2.44/2.63 tff(12755,plain,
% 2.44/2.63 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[629, 12754])).
% 2.44/2.63 tff(12756,plain,
% 2.44/2.63 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[5529])).
% 2.44/2.63 tff(12757,plain,
% 2.44/2.63 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[1275, 12756])).
% 2.44/2.63 tff(12758,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(12759,plain,
% 2.44/2.63 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(12760,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(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(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12759])).
% 2.44/2.63 tff(12761,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(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(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[12760, 12758])).
% 2.44/2.63 tff(12762,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(12763,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[12762, 12761])).
% 2.44/2.63 tff(12764,plain,
% 2.44/2.63 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12763, 453, 12757, 2611, 12755])).
% 2.44/2.63 tff(12765,plain,
% 2.44/2.63 (~b(s(elem!1), s(s(s(z))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[12764, 10751])).
% 2.44/2.63 tff(12766,plain,
% 2.44/2.63 (~b(s(elem!1), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[8264, 629, 1275, 499])).
% 2.44/2.63 tff(12767,plain,
% 2.44/2.63 (r(s(elem!1), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[353, 12766, 197])).
% 2.44/2.63 tff(12768,plain,
% 2.44/2.63 (~r(s(elem!1), s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[3055, 12767, 257])).
% 2.44/2.63 tff(12769,plain,
% 2.44/2.63 (b(s(elem!1), s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1305, 12768, 10748])).
% 2.44/2.63 tff(12770,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12769, 12765])).
% 2.44/2.63 tff(12771,plain,((~b(s(elem!1), elem!1)) | (~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (s(elem!1) = s(z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(12772,plain,
% 2.44/2.63 (~b(s(elem!1), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12771, 12737, 228, 12735, 12745, 12732, 10654])).
% 2.44/2.63 tff(12773,plain,
% 2.44/2.63 (r(s(elem!1), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2440, 12772, 12751])).
% 2.44/2.63 tff(12774,plain,
% 2.44/2.63 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[10773, 12773, 12735])).
% 2.44/2.63 tff(12775,plain,
% 2.44/2.63 (s(elem!1) = s(s(s(s(s(s(z))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12735])).
% 2.44/2.63 tff(12776,plain,
% 2.44/2.63 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 2.44/2.63 inference(symmetry,[status(thm)],[12775])).
% 2.44/2.63 tff(12777,plain,
% 2.44/2.63 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12776])).
% 2.44/2.63 tff(12778,plain,
% 2.44/2.63 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.44/2.63 inference(symmetry,[status(thm)],[12777])).
% 2.44/2.63 tff(12779,plain,
% 2.44/2.63 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12776])).
% 2.44/2.63 tff(12780,plain,
% 2.44/2.63 ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) <=> (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12779])).
% 2.44/2.63 tff(12781,plain,
% 2.44/2.63 (r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12776])).
% 2.44/2.63 tff(12782,plain,
% 2.44/2.63 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.44/2.63 inference(symmetry,[status(thm)],[12781])).
% 2.44/2.63 tff(12783,plain,
% 2.44/2.63 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[501, 221, 10654])).
% 2.44/2.63 tff(12784,plain,
% 2.44/2.63 (~(s(s(s(z))) = elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[81, 12783])).
% 2.44/2.63 tff(12785,plain,
% 2.44/2.63 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4144, 12784])).
% 2.44/2.63 tff(12786,plain,
% 2.44/2.63 (~(s(z) = s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[5029, 12745])).
% 2.44/2.63 tff(12787,plain,
% 2.44/2.63 (~r(s(elem!1), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[9570, 12773, 238])).
% 2.44/2.63 tff(12788,plain,
% 2.44/2.63 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[12441, 12787, 492, 12786, 12773, 1764])).
% 2.44/2.63 tff(12789,plain,
% 2.44/2.63 (r(s(s(s(s(z)))), s(elem!1))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2398, 12788, 12785])).
% 2.44/2.63 tff(12790,plain,
% 2.44/2.63 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[12789, 12782])).
% 2.44/2.63 tff(12791,plain,
% 2.44/2.63 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[12735])).
% 2.44/2.63 tff(12792,plain,
% 2.44/2.63 (r(s(s(s(s(z)))), elem!1)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[254, 12733, 3])).
% 2.44/2.64 tff(12793,plain,
% 2.44/2.64 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[12792, 12791])).
% 2.44/2.64 tff(12794,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.44/2.64 tff(12795,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(12796,plain,
% 2.44/2.64 (((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(12797,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[12796])).
% 2.44/2.64 tff(12798,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[12797, 12795])).
% 2.44/2.64 tff(12799,plain,
% 2.44/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(12800,plain,
% 2.44/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[12799, 12798])).
% 2.44/2.64 tff(12801,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12800, 268, 418, 2040, 12794])).
% 2.44/2.64 tff(12802,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(12803,plain,
% 2.44/2.64 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12802, 12793, 12790])).
% 2.44/2.64 tff(12804,plain,
% 2.44/2.64 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[12803, 12780])).
% 2.44/2.64 tff(12805,plain,
% 2.44/2.64 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2142, 12804, 10372])).
% 2.44/2.64 tff(12806,plain,
% 2.44/2.64 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[12805, 12778])).
% 2.44/2.64 tff(12807,plain,
% 2.44/2.64 (~b(s(s(s(z))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[5465, 12732, 1291, 10654])).
% 2.44/2.64 tff(12808,plain,
% 2.44/2.64 (r(s(s(s(z))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[134, 12807])).
% 2.44/2.64 tff(12809,plain,
% 2.44/2.64 (~r(s(z), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[5592, 12734, 4541])).
% 2.44/2.64 tff(12810,plain,
% 2.44/2.64 (b(s(z), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[372, 12809])).
% 2.44/2.64 tff(12811,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.44/2.64 tff(12812,plain,
% 2.44/2.64 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[5787])).
% 2.44/2.64 tff(12813,plain,
% 2.44/2.64 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(symmetry,[status(thm)],[12812])).
% 2.44/2.64 tff(12814,plain,
% 2.44/2.64 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[10689, 12813])).
% 2.44/2.64 tff(12815,assumption,(~b(s(s(elem!1)), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.44/2.64 tff(12816,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12815, 12814])).
% 2.44/2.64 tff(12817,plain,(b(s(s(elem!1)), s(s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(12818,plain,
% 2.44/2.64 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12817, 10689, 5529])).
% 2.44/2.64 tff(12819,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(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(12820,plain,
% 2.44/2.64 (((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(12821,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(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[12820])).
% 2.44/2.64 tff(12822,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(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[12821, 12819])).
% 2.44/2.64 tff(12823,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(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(12824,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[12823, 12822])).
% 2.44/2.64 tff(12825,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12824, 453, 1050, 443, 12811, 5798])).
% 2.44/2.64 tff(12826,plain,((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(12827,plain,
% 2.44/2.64 (~b(s(s(elem!1)), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12826, 5798, 443, 12811])).
% 2.44/2.64 tff(12828,plain,
% 2.44/2.64 (r(s(s(elem!1)), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1047, 12827])).
% 2.44/2.64 tff(12829,plain,
% 2.44/2.64 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[12828, 10687])).
% 2.44/2.64 tff(12830,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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(12831,plain,
% 2.44/2.64 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(12832,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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[12831])).
% 2.44/2.64 tff(12833,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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[12832, 12830])).
% 2.44/2.64 tff(12834,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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(12835,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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[12834, 12833])).
% 2.44/2.64 tff(12836,plain,
% 2.44/2.64 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12835, 453, 1779, 2611, 10689])).
% 2.44/2.64 tff(12837,plain,
% 2.44/2.64 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1238, 69, 2663, 12836])).
% 2.44/2.64 tff(12838,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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(12839,plain,
% 2.44/2.64 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(12840,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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(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(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[12839])).
% 2.44/2.64 tff(12841,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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(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(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[12840, 12838])).
% 2.44/2.64 tff(12842,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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(12843,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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[12842, 12841])).
% 2.44/2.64 tff(12844,plain,
% 2.44/2.64 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12843, 453, 1779, 2611, 10689])).
% 2.44/2.64 tff(12845,plain,
% 2.44/2.64 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[7740, 3475])).
% 2.44/2.64 tff(12846,plain,
% 2.44/2.64 (r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12845, 12844])).
% 2.44/2.64 tff(12847,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(12848,plain,
% 2.44/2.64 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(12849,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[12848])).
% 2.44/2.64 tff(12850,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[12849, 12847])).
% 2.44/2.64 tff(12851,plain,
% 2.44/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(12852,plain,
% 2.44/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[12851, 12850])).
% 2.44/2.64 tff(12853,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12852, 268, 233, 12846, 12837, 12829])).
% 2.44/2.64 tff(12854,plain,((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(12855,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12854, 12818, 10689, 5529, 443, 233, 1779, 2611, 12811])).
% 2.44/2.64 tff(12856,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(12857,plain,
% 2.44/2.64 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12856, 12735, 12810, 12808, 12739, 12737, 12806])).
% 2.44/2.64 tff(12858,plain,
% 2.44/2.64 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[11422, 12857])).
% 2.44/2.64 tff(12859,plain,
% 2.44/2.64 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10846, 12858, 12735, 12774, 12746])).
% 2.44/2.64 tff(12860,plain,
% 2.44/2.64 (~r(s(s(z)), elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[10851, 12859, 12735])).
% 2.44/2.64 tff(12861,plain,
% 2.44/2.64 (b(s(s(z)), elem!1)),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[782, 12860, 12744])).
% 2.44/2.64 tff(12862,plain,
% 2.44/2.64 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[5529])).
% 2.44/2.64 tff(12863,plain,
% 2.44/2.64 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[922, 12862])).
% 2.44/2.64 tff(12864,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[9052, 12863])).
% 2.44/2.64 tff(12865,plain,((~b(s(s(z)), elem!1)) | b(s(s(z)), s(s(s(s(s(z)))))) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(12866,plain,
% 2.44/2.64 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12865, 12861, 12735])).
% 2.44/2.64 tff(12867,plain,
% 2.44/2.64 (~b(s(s(s(z))), s(s(z)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[9064, 12866, 12739, 12737])).
% 2.44/2.64 tff(12868,assumption,(~r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 2.44/2.64 tff(12869,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2534, 69, 160, 10375, 12868])).
% 2.44/2.64 tff(12870,plain,(r(s(s(s(z))), s(s(z))) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(12871,plain,
% 2.44/2.64 (r(s(s(s(z))), s(s(z)))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[12870, 12867])).
% 2.44/2.64 tff(12872,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)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), 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(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(12873,plain,
% 2.44/2.64 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(12874,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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[12873])).
% 2.44/2.64 tff(12875,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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[12874, 12872])).
% 2.44/2.65 tff(12876,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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(12877,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[12876, 12875])).
% 2.44/2.65 tff(12878,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[12877, 453, 443, 1779, 1008, 8943])).
% 2.44/2.65 tff(12879,plain,((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(12880,plain,
% 2.44/2.65 (~b(s(z), s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[12879, 12866, 12739, 12810])).
% 2.44/2.65 tff(12881,plain,
% 2.44/2.65 (r(s(z), s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[757, 12880])).
% 2.44/2.65 tff(12882,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[9038, 12881, 12871, 228])).
% 2.44/2.65 tff(12883,plain,(b(s(z), s(s(s(z)))) | (s(z) = elem!1) | (~b(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | r(s(z), elem!1) | b(elem!1, s(z)) | r(s(s(s(z))), elem!1) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(12884,plain,
% 2.44/2.65 (b(s(z), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[12883, 2, 10345, 238, 10653, 4541, 10, 492, 3])).
% 2.44/2.65 tff(12885,plain,
% 2.44/2.65 (~b(elem!1, s(elem!1))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[9505, 12884, 10653, 10654])).
% 2.44/2.65 tff(12886,plain,
% 2.44/2.65 (s(s(s(z))) = elem!1),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[4487, 4484])).
% 2.44/2.65 tff(12887,plain,
% 2.44/2.65 (s(elem!1) = s(s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[81, 12886])).
% 2.44/2.65 tff(12888,plain,
% 2.44/2.65 (~(s(z) = s(elem!1))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[171, 12887])).
% 2.44/2.65 tff(12889,plain,
% 2.44/2.65 (b(s(elem!1), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1795, 12887, 1764])).
% 2.44/2.65 tff(12890,plain,
% 2.44/2.65 (~(s(elem!1) = elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[4342, 12889, 10])).
% 2.44/2.65 tff(12891,plain,
% 2.44/2.65 (~(elem!1 = s(elem!1))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8957, 12890])).
% 2.44/2.65 tff(12892,plain,
% 2.44/2.65 (r(elem!1, s(elem!1))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1069, 12891, 10391])).
% 2.44/2.65 tff(12893,plain,
% 2.44/2.65 (~r(s(z), s(elem!1))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1496, 12892, 238])).
% 2.44/2.65 tff(12894,plain,
% 2.44/2.65 (b(s(z), s(elem!1))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[397, 12893, 12888])).
% 2.44/2.65 tff(12895,plain,
% 2.44/2.65 (b(s(z), s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1758, 12894, 12887])).
% 2.44/2.65 tff(12896,plain,
% 2.44/2.65 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1992, 12895, 256, 238, 12887, 1764])).
% 2.44/2.65 tff(12897,plain,
% 2.44/2.65 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[518, 12896])).
% 2.44/2.65 tff(12898,plain,
% 2.44/2.65 (b(s(s(s(s(z)))), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[4123, 12897, 12886])).
% 2.44/2.65 tff(12899,plain,
% 2.44/2.65 (elem!1 = s(s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[2267, 12898, 12886, 10])).
% 2.44/2.65 tff(12900,plain,
% 2.44/2.65 (s(s(s(s(s(z))))) = elem!1),
% 2.44/2.65 inference(symmetry,[status(thm)],[12899])).
% 2.44/2.65 tff(12901,plain,
% 2.44/2.65 (s(s(s(s(s(z))))) = s(s(s(z)))),
% 2.44/2.65 inference(transitivity,[status(thm)],[12900, 4484])).
% 2.44/2.65 tff(12902,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[111, 12901])).
% 2.44/2.65 tff(12903,plain,((~(elem!1 = s(s(s(z))))) | b(elem!1, s(z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(12904,plain,
% 2.44/2.65 (~(elem!1 = s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[12903, 256, 10, 238, 1764, 10391])).
% 2.44/2.65 tff(12905,plain,
% 2.44/2.65 (b(elem!1, s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[4492, 12904, 1200])).
% 2.44/2.65 tff(12906,plain,
% 2.44/2.65 (~b(s(s(s(s(z)))), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[5423, 12905, 1764, 499])).
% 2.44/2.65 tff(12907,plain,
% 2.44/2.65 (s(s(s(s(s(z))))) = elem!1),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8833, 12906, 10, 2])).
% 2.44/2.65 tff(12908,plain,
% 2.44/2.65 (elem!1 = s(s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[5538, 12907])).
% 2.44/2.65 tff(12909,plain,
% 2.44/2.65 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[12908])).
% 2.44/2.65 tff(12910,plain,
% 2.44/2.65 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.44/2.65 inference(symmetry,[status(thm)],[12909])).
% 2.44/2.65 tff(12911,plain,
% 2.44/2.65 (r(elem!1, s(s(s(z))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[256, 12910])).
% 2.44/2.65 tff(12912,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1200, 12911])).
% 2.44/2.65 tff(12913,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | r(elem!1, s(s(s(z)))) | b(elem!1, s(z)) | r(s(s(s(z))), elem!1) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~r(elem!1, s(z))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(12914,plain,
% 2.44/2.65 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[12913, 2, 10, 1200, 10345, 10654, 238, 12885])).
% 2.44/2.65 tff(12915,plain,
% 2.44/2.65 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[687, 12914])).
% 2.44/2.65 tff(12916,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))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(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(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(12917,plain,
% 2.44/2.65 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(12918,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))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[12917])).
% 2.44/2.65 tff(12919,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))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[12918, 12916])).
% 2.44/2.65 tff(12920,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))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(12921,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))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[12920, 12919])).
% 2.44/2.65 tff(12922,plain,
% 2.44/2.65 (~b(s(z), s(s(s(s(s(z))))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[12921, 453, 10653, 12915, 12884])).
% 2.44/2.65 tff(12923,plain,
% 2.44/2.65 (r(s(z), s(s(s(s(s(z))))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[372, 12922])).
% 2.44/2.65 tff(12924,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))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(12925,plain,
% 2.44/2.65 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(12926,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))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[12925])).
% 2.44/2.65 tff(12927,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))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[12926, 12924])).
% 2.44/2.65 tff(12928,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))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(12929,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[12928, 12927])).
% 2.44/2.65 tff(12930,plain,
% 2.44/2.65 (~b(s(s(s(s(s(z))))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[12929, 453, 10653, 12915, 12884])).
% 2.44/2.65 tff(12931,plain,
% 2.44/2.65 (r(s(s(s(s(s(z))))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[297, 12930])).
% 2.44/2.65 tff(12932,plain,
% 2.44/2.65 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[3465, 12931, 238])).
% 2.44/2.65 tff(12933,plain,
% 2.44/2.65 (s(s(s(s(s(z))))) = elem!1),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[4324, 12931, 238, 10653, 12915, 12932])).
% 2.44/2.65 tff(12934,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[5592, 12933, 12923, 4541])).
% 2.44/2.65 tff(12935,plain,(r(s(s(s(z))), elem!1) | r(s(z), elem!1) | (~r(elem!1, s(z))) | b(elem!1, s(z)) | r(elem!1, s(s(s(z)))) | (s(z) = elem!1) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(12936,plain,
% 2.44/2.65 (r(s(s(s(z))), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[12935, 7928, 4541, 10, 1200, 4495, 3])).
% 2.44/2.65 tff(12937,plain,
% 2.44/2.65 (~r(s(s(s(z))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1586, 12936, 7928])).
% 2.44/2.65 tff(12938,plain,
% 2.44/2.65 (b(s(s(s(z))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[134, 12937])).
% 2.44/2.65 tff(12939,plain,
% 2.44/2.65 (~b(elem!1, s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[5465, 12938, 10653, 9870])).
% 2.44/2.65 tff(12940,plain,
% 2.44/2.65 (~(s(s(s(z))) = elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[6652, 12937, 7928])).
% 2.44/2.65 tff(12941,plain,
% 2.44/2.65 (~(elem!1 = s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[4487, 12940])).
% 2.44/2.65 tff(12942,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[4492, 12941, 12939, 1200])).
% 2.44/2.65 tff(12943,plain,((elem!1 = s(z)) | r(elem!1, s(s(s(z)))) | r(s(z), elem!1) | b(elem!1, s(z)) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(12944,plain,
% 2.44/2.65 (elem!1 = s(z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[12943, 3, 4541, 10, 1200])).
% 2.44/2.65 tff(12945,plain,
% 2.44/2.65 (s(s(s(z))) = s(s(elem!1))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[3026, 12944])).
% 2.44/2.65 tff(12946,plain,
% 2.44/2.65 (s(z) = elem!1),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[547, 12945])).
% 2.44/2.65 tff(12947,plain,
% 2.44/2.65 (b(s(s(s(s(z)))), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[10531, 12946, 10345])).
% 2.44/2.65 tff(12948,plain,
% 2.44/2.65 (b(s(s(s(z))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8856, 12944, 10653])).
% 2.44/2.65 tff(12949,plain,
% 2.44/2.65 (~(s(s(s(z))) = elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[122, 12948, 10])).
% 2.44/2.65 tff(12950,plain,
% 2.44/2.65 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[4144, 12949])).
% 2.44/2.65 tff(12951,plain,
% 2.44/2.65 (s(s(s(s(s(z))))) = elem!1),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[9331, 12950, 10653, 12947, 12944])).
% 2.44/2.65 tff(12952,plain,
% 2.44/2.65 (elem!1 = s(s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[5538, 12951])).
% 2.44/2.65 tff(12953,plain,
% 2.44/2.65 (s(z) = elem!1),
% 2.44/2.65 inference(symmetry,[status(thm)],[12944])).
% 2.44/2.65 tff(12954,plain,
% 2.44/2.65 (s(z) = s(s(s(s(s(z)))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[12953, 12952])).
% 2.44/2.65 tff(12955,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[289, 12954])).
% 2.44/2.65 tff(12956,plain,((s(s(s(s(z)))) = elem!1) | b(elem!1, s(z)) | r(s(z), elem!1) | r(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(12957,plain,
% 2.44/2.65 (s(s(s(s(z)))) = elem!1),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[12956, 1200, 4541, 10])).
% 2.44/2.65 tff(12958,plain,
% 2.44/2.65 ((s(z) = s(s(s(s(z))))) <=> (s(z) = elem!1)),
% 2.44/2.65 inference(monotonicity,[status(thm)],[12957])).
% 2.44/2.65 tff(12959,plain,
% 2.44/2.65 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(z) = elem!1))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[12958])).
% 2.44/2.65 tff(12960,plain,
% 2.44/2.65 (~(s(z) = elem!1)),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[50, 12959])).
% 2.44/2.65 tff(12961,plain,
% 2.44/2.65 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[4108, 12957])).
% 2.44/2.65 tff(12962,plain,
% 2.44/2.65 (s(elem!1) = s(s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[4499, 12961])).
% 2.44/2.65 tff(12963,plain,
% 2.44/2.65 (~b(s(s(s(s(z)))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[4309, 12962, 10])).
% 2.44/2.65 tff(12964,plain,
% 2.44/2.65 (r(s(s(s(s(z)))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1098, 12963])).
% 2.44/2.65 tff(12965,plain,
% 2.44/2.65 (r(elem!1, s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[4551, 12964, 12957])).
% 2.44/2.65 tff(12966,plain,
% 2.44/2.65 (~b(s(s(s(s(z)))), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[9368, 12961])).
% 2.44/2.65 tff(12967,plain,
% 2.44/2.65 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.44/2.65 inference(monotonicity,[status(thm)],[12957])).
% 2.44/2.65 tff(12968,plain,
% 2.44/2.65 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[12967, 55])).
% 2.44/2.65 tff(12969,plain,
% 2.44/2.65 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.44/2.65 inference(transitivity,[status(thm)],[12968, 56])).
% 2.44/2.65 tff(12970,plain,
% 2.44/2.65 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[12969])).
% 2.44/2.65 tff(12971,plain,
% 2.44/2.65 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[319, 12970])).
% 2.44/2.65 tff(12972,plain,
% 2.44/2.65 (r(s(s(s(z))), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8833, 12971, 10, 12966])).
% 2.44/2.65 tff(12973,plain,
% 2.44/2.65 (~r(s(s(s(z))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1586, 12972, 12965])).
% 2.44/2.65 tff(12974,plain,
% 2.44/2.65 (b(s(s(s(z))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[134, 12973])).
% 2.44/2.65 tff(12975,plain,
% 2.44/2.65 (b(s(z), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[506, 12960, 4541])).
% 2.44/2.65 tff(12976,plain,
% 2.44/2.65 (~(s(s(s(z))) = elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[9879, 12964, 10])).
% 2.44/2.65 tff(12977,plain,
% 2.44/2.65 (~(elem!1 = s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[4487, 12976])).
% 2.44/2.65 tff(12978,plain,
% 2.44/2.65 (b(elem!1, s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[4492, 12977, 1200])).
% 2.44/2.65 tff(12979,plain,
% 2.44/2.65 (~b(s(z), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[10307, 12974, 12978, 12975])).
% 2.44/2.65 tff(12980,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[5502, 12220, 10654, 221, 120, 1057])).
% 2.44/2.65 tff(12981,plain,((s(z) = elem!1) | b(s(z), s(s(s(z)))) | (~b(s(s(s(z))), s(z))) | b(s(s(s(s(z)))), s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(12982,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[12981, 12979, 12974, 4541, 12963, 12960])).
% 2.44/2.65 tff(12983,plain,(r(elem!1, s(s(s(z)))) | r(s(z), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(12984,plain,
% 2.44/2.65 (r(elem!1, s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[12983, 10, 4541])).
% 2.44/2.65 tff(12985,plain,
% 2.44/2.65 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[8869])).
% 2.44/2.65 tff(12986,plain,
% 2.44/2.65 (~b(s(s(s(s(z)))), elem!1)),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[1057, 12985])).
% 2.44/2.65 tff(12987,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8833, 12986, 10265, 10, 2])).
% 2.44/2.65 tff(12988,plain,((~(elem!1 = s(z))) | b(elem!1, s(z)) | r(s(s(s(z))), elem!1) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(12989,plain,
% 2.44/2.65 (~(elem!1 = s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[12988, 2, 10, 1057])).
% 2.44/2.65 tff(12990,plain,
% 2.44/2.65 (r(elem!1, s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1130, 12989, 10])).
% 2.44/2.65 tff(12991,plain,
% 2.44/2.65 (~r(s(s(s(s(z)))), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8459, 12990, 12984, 1099])).
% 2.44/2.65 tff(12992,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1596, 268, 238, 1132, 419])).
% 2.44/2.65 tff(12993,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(12994,plain,
% 2.44/2.65 (~r(elem!1, s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[12993, 12990, 1099])).
% 2.44/2.65 tff(12995,plain,
% 2.44/2.65 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[7911, 12989, 1057])).
% 2.44/2.65 tff(12996,plain,
% 2.44/2.65 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1656, 12995])).
% 2.44/2.65 tff(12997,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1641, 6656, 6655, 1291, 1633])).
% 2.44/2.65 tff(12998,plain,((s(s(s(s(z)))) = elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | r(elem!1, s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(12999,plain,
% 2.44/2.65 (s(s(s(s(z)))) = elem!1),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[12998, 8836, 12996, 12994, 12991])).
% 2.44/2.65 tff(13000,plain,
% 2.44/2.65 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[12999])).
% 2.44/2.65 tff(13001,plain,
% 2.44/2.65 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.65 inference(symmetry,[status(thm)],[13000])).
% 2.44/2.65 tff(13002,plain,
% 2.44/2.65 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[12984, 13001])).
% 2.44/2.65 tff(13003,plain,
% 2.44/2.65 (~(s(z) = elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1125, 12989])).
% 2.44/2.65 tff(13004,plain,
% 2.44/2.65 (b(s(z), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[506, 13003, 4541])).
% 2.44/2.65 tff(13005,plain,
% 2.44/2.65 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[4108, 12999])).
% 2.44/2.65 tff(13006,plain,
% 2.44/2.65 (~b(s(s(s(s(z)))), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[9368, 13005])).
% 2.44/2.65 tff(13007,plain,
% 2.44/2.65 (s(s(s(s(s(z))))) = elem!1),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8833, 13006, 10, 2])).
% 2.44/2.65 tff(13008,plain,
% 2.44/2.65 (elem!1 = s(s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[5538, 13007])).
% 2.44/2.65 tff(13009,plain,
% 2.44/2.65 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[5534, 13008, 12994])).
% 2.44/2.65 tff(13010,plain,
% 2.44/2.65 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[328, 13009])).
% 2.44/2.65 tff(13011,plain,
% 2.44/2.65 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.65 inference(symmetry,[status(thm)],[5964])).
% 2.44/2.65 tff(13012,plain,
% 2.44/2.65 ((~b(elem!1, s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[13011])).
% 2.44/2.65 tff(13013,plain,
% 2.44/2.65 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[1084, 13012])).
% 2.44/2.65 tff(13014,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1780, 13013])).
% 2.44/2.65 tff(13015,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | b(elem!1, s(s(s(s(z))))) | (~(s(s(s(s(s(z))))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(13016,plain,
% 2.44/2.65 (b(elem!1, s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[13015, 13010, 13007])).
% 2.44/2.65 tff(13017,plain,
% 2.44/2.65 (~b(s(s(s(z))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[7149, 13016, 13004, 8836])).
% 2.44/2.65 tff(13018,plain,
% 2.44/2.65 (r(s(s(s(z))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[134, 13017])).
% 2.44/2.65 tff(13019,plain,
% 2.44/2.65 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[4119, 13018, 1099])).
% 2.44/2.65 tff(13020,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[13019, 13002])).
% 2.44/2.65 tff(13021,plain,(r(s(s(s(z))), elem!1) | b(elem!1, s(z)) | r(s(z), elem!1) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(13022,plain,
% 2.44/2.65 (r(s(s(s(z))), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[13021, 1057, 4541, 10])).
% 2.44/2.65 tff(13023,plain,
% 2.44/2.65 (~r(elem!1, s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[12993, 7928, 1132])).
% 2.44/2.65 tff(13024,plain,
% 2.44/2.65 (b(elem!1, s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1087, 13023, 9])).
% 2.44/2.65 tff(13025,plain,
% 2.44/2.65 (~r(s(s(s(s(z)))), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8459, 7928, 12984, 1132])).
% 2.44/2.65 tff(13026,plain,
% 2.44/2.65 (b(s(s(s(s(z)))), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[254, 13025, 3])).
% 2.44/2.65 tff(13027,plain,
% 2.44/2.65 (~b(s(s(z)), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[7163, 13026, 1132, 9870, 13024])).
% 2.44/2.65 tff(13028,plain,
% 2.44/2.65 (b(s(z), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[12253, 3, 4541, 12984])).
% 2.44/2.65 tff(13029,plain,
% 2.44/2.65 (~r(s(s(s(z))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1586, 7928, 1545])).
% 2.44/2.65 tff(13030,plain,
% 2.44/2.65 (b(s(s(s(z))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[134, 13029])).
% 2.44/2.65 tff(13031,plain,
% 2.44/2.65 (~r(s(s(z)), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[7183, 13030, 1545, 13028, 7928])).
% 2.44/2.65 tff(13032,plain,
% 2.44/2.65 (s(s(z)) = elem!1),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[782, 13031, 13027])).
% 2.44/2.65 tff(13033,plain,
% 2.44/2.65 (s(s(s(z))) = s(elem!1)),
% 2.44/2.65 inference(monotonicity,[status(thm)],[13032])).
% 2.44/2.65 tff(13034,plain,
% 2.44/2.65 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[13033])).
% 2.44/2.65 tff(13035,plain,
% 2.44/2.65 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[13034])).
% 2.44/2.65 tff(13036,plain,
% 2.44/2.65 (b(s(s(s(s(s(z))))), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[7218, 13032, 1545, 7928, 13028, 13030])).
% 2.44/2.65 tff(13037,plain,
% 2.44/2.65 (~b(s(s(s(s(s(z))))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[3620, 13036, 9870, 13024])).
% 2.44/2.65 tff(13038,plain,
% 2.44/2.65 (r(s(s(s(s(s(z))))), s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[297, 13037])).
% 2.44/2.65 tff(13039,plain,
% 2.44/2.65 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[2414, 13038, 1132])).
% 2.44/2.65 tff(13040,plain,
% 2.44/2.65 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[328, 13039])).
% 2.44/2.65 tff(13041,plain,
% 2.44/2.65 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13040, 13035])).
% 2.44/2.65 tff(13042,plain,
% 2.44/2.65 (~r(s(s(elem!1)), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[7866, 13030, 1545, 13028, 7928, 4877])).
% 2.44/2.65 tff(13043,plain,
% 2.44/2.65 (~(s(s(elem!1)) = elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[3501, 13032])).
% 2.44/2.65 tff(13044,plain,
% 2.44/2.65 (b(s(s(elem!1)), elem!1)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[2240, 13043, 13042])).
% 2.44/2.65 tff(13045,plain,
% 2.44/2.65 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.44/2.65 inference(symmetry,[status(thm)],[13034])).
% 2.44/2.65 tff(13046,plain,
% 2.44/2.65 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[13045])).
% 2.44/2.65 tff(13047,plain,
% 2.44/2.65 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 2.44/2.65 inference(symmetry,[status(thm)],[13046])).
% 2.44/2.65 tff(13048,plain,
% 2.44/2.65 (b(elem!1, s(s(elem!1)))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[13024, 13047])).
% 2.44/2.65 tff(13049,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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(13050,plain,
% 2.44/2.65 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(13051,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[13050])).
% 2.44/2.65 tff(13052,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.44/2.65 inference(transitivity,[status(thm)],[13051, 13049])).
% 2.44/2.65 tff(13053,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(13054,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[13053, 13052])).
% 2.44/2.66 tff(13055,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13054, 453, 13048, 13044, 13036, 13041])).
% 2.44/2.66 tff(13056,plain,((elem!1 = s(z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), elem!1)) | (s(s(s(s(z)))) = elem!1) | r(s(z), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(13057,plain,
% 2.44/2.66 (elem!1 = s(z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13056, 3, 13022, 1099, 4541, 10])).
% 2.44/2.66 tff(13058,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), elem!1)),
% 2.44/2.66 inference(symmetry,[status(thm)],[9910])).
% 2.44/2.66 tff(13059,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), elem!1)),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[1099, 13058])).
% 2.44/2.66 tff(13060,plain,
% 2.44/2.66 (~b(s(s(s(z))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4875, 1100, 58])).
% 2.44/2.66 tff(13061,plain,
% 2.44/2.66 (r(s(s(s(z))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[134, 13060])).
% 2.44/2.66 tff(13062,plain,
% 2.44/2.66 (~r(s(s(s(s(z)))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[10292, 13061, 1057, 10, 58, 3])).
% 2.44/2.66 tff(13063,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13062, 13059])).
% 2.44/2.66 tff(13064,plain,((~(elem!1 = s(z))) | b(s(s(s(s(z)))), s(z)) | b(elem!1, s(z)) | b(s(s(s(z))), elem!1) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(13065,plain,
% 2.44/2.66 (b(s(s(s(z))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13064, 13057, 10, 1057, 3])).
% 2.44/2.66 tff(13066,plain,
% 2.44/2.66 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13057])).
% 2.44/2.66 tff(13067,plain,
% 2.44/2.66 (r(s(s(s(z))), s(z))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[13022, 13066])).
% 2.44/2.66 tff(13068,plain,
% 2.44/2.66 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4117, 268, 13067, 1099])).
% 2.44/2.66 tff(13069,plain,
% 2.44/2.66 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[518, 13068])).
% 2.44/2.66 tff(13070,plain,
% 2.44/2.66 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(z) = s(s(s(s(s(z))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13057])).
% 2.44/2.66 tff(13071,plain,
% 2.44/2.66 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.44/2.66 inference(symmetry,[status(thm)],[13070])).
% 2.44/2.66 tff(13072,plain,
% 2.44/2.66 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13071])).
% 2.44/2.66 tff(13073,plain,
% 2.44/2.66 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[289, 13072])).
% 2.44/2.66 tff(13074,plain,
% 2.44/2.66 (b(s(s(s(z))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8856, 13065, 13057])).
% 2.44/2.66 tff(13075,plain,
% 2.44/2.66 (s(elem!1) = s(s(z))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13057])).
% 2.44/2.66 tff(13076,plain,
% 2.44/2.66 (s(s(elem!1)) = s(s(s(z)))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13075])).
% 2.44/2.66 tff(13077,plain,
% 2.44/2.66 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13076])).
% 2.44/2.66 tff(13078,plain,
% 2.44/2.66 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.44/2.66 inference(symmetry,[status(thm)],[13077])).
% 2.44/2.66 tff(13079,plain,
% 2.44/2.66 (b(s(s(elem!1)), s(z))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[13074, 13078])).
% 2.44/2.66 tff(13080,plain,
% 2.44/2.66 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.44/2.66 inference(transitivity,[status(thm)],[13071, 56])).
% 2.44/2.66 tff(13081,plain,
% 2.44/2.66 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13080])).
% 2.44/2.66 tff(13082,plain,
% 2.44/2.66 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[289, 13081])).
% 2.44/2.66 tff(13083,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13057])).
% 2.44/2.66 tff(13084,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), elem!1)),
% 2.44/2.66 inference(symmetry,[status(thm)],[13083])).
% 2.44/2.66 tff(13085,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), elem!1)),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[1099, 13084])).
% 2.44/2.66 tff(13086,plain,
% 2.44/2.66 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9917, 13085, 13057, 13067, 13022])).
% 2.44/2.66 tff(13087,plain,
% 2.44/2.66 (b(s(s(s(s(s(z))))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[643, 13086, 13082])).
% 2.44/2.66 tff(13088,plain,
% 2.44/2.66 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13057])).
% 2.44/2.66 tff(13089,plain,
% 2.44/2.66 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 2.44/2.66 inference(symmetry,[status(thm)],[13088])).
% 2.44/2.66 tff(13090,plain,
% 2.44/2.66 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 2.44/2.66 inference(transitivity,[status(thm)],[13078, 13089])).
% 2.44/2.66 tff(13091,plain,
% 2.44/2.66 (b(s(s(elem!1)), elem!1)),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[13074, 13090])).
% 2.44/2.66 tff(13092,plain,
% 2.44/2.66 (~r(s(s(s(s(s(z))))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2921, 13091, 1099, 13065, 13074, 13057])).
% 2.44/2.66 tff(13093,plain,
% 2.44/2.66 (b(s(s(s(s(s(z))))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[297, 13092])).
% 2.44/2.66 tff(13094,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[3198, 13093, 13087, 13057, 13079, 1099, 13074, 13073, 13069, 13065])).
% 2.44/2.66 tff(13095,plain,((s(s(s(s(z)))) = elem!1) | b(elem!1, s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(13096,plain,
% 2.44/2.66 (s(s(s(s(z)))) = elem!1),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13095, 1057, 10, 4541])).
% 2.44/2.66 tff(13097,plain,
% 2.44/2.66 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), elem!1)),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13096])).
% 2.44/2.66 tff(13098,plain,
% 2.44/2.66 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.66 inference(symmetry,[status(thm)],[13097])).
% 2.44/2.66 tff(13099,plain,
% 2.44/2.66 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[13022, 13098])).
% 2.44/2.66 tff(13100,plain,
% 2.44/2.66 ((s(z) = s(s(s(s(z))))) <=> (s(z) = elem!1)),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13096])).
% 2.44/2.66 tff(13101,plain,
% 2.44/2.66 ((s(z) = s(s(s(s(z))))) <=> (elem!1 = s(z))),
% 2.44/2.66 inference(transitivity,[status(thm)],[13100, 1120])).
% 2.44/2.66 tff(13102,plain,
% 2.44/2.66 ((~(s(z) = s(s(s(s(z)))))) <=> (~(elem!1 = s(z)))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13101])).
% 2.44/2.66 tff(13103,plain,
% 2.44/2.66 (~(elem!1 = s(z))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[50, 13102])).
% 2.44/2.66 tff(13104,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[7911, 13103, 13099, 1057])).
% 2.44/2.66 tff(13105,plain,(b(s(s(s(s(z)))), s(z)) | b(elem!1, s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(13106,plain,
% 2.44/2.66 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13105, 10, 4541])).
% 2.44/2.66 tff(13107,plain,
% 2.44/2.66 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4309, 13106, 10])).
% 2.44/2.66 tff(13108,plain,
% 2.44/2.66 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4499, 13107])).
% 2.44/2.66 tff(13109,plain,
% 2.44/2.66 (~(s(s(s(s(z)))) = elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4108, 13108])).
% 2.44/2.66 tff(13110,plain,
% 2.44/2.66 (b(s(z), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[12253, 13109, 4541, 12984])).
% 2.44/2.66 tff(13111,plain,
% 2.44/2.66 (~b(elem!1, s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9505, 9870, 13110, 8836])).
% 2.44/2.66 tff(13112,plain,
% 2.44/2.66 (s(s(s(s(s(z))))) = elem!1),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8833, 249, 10, 2])).
% 2.44/2.66 tff(13113,plain,
% 2.44/2.66 (elem!1 = s(s(s(s(s(z)))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[5538, 13112])).
% 2.44/2.66 tff(13114,plain,
% 2.44/2.66 (s(elem!1) = s(s(s(s(s(s(z))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13113])).
% 2.44/2.66 tff(13115,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13114])).
% 2.44/2.66 tff(13116,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[254, 249, 4501])).
% 2.44/2.66 tff(13117,plain,
% 2.44/2.66 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8475, 13116, 1149])).
% 2.44/2.66 tff(13118,plain,
% 2.44/2.66 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[518, 13117])).
% 2.44/2.66 tff(13119,plain,
% 2.44/2.66 (~(s(s(s(z))) = elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4123, 13118, 249])).
% 2.44/2.66 tff(13120,plain,
% 2.44/2.66 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4144, 13119])).
% 2.44/2.66 tff(13121,plain,
% 2.44/2.66 (~(s(elem!1) = s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[5852, 13112])).
% 2.44/2.66 tff(13122,plain,
% 2.44/2.66 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13113])).
% 2.44/2.66 tff(13123,plain,
% 2.44/2.66 ((s(elem!1) = elem!1) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 2.44/2.66 inference(transitivity,[status(thm)],[13122, 623])).
% 2.44/2.66 tff(13124,plain,
% 2.44/2.66 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 2.44/2.66 inference(symmetry,[status(thm)],[13123])).
% 2.44/2.66 tff(13125,plain,
% 2.44/2.66 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 2.44/2.66 inference(transitivity,[status(thm)],[13124, 1028])).
% 2.44/2.66 tff(13126,plain,
% 2.44/2.66 ((~(s(s(s(s(s(z))))) = s(elem!1))) <=> (~(elem!1 = s(elem!1)))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13125])).
% 2.44/2.66 tff(13127,plain,
% 2.44/2.66 (~(elem!1 = s(elem!1))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[4500, 13126])).
% 2.44/2.66 tff(13128,plain,
% 2.44/2.66 (r(elem!1, s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1069, 13127, 10391])).
% 2.44/2.66 tff(13129,plain,
% 2.44/2.66 (~r(s(elem!1), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[348, 13128, 238])).
% 2.44/2.66 tff(13130,plain,
% 2.44/2.66 (b(s(elem!1), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[353, 13129, 13121])).
% 2.44/2.66 tff(13131,plain,
% 2.44/2.66 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[12426, 13130, 1764, 499])).
% 2.44/2.66 tff(13132,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2398, 13131, 13120])).
% 2.44/2.66 tff(13133,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[13132, 13115])).
% 2.44/2.66 tff(13134,plain,
% 2.44/2.66 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 2.44/2.66 inference(symmetry,[status(thm)],[13114])).
% 2.44/2.66 tff(13135,plain,
% 2.44/2.66 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13134])).
% 2.44/2.66 tff(13136,plain,
% 2.44/2.66 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.44/2.66 inference(symmetry,[status(thm)],[13135])).
% 2.44/2.66 tff(13137,plain,
% 2.44/2.66 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13113])).
% 2.44/2.66 tff(13138,plain,
% 2.44/2.66 ((~b(elem!1, s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13137])).
% 2.44/2.66 tff(13139,plain,
% 2.44/2.66 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[10391, 13138])).
% 2.44/2.66 tff(13140,plain,
% 2.44/2.66 (r(s(s(s(s(s(z))))), s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2142, 13139, 4500])).
% 2.44/2.66 tff(13141,plain,
% 2.44/2.66 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[13140, 13136])).
% 2.44/2.66 tff(13142,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13113])).
% 2.44/2.66 tff(13143,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[13116, 13142])).
% 2.44/2.66 tff(13144,plain,
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% 2.44/2.66 inference(unit_resolution,[status(thm)],[12800, 268, 13143, 13141, 13133])).
% 2.44/2.66 tff(13145,plain,(b(s(s(s(s(z)))), elem!1) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~r(elem!1, s(z))) | b(elem!1, s(elem!1)) | (~r(elem!1, s(s(s(z))))) | b(elem!1, s(z)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(13146,plain,
% 2.44/2.66 (b(s(s(s(s(z)))), elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13145, 9870, 13106, 7928, 13111, 12984, 10, 2])).
% 2.44/2.66 tff(13147,plain,
% 2.44/2.66 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[5538, 2073])).
% 2.44/2.66 tff(13148,plain,
% 2.44/2.66 (b(s(s(s(z))), s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9868, 13147, 10, 2])).
% 2.44/2.66 tff(13149,plain,
% 2.44/2.66 (~b(elem!1, s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9505, 499, 2090, 8836])).
% 2.44/2.66 tff(13150,plain,
% 2.44/2.66 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4096, 499, 2090, 8836])).
% 2.44/2.66 tff(13151,plain,
% 2.44/2.66 (r(elem!1, s(s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[466, 2073, 13150])).
% 2.44/2.66 tff(13152,plain,
% 2.44/2.66 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9415, 13151, 1149])).
% 2.44/2.66 tff(13153,plain,
% 2.44/2.66 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2570, 13152])).
% 2.44/2.66 tff(13154,plain,
% 2.44/2.66 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9467, 258, 637, 492, 1291, 299, 238])).
% 2.44/2.66 tff(13155,plain,
% 2.44/2.66 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[518, 13154])).
% 2.44/2.66 tff(13156,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9818, 13155, 8715, 1291, 299])).
% 2.44/2.66 tff(13157,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (s(z) = elem!1) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(13158,plain,
% 2.44/2.66 (~r(s(s(s(s(s(z))))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13157, 13147, 8836, 238, 299, 492])).
% 2.44/2.66 tff(13159,plain,
% 2.44/2.66 (b(s(s(s(s(s(z))))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[297, 13158])).
% 2.44/2.66 tff(13160,plain,
% 2.44/2.66 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[11671, 13159, 13153, 13148])).
% 2.44/2.66 tff(13161,plain,
% 2.44/2.66 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[659, 13160, 3700])).
% 2.44/2.66 tff(13162,plain,
% 2.44/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(13163,plain,
% 2.44/2.66 (((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(13164,plain,
% 2.44/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13163])).
% 2.44/2.66 tff(13165,plain,
% 2.44/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[13164, 13162])).
% 2.44/2.66 tff(13166,plain,
% 2.44/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(elem!1, s(elem!1))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(13167,plain,
% 2.44/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[13166, 13165])).
% 2.44/2.66 tff(13168,plain,
% 2.44/2.66 (~r(elem!1, s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13167, 268, 13151, 13161])).
% 2.44/2.66 tff(13169,plain,
% 2.44/2.66 (elem!1 = s(elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1069, 13168, 13149])).
% 2.44/2.66 tff(13170,plain,
% 2.44/2.66 (b(s(z), elem!1) <=> b(s(z), s(elem!1))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13169])).
% 2.44/2.66 tff(13171,plain,
% 2.44/2.66 (b(s(z), s(elem!1))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[499, 13170])).
% 2.44/2.66 tff(13172,plain,
% 2.44/2.66 (b(elem!1, s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13169])).
% 2.44/2.66 tff(13173,plain,
% 2.44/2.66 (~(s(s(s(s(z)))) = elem!1)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[4108, 11207])).
% 2.44/2.66 tff(13174,plain,
% 2.44/2.66 (~(elem!1 = s(s(s(s(z)))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8, 13173])).
% 2.44/2.66 tff(13175,plain,
% 2.44/2.66 (~b(elem!1, s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9830, 523, 1291, 299])).
% 2.44/2.66 tff(13176,plain,
% 2.44/2.66 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9818, 523, 1291, 299])).
% 2.44/2.66 tff(13177,plain,
% 2.44/2.66 (r(elem!1, s(s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[466, 13176, 2073])).
% 2.44/2.66 tff(13178,plain,
% 2.44/2.66 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[9415, 13177, 1149])).
% 2.44/2.66 tff(13179,plain,
% 2.44/2.66 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2570, 13178])).
% 2.44/2.66 tff(13180,plain,
% 2.44/2.66 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[11671, 13179, 11663, 374])).
% 2.44/2.66 tff(13181,plain,
% 2.44/2.66 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[659, 13180, 9486])).
% 2.44/2.66 tff(13182,plain,
% 2.44/2.66 (~r(elem!1, s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13167, 268, 13177, 13181])).
% 2.44/2.66 tff(13183,plain,
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% 2.44/2.66 inference(unit_resolution,[status(thm)],[1069, 13182, 13175])).
% 2.44/2.66 tff(13184,plain,
% 2.44/2.66 (b(elem!1, s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13183])).
% 2.44/2.66 tff(13185,plain,
% 2.44/2.66 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[8954])).
% 2.44/2.66 tff(13186,plain,
% 2.44/2.66 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = elem!1)),
% 2.44/2.66 inference(monotonicity,[status(thm)],[12094])).
% 2.44/2.66 tff(13187,plain,
% 2.44/2.66 ((s(s(s(elem!1))) = s(elem!1)) <=> (elem!1 = s(s(s(elem!1))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[13186, 1391])).
% 2.44/2.66 tff(13188,plain,
% 2.44/2.66 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = elem!1)),
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% 2.44/2.66 tff(13189,plain,
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% 2.44/2.66 inference(unit_resolution,[status(thm)],[8957, 8954])).
% 2.44/2.66 tff(13190,plain,
% 2.44/2.66 (elem!1 = s(s(elem!1))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[3351, 13189])).
% 2.44/2.66 tff(13191,plain,
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% 2.44/2.66 inference(unit_resolution,[status(thm)],[4223, 13190])).
% 2.44/2.66 tff(13192,plain,
% 2.44/2.66 (s(s(s(elem!1))) = elem!1),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[13191, 13188])).
% 2.44/2.66 tff(13193,plain,
% 2.44/2.66 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(13194,plain,
% 2.44/2.66 (inj_0(s(s(s(s(s(s(s(s(s(z)))))))))) = s(s(s(s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13193, 21])).
% 2.44/2.66 tff(13195,plain,
% 2.44/2.66 (s(s(elem!1)) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[2330])).
% 2.44/2.66 tff(13196,plain,
% 2.44/2.66 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 2.44/2.66 inference(transitivity,[status(thm)],[2336, 3805, 85, 187])).
% 2.44/2.66 tff(13197,plain,
% 2.44/2.66 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(elem!1))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13196])).
% 2.44/2.66 tff(13198,plain,
% 2.44/2.66 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(s(s(z)))))))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[1375, 13197, 550, 13195])).
% 2.44/2.66 tff(13199,plain,
% 2.44/2.66 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(s(s(s(s(s(z))))))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13198])).
% 2.44/2.66 tff(13200,plain,
% 2.44/2.66 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[808, 13199, 13194])).
% 2.44/2.66 tff(13201,plain,
% 2.44/2.66 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(s(z)))))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13200])).
% 2.44/2.66 tff(13202,plain,
% 2.44/2.66 (s(s(s(s(z)))) = elem!1),
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% 2.44/2.66 tff(13203,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[3, 13202])).
% 2.44/2.66 tff(13204,plain,((~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))) | (s(s(s(s(z)))) = elem!1) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(13205,plain,
% 2.44/2.66 (~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13204, 13192, 3])).
% 2.44/2.66 tff(13206,plain,
% 2.44/2.66 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[3822, 13205])).
% 2.44/2.66 tff(13207,plain,
% 2.44/2.66 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[8954])).
% 2.44/2.66 tff(13208,plain,
% 2.44/2.66 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(symmetry,[status(thm)],[13207])).
% 2.44/2.66 tff(13209,plain,
% 2.44/2.66 ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) <=> (~r(elem!1, s(s(s(s(s(s(s(z)))))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13208])).
% 2.44/2.66 tff(13210,plain,
% 2.44/2.66 (r(elem!1, s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[8954])).
% 2.44/2.66 tff(13211,plain,
% 2.44/2.66 (r(s(elem!1), s(s(s(z))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[1149, 13210])).
% 2.44/2.66 tff(13212,plain,
% 2.44/2.66 (r(elem!1, s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[8954])).
% 2.44/2.66 tff(13213,plain,
% 2.44/2.66 (r(s(elem!1), s(s(s(s(z)))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[419, 13212])).
% 2.44/2.66 tff(13214,assumption,(r(s(elem!1), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.44/2.66 tff(13215,plain,
% 2.44/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(13216,plain,
% 2.44/2.66 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(13217,plain,
% 2.44/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13216])).
% 2.44/2.66 tff(13218,plain,
% 2.44/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[13217, 13215])).
% 2.44/2.66 tff(13219,plain,
% 2.44/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(13220,plain,
% 2.44/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[13219, 13218])).
% 2.44/2.66 tff(13221,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13220, 268, 9650, 13214, 2637])).
% 2.44/2.66 tff(13222,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(13223,plain,
% 2.44/2.66 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13222, 13214, 9650])).
% 2.44/2.66 tff(13224,plain,
% 2.44/2.66 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2696, 13223])).
% 2.44/2.66 tff(13225,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.44/2.66 tff(13226,plain,
% 2.44/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(13227,plain,
% 2.44/2.66 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(13228,plain,
% 2.44/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[13227])).
% 2.44/2.66 tff(13229,plain,
% 2.44/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[13228, 13226])).
% 2.44/2.66 tff(13230,plain,
% 2.44/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(13231,plain,
% 2.44/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[13230, 13229])).
% 2.44/2.66 tff(13232,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13231, 268, 9650, 13225, 13214])).
% 2.44/2.66 tff(13233,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(13234,plain,
% 2.44/2.66 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[13233, 13214, 9650])).
% 2.44/2.66 tff(13235,plain,
% 2.44/2.66 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[6308, 13234])).
% 2.44/2.67 tff(13236,assumption,(r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.44/2.67 tff(13237,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[8159, 268, 13236, 13214, 3047])).
% 2.44/2.67 tff(13238,plain,((~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(13239,plain,
% 2.44/2.67 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13238, 13214, 3047])).
% 2.44/2.67 tff(13240,plain,
% 2.44/2.67 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[7740, 13239, 3475])).
% 2.44/2.67 tff(13241,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13242,plain,
% 2.44/2.67 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13243,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(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[13242])).
% 2.44/2.67 tff(13244,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(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[13243, 13241])).
% 2.44/2.67 tff(13245,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(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(13246,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13245, 13244])).
% 2.44/2.67 tff(13247,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13246, 453, 523, 13240, 13235, 13224])).
% 2.44/2.67 tff(13248,plain,((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(13249,plain,
% 2.44/2.67 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13248, 13213, 523, 13211])).
% 2.44/2.67 tff(13250,plain,
% 2.44/2.67 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13249, 13209])).
% 2.44/2.67 tff(13251,plain,
% 2.44/2.67 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[3856, 13250, 13206])).
% 2.44/2.67 tff(13252,plain,
% 2.44/2.67 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13251, 13185])).
% 2.44/2.67 tff(13253,plain,
% 2.44/2.67 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[8954])).
% 2.44/2.67 tff(13254,plain,
% 2.44/2.67 (b(s(s(s(s(z)))), s(elem!1))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[299, 13253])).
% 2.44/2.67 tff(13255,plain,
% 2.44/2.67 (s(elem!1) = s(s(elem!1))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[8905, 13189])).
% 2.44/2.67 tff(13256,plain,
% 2.44/2.67 (b(s(s(s(z))), s(elem!1))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[9349, 13255, 2, 555])).
% 2.44/2.67 tff(13257,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13258,plain,
% 2.44/2.67 (((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13259,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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[13258])).
% 2.44/2.67 tff(13260,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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[13259, 13257])).
% 2.44/2.67 tff(13261,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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(13262,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13261, 13260])).
% 2.44/2.67 tff(13263,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13262, 453, 523, 13256, 13254, 13252])).
% 2.44/2.67 tff(13264,plain,((~(elem!1 = s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | r(s(s(s(z))), elem!1) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(13265,plain,
% 2.44/2.67 (~r(elem!1, s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13264, 13183, 9370, 299, 1149, 523, 2, 555])).
% 2.44/2.67 tff(13266,plain,
% 2.44/2.67 (b(elem!1, s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[1087, 13265, 9371])).
% 2.44/2.67 tff(13267,plain,
% 2.44/2.67 (b(s(elem!1), s(s(s(s(z)))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13266, 13184])).
% 2.44/2.67 tff(13268,plain,
% 2.44/2.67 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[13183])).
% 2.44/2.67 tff(13269,plain,
% 2.44/2.67 (b(s(s(s(s(z)))), s(elem!1))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[299, 13268])).
% 2.44/2.67 tff(13270,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(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13271,plain,
% 2.44/2.67 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13272,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(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[13271])).
% 2.44/2.67 tff(13273,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(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[13272, 13270])).
% 2.44/2.67 tff(13274,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(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(13275,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13274, 13273])).
% 2.44/2.67 tff(13276,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13275, 453, 523, 11663, 13269, 13267])).
% 2.44/2.67 tff(13277,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | r(s(s(s(z))), elem!1) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(13278,plain,
% 2.44/2.67 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13277, 13159, 2, 1149, 2073, 548, 299, 13148, 8836])).
% 2.44/2.67 tff(13279,plain,
% 2.44/2.67 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[518, 13278])).
% 2.44/2.67 tff(13280,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[9400, 268, 11, 419, 1149])).
% 2.44/2.67 tff(13281,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(13282,plain,
% 2.44/2.67 (~r(elem!1, s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13281, 13279, 1149])).
% 2.44/2.67 tff(13283,plain,
% 2.44/2.67 (b(elem!1, s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[1087, 13282, 13174])).
% 2.44/2.67 tff(13284,plain,
% 2.44/2.67 (b(s(elem!1), s(s(s(s(z)))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13283, 13172])).
% 2.44/2.67 tff(13285,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(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13286,plain,
% 2.44/2.67 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(13287,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(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), 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(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z)))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[13286])).
% 2.44/2.67 tff(13288,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(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), 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(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[13287, 13285])).
% 2.44/2.67 tff(13289,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(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(13290,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z)))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13289, 13288])).
% 2.44/2.67 tff(13291,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13290, 453, 1549, 11663, 9384, 2090])).
% 2.44/2.67 tff(13292,plain,((~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(13293,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13292, 13284, 13171, 2090, 13148])).
% 2.44/2.67 tff(13294,plain,((elem!1 = s(s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (s(elem!1) = s(s(s(s(s(z)))))) | r(s(s(s(z))), elem!1) | (~b(s(s(s(s(z)))), elem!1)) | b(elem!1, s(z)) | (~r(elem!1, s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(13295,plain,
% 2.44/2.67 (elem!1 = s(s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13294, 9870, 13110, 12984, 13107, 2, 13146, 10, 7928, 4495])).
% 2.44/2.67 tff(13296,plain,
% 2.44/2.67 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[13295])).
% 2.44/2.67 tff(13297,plain,
% 2.44/2.67 ((s(s(s(z))) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[13296, 57])).
% 2.44/2.67 tff(13298,plain,
% 2.44/2.67 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 2.44/2.67 inference(symmetry,[status(thm)],[13297])).
% 2.44/2.67 tff(13299,plain,
% 2.44/2.67 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[13298])).
% 2.44/2.67 tff(13300,plain,
% 2.44/2.67 (~(s(s(s(z))) = elem!1)),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[111, 13299])).
% 2.44/2.67 tff(13301,plain,
% 2.44/2.67 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[4144, 13300])).
% 2.44/2.67 tff(13302,plain,
% 2.44/2.67 (s(s(s(s(s(z))))) = elem!1),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[8839, 13295])).
% 2.44/2.67 tff(13303,plain,
% 2.44/2.67 (~(s(elem!1) = s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[5852, 13302])).
% 2.44/2.67 tff(13304,plain,
% 2.44/2.67 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[13295])).
% 2.44/2.67 tff(13305,plain,
% 2.44/2.67 ((s(elem!1) = elem!1) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 2.44/2.67 inference(transitivity,[status(thm)],[13304, 623])).
% 2.44/2.67 tff(13306,plain,
% 2.44/2.67 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 2.44/2.67 inference(symmetry,[status(thm)],[13305])).
% 2.44/2.67 tff(13307,plain,
% 2.44/2.67 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 2.44/2.67 inference(transitivity,[status(thm)],[13306, 1028])).
% 2.44/2.67 tff(13308,plain,
% 2.44/2.67 ((~(s(s(s(s(s(z))))) = s(elem!1))) <=> (~(elem!1 = s(elem!1)))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[13307])).
% 2.44/2.67 tff(13309,plain,
% 2.44/2.67 (~(elem!1 = s(elem!1))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13108, 13308])).
% 2.44/2.67 tff(13310,plain,
% 2.44/2.67 (r(elem!1, s(elem!1))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[1069, 13309, 13111])).
% 2.44/2.67 tff(13311,plain,
% 2.44/2.67 (~r(s(elem!1), s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[348, 13310, 7928])).
% 2.44/2.67 tff(13312,plain,
% 2.44/2.67 (b(s(elem!1), s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[353, 13311, 13303])).
% 2.44/2.67 tff(13313,plain,
% 2.44/2.67 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[12426, 13312, 13106, 9870])).
% 2.44/2.67 tff(13314,plain,
% 2.44/2.67 (~r(s(z), s(s(s(s(s(z))))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[5592, 13302, 4541])).
% 2.44/2.67 tff(13315,plain,
% 2.44/2.67 (b(s(z), s(s(s(s(s(z))))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[372, 13314])).
% 2.44/2.67 tff(13316,plain,
% 2.44/2.67 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[13295])).
% 2.44/2.67 tff(13317,plain,
% 2.44/2.67 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[13146, 13316])).
% 2.44/2.67 tff(13318,plain,
% 2.44/2.67 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[8186, 13317, 13106, 13315])).
% 2.44/2.67 tff(13319,plain,
% 2.44/2.67 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[328, 13318])).
% 2.44/2.67 tff(13320,plain,
% 2.44/2.67 (r(elem!1, s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[5534, 13319, 13295])).
% 2.44/2.67 tff(13321,plain,
% 2.44/2.67 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[4946, 13320, 13310])).
% 2.44/2.67 tff(13322,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[2398, 13321, 13313, 13301])).
% 2.44/2.67 tff(13323,plain,((elem!1 = s(z)) | r(s(z), elem!1) | r(s(s(s(z))), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(13324,plain,
% 2.44/2.67 (elem!1 = s(z)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13323, 2, 4541, 10])).
% 2.44/2.67 tff(13325,plain,
% 2.44/2.67 (s(s(s(z))) = s(s(elem!1))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[3026, 13324])).
% 2.44/2.67 tff(13326,plain,
% 2.44/2.67 (s(z) = elem!1),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[547, 13325])).
% 2.44/2.67 tff(13327,plain,
% 2.44/2.67 (b(s(s(s(s(z)))), elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[10531, 13326, 13106])).
% 2.44/2.67 tff(13328,plain,
% 2.44/2.67 (b(s(s(s(z))), s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[8856, 13324, 8836])).
% 2.44/2.67 tff(13329,plain,
% 2.44/2.67 (~(s(s(s(z))) = elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[122, 13328, 10])).
% 2.44/2.67 tff(13330,plain,
% 2.44/2.67 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[4144, 13329])).
% 2.44/2.67 tff(13331,plain,
% 2.44/2.67 (s(s(s(s(s(z))))) = elem!1),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[9331, 13330, 13324, 13327, 8836])).
% 2.44/2.67 tff(13332,plain,
% 2.44/2.67 (elem!1 = s(s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[5538, 13331])).
% 2.44/2.67 tff(13333,plain,
% 2.44/2.67 (s(z) = elem!1),
% 2.44/2.67 inference(symmetry,[status(thm)],[13324])).
% 2.44/2.67 tff(13334,plain,
% 2.44/2.67 (s(z) = s(s(s(s(s(z)))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[13333, 13332])).
% 2.44/2.67 tff(13335,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[289, 13334])).
% 2.44/2.67 tff(13336,plain,(r(s(s(s(z))), elem!1) | b(elem!1, s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(13337,plain,
% 2.44/2.67 (r(s(s(s(z))), elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13336, 10, 4541])).
% 2.44/2.67 tff(13338,plain,
% 2.44/2.67 (~b(s(s(s(z))), s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[3782, 13118, 1764, 2090])).
% 2.44/2.67 tff(13339,plain,
% 2.44/2.67 (~(s(z) = elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[10531, 249, 1764])).
% 2.44/2.67 tff(13340,plain,
% 2.44/2.67 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[547, 13339])).
% 2.44/2.67 tff(13341,plain,
% 2.44/2.67 (~(elem!1 = s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[3026, 13340])).
% 2.44/2.67 tff(13342,plain,
% 2.44/2.67 (r(elem!1, s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[1130, 13341, 10])).
% 2.44/2.67 tff(13343,plain,
% 2.44/2.67 (~r(s(s(s(z))), s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[1586, 13342, 1545])).
% 2.44/2.67 tff(13344,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[134, 13343, 13338])).
% 2.44/2.67 tff(13345,plain,(b(s(s(s(s(z)))), elem!1) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | b(elem!1, s(z)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(13346,plain,
% 2.44/2.67 (b(s(s(s(s(z)))), elem!1)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[13345, 13337, 13106, 13110, 10, 12984])).
% 2.44/2.67 tff(13347,plain,
% 2.44/2.67 (~(elem!1 = s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[8, 13109])).
% 2.44/2.67 tff(13348,plain,
% 2.44/2.67 (~r(s(s(s(z))), s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[1586, 7928, 13337])).
% 2.44/2.67 tff(13349,plain,
% 2.44/2.67 (b(s(s(s(z))), s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[134, 13348])).
% 2.44/2.67 tff(13350,plain,
% 2.44/2.67 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[3782, 13349, 13106, 13110])).
% 2.44/2.68 tff(13351,plain,
% 2.44/2.68 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[518, 13350])).
% 2.44/2.68 tff(13352,plain,
% 2.44/2.68 (~r(elem!1, s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13281, 13351, 12984])).
% 2.44/2.68 tff(13353,plain,
% 2.44/2.68 (b(elem!1, s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1087, 13352, 13347])).
% 2.44/2.68 tff(13354,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), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(13355,plain,
% 2.44/2.68 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(13356,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13355])).
% 2.44/2.68 tff(13357,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[13356, 13354])).
% 2.44/2.68 tff(13358,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(13359,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13358, 13357])).
% 2.44/2.68 tff(13360,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13359, 453, 9870, 13106, 13353, 13346])).
% 2.44/2.68 tff(13361,plain,((elem!1 = s(z)) | r(s(z), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(13362,plain,
% 2.44/2.68 (elem!1 = s(z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13361, 10, 4541])).
% 2.44/2.68 tff(13363,plain,
% 2.44/2.68 (~(s(elem!1) = s(s(elem!1)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2287, 13362])).
% 2.44/2.68 tff(13364,plain,
% 2.44/2.68 (~(s(elem!1) = elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8905, 13363])).
% 2.44/2.68 tff(13365,plain,
% 2.44/2.68 (b(elem!1, s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13362])).
% 2.44/2.68 tff(13366,plain,
% 2.44/2.68 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13365])).
% 2.44/2.68 tff(13367,plain,
% 2.44/2.68 (b(elem!1, s(s(s(z))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13110, 13366])).
% 2.44/2.68 tff(13368,plain,
% 2.44/2.68 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13362])).
% 2.44/2.68 tff(13369,plain,
% 2.44/2.68 (r(s(s(s(z))), s(z))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13337, 13368])).
% 2.44/2.68 tff(13370,plain,
% 2.44/2.68 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[10507, 13369, 13337, 13108, 13110, 13362, 13106, 13367])).
% 2.44/2.68 tff(13371,plain,
% 2.44/2.68 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[518, 13370])).
% 2.44/2.68 tff(13372,plain,
% 2.44/2.68 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(z) = s(s(s(s(s(z))))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13362])).
% 2.44/2.68 tff(13373,plain,
% 2.44/2.68 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13372])).
% 2.44/2.68 tff(13374,plain,
% 2.44/2.68 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.44/2.68 inference(transitivity,[status(thm)],[13373, 56])).
% 2.44/2.68 tff(13375,plain,
% 2.44/2.68 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13374])).
% 2.44/2.68 tff(13376,plain,
% 2.44/2.68 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[289, 13375])).
% 2.44/2.68 tff(13377,plain,
% 2.44/2.68 (s(s(s(z))) = s(s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[3026, 13362])).
% 2.44/2.68 tff(13378,plain,
% 2.44/2.68 (s(z) = elem!1),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[547, 13377])).
% 2.44/2.68 tff(13379,plain,
% 2.44/2.68 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13362])).
% 2.44/2.68 tff(13380,plain,
% 2.44/2.68 (r(s(z), s(s(s(z))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[12984, 13379])).
% 2.44/2.68 tff(13381,plain,
% 2.44/2.68 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[11340, 13380, 13106, 13108, 13347, 13378, 13376, 13337])).
% 2.44/2.68 tff(13382,plain,
% 2.44/2.68 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[687, 13381])).
% 2.44/2.68 tff(13383,plain,
% 2.44/2.68 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13362])).
% 2.44/2.68 tff(13384,plain,
% 2.44/2.68 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13383])).
% 2.44/2.68 tff(13385,plain,
% 2.44/2.68 (s(elem!1) = s(s(z))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13362])).
% 2.44/2.68 tff(13386,plain,
% 2.44/2.68 (s(s(elem!1)) = s(s(s(z)))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13385])).
% 2.44/2.68 tff(13387,plain,
% 2.44/2.68 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13386])).
% 2.44/2.68 tff(13388,plain,
% 2.44/2.68 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13387])).
% 2.44/2.68 tff(13389,plain,
% 2.44/2.68 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.44/2.68 inference(transitivity,[status(thm)],[13388, 13384])).
% 2.44/2.68 tff(13390,plain,
% 2.44/2.68 (b(elem!1, s(s(elem!1)))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13110, 13389])).
% 2.44/2.68 tff(13391,plain,
% 2.44/2.68 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2102, 13371, 13106, 13110])).
% 2.44/2.68 tff(13392,plain,
% 2.44/2.68 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1656, 13391])).
% 2.44/2.68 tff(13393,plain,
% 2.44/2.68 (~b(s(elem!1), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[10617, 13392, 13362, 13337, 13390, 13382, 13107, 13371, 13106, 13367])).
% 2.44/2.68 tff(13394,plain,
% 2.44/2.68 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[10484, 13382, 13378])).
% 2.44/2.68 tff(13395,plain,
% 2.44/2.68 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13385])).
% 2.44/2.68 tff(13396,plain,
% 2.44/2.68 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.44/2.68 inference(transitivity,[status(thm)],[13395, 1])).
% 2.44/2.68 tff(13397,plain,
% 2.44/2.68 ((s(s(s(s(z)))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13396])).
% 2.44/2.68 tff(13398,plain,
% 2.44/2.68 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13397])).
% 2.44/2.68 tff(13399,plain,
% 2.44/2.68 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[153, 13398])).
% 2.44/2.68 tff(13400,plain,
% 2.44/2.68 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.44/2.68 inference(transitivity,[status(thm)],[13397, 2373])).
% 2.44/2.68 tff(13401,plain,
% 2.44/2.68 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13400])).
% 2.44/2.68 tff(13402,plain,
% 2.44/2.68 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[153, 13401])).
% 2.44/2.68 tff(13403,plain,
% 2.44/2.68 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[11678, 13382, 12984, 13107, 13106, 13347, 13378, 13402, 13337, 13376])).
% 2.44/2.68 tff(13404,plain,
% 2.44/2.68 (r(s(elem!1), s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[9382, 13403, 13399])).
% 2.44/2.68 tff(13405,plain,
% 2.44/2.68 (~r(s(elem!1), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[11689, 13404, 13107, 13378, 13346, 13347, 13376, 13337, 13394])).
% 2.44/2.68 tff(13406,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2440, 13405, 13393, 13364])).
% 2.44/2.68 tff(13407,plain,(b(elem!1, s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(13408,plain,
% 2.44/2.68 (b(elem!1, s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13407, 4541])).
% 2.44/2.68 tff(13409,plain,
% 2.44/2.68 (b(elem!1, s(z)) <=> b(elem!1, elem!1)),
% 2.44/2.68 inference(monotonicity,[status(thm)],[2277])).
% 2.44/2.68 tff(13410,plain,
% 2.44/2.68 (b(elem!1, elem!1) <=> b(elem!1, s(z))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13409])).
% 2.44/2.68 tff(13411,plain,
% 2.44/2.68 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(z)))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13410])).
% 2.44/2.68 tff(13412,plain,
% 2.44/2.68 (~b(elem!1, s(z))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[1707, 13411])).
% 2.44/2.68 tff(13413,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2077, 13412])).
% 2.44/2.68 tff(13414,plain,((~(elem!1 = s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(13415,plain,
% 2.44/2.68 (~(elem!1 = s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13414, 13408])).
% 2.44/2.68 tff(13416,plain,
% 2.44/2.68 (~(s(z) = elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1125, 13415])).
% 2.44/2.68 tff(13417,plain,
% 2.44/2.68 (b(s(z), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[506, 13416, 4541])).
% 2.44/2.68 tff(13418,plain,
% 2.44/2.68 (b(s(s(s(s(z)))), s(z)) <=> b(elem!1, s(z))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[1170])).
% 2.44/2.68 tff(13419,plain,
% 2.44/2.68 (b(elem!1, s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13418])).
% 2.44/2.68 tff(13420,plain,
% 2.44/2.68 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[2077, 13419])).
% 2.44/2.68 tff(13421,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1057, 13420])).
% 2.44/2.68 tff(13422,plain,((~(s(s(s(s(z)))) = elem!1)) | b(s(s(s(s(z)))), s(z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(13423,plain,
% 2.44/2.68 (~(s(s(s(s(z)))) = elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13422, 1057, 13408])).
% 2.44/2.68 tff(13424,plain,
% 2.44/2.68 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[7911, 1123, 1057])).
% 2.44/2.68 tff(13425,plain,
% 2.44/2.68 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1656, 13424])).
% 2.44/2.68 tff(13426,plain,
% 2.44/2.68 (~(s(s(s(z))) = elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2080, 128, 13408])).
% 2.44/2.68 tff(13427,plain,
% 2.44/2.68 (b(s(s(s(z))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[74, 13426, 2])).
% 2.44/2.68 tff(13428,plain,
% 2.44/2.68 (~b(s(s(z)), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[11076, 13427, 4541, 2076, 1123, 3448])).
% 2.44/2.68 tff(13429,plain,
% 2.44/2.68 (~b(s(z), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[5513, 13427, 13408, 9870])).
% 2.44/2.68 tff(13430,plain,
% 2.44/2.68 (r(s(z), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[227, 13429])).
% 2.44/2.68 tff(13431,plain,
% 2.44/2.68 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[11061, 13430, 2076, 3448, 13426])).
% 2.44/2.68 tff(13432,plain,
% 2.44/2.68 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[11146, 13431, 13408, 1132, 9870, 1159])).
% 2.44/2.68 tff(13433,plain,
% 2.44/2.68 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[328, 13432])).
% 2.44/2.68 tff(13434,plain,
% 2.44/2.68 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[4119, 3448, 1132])).
% 2.44/2.68 tff(13435,plain,
% 2.44/2.68 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[518, 13434])).
% 2.44/2.68 tff(13436,plain,
% 2.44/2.68 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1788, 13433, 1633, 13435])).
% 2.44/2.68 tff(13437,plain,
% 2.44/2.68 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[687, 13436])).
% 2.44/2.68 tff(13438,plain,
% 2.44/2.68 (~r(s(z), s(s(s(s(s(z))))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[3160, 13437, 13430])).
% 2.44/2.68 tff(13439,plain,
% 2.44/2.68 (b(s(z), s(s(s(s(s(z))))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[372, 13438])).
% 2.44/2.68 tff(13440,plain,
% 2.44/2.68 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[11166, 13439, 13408, 9870])).
% 2.44/2.68 tff(13441,plain,
% 2.44/2.68 (r(s(s(s(s(s(z))))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[643, 13440, 13431])).
% 2.44/2.68 tff(13442,plain,
% 2.44/2.68 (~(elem!1 = s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[4487, 13426])).
% 2.44/2.68 tff(13443,plain,
% 2.44/2.68 (b(elem!1, s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[4492, 13442, 1200])).
% 2.44/2.68 tff(13444,plain,
% 2.44/2.68 (~b(elem!1, s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8169, 453, 13435, 13427, 13443])).
% 2.44/2.68 tff(13445,plain,
% 2.44/2.68 (r(elem!1, s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1087, 13444, 1055])).
% 2.44/2.68 tff(13446,plain,
% 2.44/2.68 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8839, 13431])).
% 2.44/2.68 tff(13447,plain,
% 2.44/2.68 (~r(s(s(s(s(s(z))))), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[276, 13437, 13430])).
% 2.44/2.68 tff(13448,plain,
% 2.44/2.68 (b(s(s(s(s(s(z))))), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[297, 13447])).
% 2.44/2.68 tff(13449,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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(13450,plain,
% 2.44/2.68 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(13451,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13450])).
% 2.44/2.68 tff(13452,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[13451, 13449])).
% 2.44/2.68 tff(13453,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(13454,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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13453, 13452])).
% 2.44/2.68 tff(13455,plain,
% 2.44/2.68 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13454, 453, 9870, 13408, 13448])).
% 2.44/2.68 tff(13456,plain,
% 2.44/2.68 (r(elem!1, s(s(s(s(s(z))))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[466, 13455, 13446])).
% 2.44/2.68 tff(13457,plain,
% 2.44/2.68 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[427, 13456, 13445])).
% 2.44/2.68 tff(13458,plain,
% 2.44/2.68 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[10556, 13457])).
% 2.44/2.68 tff(13459,plain,
% 2.44/2.68 (~r(s(s(z)), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[6602, 13458, 1159, 1132, 13441, 13433])).
% 2.44/2.68 tff(13460,plain,
% 2.44/2.68 (s(s(z)) = elem!1),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[782, 13459, 13428])).
% 2.44/2.68 tff(13461,plain,
% 2.44/2.68 (~(s(s(s(s(s(s(s(s(z)))))))) = elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[5602, 13460])).
% 2.44/2.68 tff(13462,plain,
% 2.44/2.68 (s(s(s(z))) = s(elem!1)),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13460])).
% 2.44/2.68 tff(13463,plain,
% 2.44/2.68 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13462])).
% 2.44/2.68 tff(13464,plain,
% 2.44/2.68 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13463])).
% 2.44/2.68 tff(13465,plain,
% 2.44/2.68 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13464])).
% 2.44/2.68 tff(13466,plain,
% 2.44/2.68 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13465])).
% 2.44/2.68 tff(13467,plain,
% 2.44/2.68 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13462])).
% 2.44/2.68 tff(13468,plain,
% 2.44/2.68 ((s(elem!1) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13467])).
% 2.44/2.68 tff(13469,plain,
% 2.44/2.68 ((s(elem!1) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[13468, 5661])).
% 2.44/2.68 tff(13470,plain,
% 2.44/2.68 ((~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))) <=> (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13469])).
% 2.44/2.68 tff(13471,plain,
% 2.44/2.68 (~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[3814, 13460])).
% 2.44/2.68 tff(13472,plain,
% 2.44/2.68 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13471, 13470])).
% 2.44/2.68 tff(13473,plain,
% 2.44/2.68 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2857, 13472, 1633, 13435, 13433])).
% 2.44/2.68 tff(13474,plain,
% 2.44/2.68 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2863, 13473])).
% 2.44/2.68 tff(13475,plain,
% 2.44/2.68 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13474, 13466])).
% 2.44/2.68 tff(13476,plain,
% 2.44/2.68 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13464])).
% 2.44/2.68 tff(13477,plain,
% 2.44/2.68 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13476])).
% 2.44/2.68 tff(13478,plain,
% 2.44/2.68 (r(elem!1, s(s(elem!1)))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13445, 13477])).
% 2.44/2.68 tff(13479,plain,
% 2.44/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(13480,plain,
% 2.44/2.68 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(13481,plain,
% 2.44/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13480])).
% 2.44/2.68 tff(13482,plain,
% 2.44/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[13481, 13479])).
% 2.44/2.68 tff(13483,plain,
% 2.44/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(13484,plain,
% 2.44/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13483, 13482])).
% 2.44/2.68 tff(13485,plain,
% 2.44/2.68 ((~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13484, 268, 13478])).
% 2.44/2.68 tff(13486,plain,
% 2.44/2.68 (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13485, 13475])).
% 2.44/2.68 tff(13487,plain,
% 2.44/2.68 (b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[5649, 13486, 13461])).
% 2.44/2.68 tff(13488,plain,
% 2.44/2.68 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(z))) <=> (s(s(s(s(s(s(s(s(z)))))))) = elem!1)),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13460])).
% 2.44/2.68 tff(13489,plain,
% 2.44/2.68 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(z))) <=> (elem!1 = s(s(s(s(s(s(s(s(z)))))))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[13488, 6008])).
% 2.44/2.68 tff(13490,plain,
% 2.44/2.68 ((~(s(s(s(s(s(s(s(s(z)))))))) = s(s(z)))) <=> (~(elem!1 = s(s(s(s(s(s(s(s(z))))))))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13489])).
% 2.44/2.68 tff(13491,plain,
% 2.44/2.68 (~(elem!1 = s(s(s(s(s(s(s(s(z)))))))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[12032, 13490])).
% 2.44/2.68 tff(13492,plain,
% 2.44/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(13493,plain,
% 2.44/2.68 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(13494,plain,
% 2.44/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13493])).
% 2.44/2.68 tff(13495,plain,
% 2.44/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[13494, 13492])).
% 2.44/2.68 tff(13496,plain,
% 2.44/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(13497,plain,
% 2.44/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13496, 13495])).
% 2.44/2.68 tff(13498,plain,
% 2.44/2.68 ((~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13497, 268, 13478])).
% 2.44/2.68 tff(13499,plain,
% 2.44/2.68 (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13498, 13475])).
% 2.44/2.68 tff(13500,plain,
% 2.44/2.68 (b(elem!1, s(s(s(s(s(s(s(s(z)))))))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[11518, 13499, 13491])).
% 2.44/2.68 tff(13501,plain,
% 2.44/2.68 (~b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[12047, 453, 9870, 13500, 13487])).
% 2.44/2.68 tff(13502,plain,
% 2.44/2.68 (~r(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[9968, 13472, 1132, 13435, 3448])).
% 2.44/2.68 tff(13503,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2906, 69, 13502, 2886, 13501])).
% 2.44/2.68 tff(13504,plain,(b(s(s(s(z))), s(z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (elem!1 = s(s(s(s(z))))) | r(elem!1, s(z)) | r(s(z), elem!1) | (elem!1 = s(z)) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(13505,plain,
% 2.44/2.68 (b(s(s(s(z))), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[13504, 2076, 1099, 1159, 1055, 13425, 4541, 1123, 1200, 2])).
% 2.44/2.68 tff(13506,plain,
% 2.44/2.68 (~b(s(s(s(z))), elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[12223, 13505, 4541, 4495, 2076])).
% 2.44/2.68 tff(13507,plain,
% 2.44/2.68 (s(s(s(z))) = elem!1),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[74, 13506, 2])).
% 2.44/2.68 tff(13508,plain,
% 2.44/2.68 (s(elem!1) = s(s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[81, 13507])).
% 2.44/2.68 tff(13509,plain,
% 2.44/2.68 (~(s(z) = s(elem!1))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[171, 13508])).
% 2.44/2.68 tff(13510,plain,
% 2.44/2.68 (~(s(elem!1) = s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[179, 13509])).
% 2.44/2.68 tff(13511,plain,
% 2.44/2.68 (~(s(s(s(elem!1))) = elem!1)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[199, 13510, 13507])).
% 2.44/2.68 tff(13512,plain,
% 2.44/2.68 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13508])).
% 2.44/2.68 tff(13513,plain,
% 2.44/2.68 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13512])).
% 2.44/2.68 tff(13514,plain,
% 2.44/2.68 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13513])).
% 2.44/2.68 tff(13515,plain,
% 2.44/2.68 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13514, 13508])).
% 2.44/2.68 tff(13516,plain,
% 2.44/2.68 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13515])).
% 2.44/2.68 tff(13517,plain,
% 2.44/2.68 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(s(z)))))) = s(elem!1)))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13516])).
% 2.44/2.68 tff(13518,plain,
% 2.44/2.68 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[6514, 13517])).
% 2.44/2.68 tff(13519,plain,
% 2.44/2.68 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13512, 13508])).
% 2.44/2.68 tff(13520,plain,
% 2.44/2.68 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(elem!1))),
% 2.44/2.68 inference(symmetry,[status(thm)],[13519])).
% 2.44/2.68 tff(13521,plain,
% 2.44/2.68 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13507])).
% 2.44/2.68 tff(13522,plain,
% 2.44/2.68 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[13521, 55])).
% 2.44/2.68 tff(13523,plain,
% 2.44/2.68 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.44/2.68 inference(transitivity,[status(thm)],[13522, 56])).
% 2.44/2.68 tff(13524,plain,
% 2.44/2.68 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13523])).
% 2.44/2.68 tff(13525,plain,
% 2.44/2.68 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[111, 13524])).
% 2.44/2.68 tff(13526,plain,
% 2.44/2.68 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[11146, 13525, 13408, 1099, 9870, 1159])).
% 2.44/2.68 tff(13527,plain,
% 2.44/2.68 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[328, 13526])).
% 2.44/2.68 tff(13528,plain,
% 2.44/2.68 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13527, 13520])).
% 2.44/2.68 tff(13529,plain,
% 2.44/2.68 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13512])).
% 2.44/2.68 tff(13530,plain,
% 2.44/2.68 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.44/2.68 inference(symmetry,[status(thm)],[13529])).
% 2.44/2.68 tff(13531,plain,
% 2.44/2.68 (~b(s(elem!1), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1062, 13508, 1057])).
% 2.44/2.68 tff(13532,plain,
% 2.44/2.68 (r(s(elem!1), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[353, 13531, 13510])).
% 2.44/2.68 tff(13533,plain,
% 2.44/2.68 ((s(s(s(z))) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13507])).
% 2.44/2.68 tff(13534,plain,
% 2.44/2.68 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 2.44/2.68 inference(transitivity,[status(thm)],[13533, 2170])).
% 2.44/2.68 tff(13535,plain,
% 2.44/2.68 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13534])).
% 2.44/2.68 tff(13536,plain,
% 2.44/2.68 (~(s(s(elem!1)) = elem!1)),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[4877, 13535])).
% 2.44/2.68 tff(13537,plain,
% 2.44/2.68 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13507])).
% 2.44/2.68 tff(13538,plain,
% 2.44/2.68 (b(elem!1, s(s(s(s(z)))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[13425, 13537])).
% 2.44/2.68 tff(13539,plain,
% 2.44/2.68 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2459, 268, 1132, 3699])).
% 2.44/2.68 tff(13540,plain,
% 2.44/2.68 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[10556, 13539])).
% 2.44/2.68 tff(13541,plain,
% 2.44/2.68 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[11146, 6930, 2077, 1132, 499, 1159])).
% 2.44/2.68 tff(13542,plain,
% 2.44/2.68 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[328, 13541])).
% 2.44/2.68 tff(13543,plain,
% 2.44/2.68 (elem!1 = s(s(s(z)))),
% 2.44/2.68 inference(symmetry,[status(thm)],[76])).
% 2.44/2.68 tff(13544,plain,
% 2.44/2.68 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(z))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13543])).
% 2.44/2.68 tff(13545,plain,
% 2.44/2.68 ((s(s(z)) = elem!1) <=> (s(s(s(z))) = s(s(z)))),
% 2.44/2.68 inference(transitivity,[status(thm)],[13544, 486])).
% 2.44/2.68 tff(13546,plain,
% 2.44/2.68 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.44/2.68 inference(symmetry,[status(thm)],[13545])).
% 2.44/2.68 tff(13547,plain,
% 2.44/2.68 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[13546])).
% 2.44/2.68 tff(13548,plain,
% 2.44/2.68 (~(s(s(z)) = elem!1)),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[160, 13547])).
% 2.44/2.68 tff(13549,plain,
% 2.44/2.68 (~(s(s(z)) = s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1188, 180])).
% 2.44/2.69 tff(13550,plain,
% 2.44/2.69 (~b(s(s(elem!1)), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1053, 278, 162])).
% 2.44/2.69 tff(13551,plain,
% 2.44/2.69 (r(s(s(elem!1)), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1047, 13550])).
% 2.44/2.69 tff(13552,plain,
% 2.44/2.69 (b(s(s(elem!1)), s(elem!1))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13542, 236])).
% 2.44/2.69 tff(13553,plain,
% 2.44/2.69 (r(s(elem!1), elem!1)),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[1159, 231])).
% 2.44/2.69 tff(13554,plain,
% 2.44/2.69 (~r(s(elem!1), s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[435, 13539, 76])).
% 2.44/2.69 tff(13555,plain,
% 2.44/2.69 (b(s(elem!1), s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[440, 13554, 411])).
% 2.44/2.69 tff(13556,plain,
% 2.44/2.69 (r(s(s(s(s(s(s(z)))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[1886])).
% 2.44/2.69 tff(13557,plain,
% 2.44/2.69 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(s(z)))))), s(z))),
% 2.44/2.69 inference(symmetry,[status(thm)],[13556])).
% 2.44/2.69 tff(13558,plain,
% 2.44/2.69 (b(s(s(s(s(s(s(z)))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[1886])).
% 2.44/2.69 tff(13559,plain,
% 2.44/2.69 ((~b(s(s(s(s(s(s(z)))))), s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13558])).
% 2.44/2.69 tff(13560,plain,
% 2.44/2.69 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.44/2.69 inference(monotonicity,[status(thm)],[570])).
% 2.44/2.69 tff(13561,plain,
% 2.44/2.69 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.44/2.69 inference(symmetry,[status(thm)],[13560])).
% 2.44/2.69 tff(13562,plain,
% 2.44/2.69 ((~r(s(s(s(s(s(s(z)))))), elem!1)) <=> (~r(s(s(s(elem!1))), elem!1))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13561])).
% 2.44/2.69 tff(13563,plain,
% 2.44/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(13564,plain,
% 2.44/2.69 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(13565,plain,
% 2.44/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13564])).
% 2.44/2.69 tff(13566,plain,
% 2.44/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[13565, 13563])).
% 2.44/2.69 tff(13567,plain,
% 2.44/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(13568,plain,
% 2.44/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13567, 13566])).
% 2.44/2.69 tff(13569,plain,
% 2.44/2.69 (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[13568, 268, 1033, 869, 997])).
% 2.44/2.69 tff(13570,plain,
% 2.44/2.69 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6572, 69, 13569])).
% 2.44/2.69 tff(13571,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[13570, 6562, 6546])).
% 2.44/2.69 tff(13572,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~(s(s(s(z))) = elem!1)) | (s(s(s(s(s(s(z)))))) = s(elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(13573,plain,
% 2.44/2.69 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[13572, 1033, 6555, 76, 955, 910, 869, 340, 1892])).
% 2.44/2.69 tff(13574,plain,
% 2.44/2.69 (~r(s(s(s(elem!1))), elem!1)),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13573, 13562])).
% 2.44/2.69 tff(13575,plain,
% 2.44/2.69 (b(s(s(s(elem!1))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[567, 13574, 7974])).
% 2.44/2.69 tff(13576,plain,
% 2.44/2.69 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[576, 13575, 76])).
% 2.44/2.69 tff(13577,plain,
% 2.44/2.69 (~r(s(z), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[3393, 1033, 869])).
% 2.44/2.69 tff(13578,plain,
% 2.44/2.69 (b(s(z), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[506, 13577, 246])).
% 2.44/2.69 tff(13579,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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(13580,plain,
% 2.44/2.69 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(13581,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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13580])).
% 2.44/2.69 tff(13582,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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.44/2.69 inference(transitivity,[status(thm)],[13581, 13579])).
% 2.44/2.69 tff(13583,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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(13584,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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13583, 13582])).
% 2.44/2.69 tff(13585,plain,
% 2.44/2.69 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[13584, 453, 13578, 2077, 13576])).
% 2.44/2.69 tff(13586,plain,
% 2.44/2.69 (~b(s(s(s(elem!1))), s(z))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13585, 13559])).
% 2.44/2.69 tff(13587,plain,
% 2.44/2.69 (r(s(s(s(elem!1))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[856, 13586])).
% 2.44/2.69 tff(13588,plain,
% 2.44/2.69 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13587, 13557])).
% 2.44/2.69 tff(13589,plain,
% 2.44/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(13590,plain,
% 2.44/2.69 (((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(13591,plain,
% 2.44/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(z)))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13590])).
% 2.44/2.69 tff(13592,plain,
% 2.44/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[13591, 13589])).
% 2.44/2.69 tff(13593,plain,
% 2.44/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(13594,plain,
% 2.44/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13593, 13592])).
% 2.44/2.69 tff(13595,plain,
% 2.44/2.69 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[13594, 268, 340, 13588])).
% 2.44/2.69 tff(13596,plain,
% 2.44/2.69 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[1903, 69, 955, 13595])).
% 2.44/2.69 tff(13597,plain,
% 2.44/2.69 (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6561, 453, 910, 6555, 13596])).
% 2.44/2.69 tff(13598,plain,
% 2.44/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(13599,plain,
% 2.44/2.69 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(13600,plain,
% 2.44/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13599])).
% 2.44/2.69 tff(13601,plain,
% 2.44/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[13600, 13598])).
% 2.44/2.69 tff(13602,plain,
% 2.44/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(13603,plain,
% 2.44/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13602, 13601])).
% 2.44/2.69 tff(13604,plain,
% 2.44/2.69 (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[13603, 268, 1033, 13588])).
% 2.44/2.69 tff(13605,plain,
% 2.44/2.69 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6572, 69, 13604])).
% 2.44/2.69 tff(13606,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[13605, 13597, 6546])).
% 2.44/2.69 tff(13607,plain,((~r(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~(s(s(s(z))) = elem!1)) | (s(s(s(s(s(s(z)))))) = s(elem!1)) | (~r(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (s(s(s(elem!1))) = elem!1) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(13608,plain,
% 2.44/2.69 (~r(s(s(elem!1)), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[13607, 13555, 76, 340, 13553, 13552, 2077, 200, 13551, 955])).
% 2.44/2.69 tff(13609,plain,
% 2.44/2.69 (b(s(s(elem!1)), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[2240, 13608, 5181])).
% 2.44/2.69 tff(13610,plain,
% 2.44/2.69 (~b(s(s(z)), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[12401, 13609, 2077, 13549, 499])).
% 2.44/2.69 tff(13611,plain,
% 2.44/2.69 (r(s(s(z)), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[782, 13610, 13548])).
% 2.44/2.69 tff(13612,plain,
% 2.44/2.69 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6602, 13611, 1159, 1132, 13540, 13542])).
% 2.44/2.69 tff(13613,plain,
% 2.44/2.69 (b(s(s(s(s(s(z))))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[643, 13612, 6930])).
% 2.44/2.69 tff(13614,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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(13615,plain,
% 2.44/2.69 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(13616,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(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13615])).
% 2.44/2.69 tff(13617,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(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.44/2.69 inference(transitivity,[status(thm)],[13616, 13614])).
% 2.44/2.69 tff(13618,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(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(13619,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13618, 13617])).
% 2.44/2.69 tff(13620,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[13619, 453, 13613, 13542, 530, 13540])).
% 2.44/2.69 tff(13621,plain,(b(s(s(s(s(s(z))))), s(z)) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (s(s(elem!1)) = elem!1) | (~(s(s(s(z))) = elem!1)) | (~r(s(elem!1), s(z))) | (s(s(s(s(s(s(z)))))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(13622,plain,
% 2.44/2.69 (b(s(s(s(s(s(z))))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[13621, 13538, 1159, 1099, 13408, 9870, 13536, 13507, 13532, 13518])).
% 2.44/2.69 tff(13623,plain,
% 2.44/2.69 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[5331, 13622, 13408, 9870])).
% 2.44/2.69 tff(13624,plain,
% 2.44/2.69 (r(s(s(s(s(s(z))))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[643, 13623, 13525])).
% 2.44/2.69 tff(13625,plain,
% 2.44/2.69 (r(s(s(elem!1)), elem!1)),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[13624, 13530])).
% 2.44/2.69 tff(13626,plain,
% 2.44/2.69 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13508])).
% 2.44/2.69 tff(13627,plain,
% 2.44/2.69 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.44/2.69 inference(symmetry,[status(thm)],[13626])).
% 2.44/2.69 tff(13628,plain,
% 2.44/2.69 (r(s(elem!1), elem!1)),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[1159, 13627])).
% 2.44/2.69 tff(13629,plain,
% 2.44/2.69 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13508])).
% 2.44/2.69 tff(13630,plain,
% 2.44/2.69 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[13629, 403])).
% 2.44/2.69 tff(13631,plain,
% 2.44/2.69 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(elem!1)))),
% 2.44/2.69 inference(symmetry,[status(thm)],[13630])).
% 2.44/2.69 tff(13632,plain,
% 2.44/2.69 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13512])).
% 2.44/2.69 tff(13633,plain,
% 2.44/2.69 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 2.44/2.69 inference(symmetry,[status(thm)],[13632])).
% 2.44/2.69 tff(13634,plain,
% 2.44/2.69 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(elem!1)))),
% 2.44/2.69 inference(transitivity,[status(thm)],[13633, 13631])).
% 2.44/2.69 tff(13635,plain,
% 2.44/2.69 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13634])).
% 2.44/2.69 tff(13636,plain,
% 2.44/2.69 (~(s(elem!1) = s(s(elem!1)))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[319, 13635])).
% 2.44/2.69 tff(13637,plain,
% 2.44/2.69 (~r(s(elem!1), s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[11373, 13625, 13628])).
% 2.44/2.69 tff(13638,plain,
% 2.44/2.69 (b(s(elem!1), s(s(elem!1)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[440, 13637, 13636])).
% 2.44/2.69 tff(13639,plain,
% 2.44/2.69 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6575, 13638, 13507, 13532, 13628, 13625, 13528, 13518])).
% 2.44/2.69 tff(13640,plain,
% 2.44/2.69 (~r(s(s(s(elem!1))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[992, 13639, 13508])).
% 2.44/2.69 tff(13641,plain,
% 2.44/2.69 (b(s(s(s(elem!1))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[567, 13640, 13511])).
% 2.44/2.69 tff(13642,plain,
% 2.44/2.69 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[576, 13641, 13507])).
% 2.44/2.69 tff(13643,plain,
% 2.44/2.69 (elem!1 = s(s(s(z)))),
% 2.44/2.69 inference(symmetry,[status(thm)],[13507])).
% 2.44/2.69 tff(13644,plain,
% 2.44/2.69 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(z))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13643])).
% 2.44/2.69 tff(13645,plain,
% 2.44/2.69 ((s(s(z)) = elem!1) <=> (s(s(s(z))) = s(s(z)))),
% 2.44/2.69 inference(transitivity,[status(thm)],[13644, 486])).
% 2.44/2.69 tff(13646,plain,
% 2.44/2.69 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.44/2.69 inference(symmetry,[status(thm)],[13645])).
% 2.44/2.69 tff(13647,plain,
% 2.44/2.69 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13646])).
% 2.44/2.69 tff(13648,plain,
% 2.44/2.69 (~(s(s(z)) = elem!1)),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[160, 13647])).
% 2.44/2.69 tff(13649,plain,
% 2.44/2.69 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[4516, 268, 13624, 1159])).
% 2.44/2.69 tff(13650,plain,
% 2.44/2.69 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[10556, 13649])).
% 2.44/2.69 tff(13651,plain,
% 2.44/2.69 (~r(s(s(z)), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6602, 13650, 1159, 1099, 13624, 13527])).
% 2.44/2.69 tff(13652,plain,
% 2.44/2.69 (b(s(s(z)), elem!1)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[782, 13651, 13648])).
% 2.44/2.69 tff(13653,plain,
% 2.44/2.69 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6610, 453, 13408, 13652, 13642])).
% 2.44/2.69 tff(13654,plain,
% 2.44/2.69 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[822, 69, 2661, 13653])).
% 2.44/2.69 tff(13655,plain,
% 2.44/2.69 (~b(s(s(z)), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[5570, 453, 9870, 13408, 13652])).
% 2.44/2.69 tff(13656,plain,
% 2.44/2.69 (r(s(s(z)), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[720, 69, 717, 13655])).
% 2.44/2.69 tff(13657,plain,
% 2.44/2.69 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(s(z)))))), s(z))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[13513])).
% 2.44/2.69 tff(13658,plain,
% 2.44/2.69 (b(s(z), s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[12981, 13505, 4541, 1057, 4495])).
% 2.44/2.69 tff(13659,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))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)))),
% 2.44/2.70 inference(rewrite,[status(thm)],[])).
% 2.44/2.70 tff(13660,plain,
% 2.44/2.70 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)))),
% 2.44/2.70 inference(rewrite,[status(thm)],[])).
% 2.44/2.70 tff(13661,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), 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))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1))))),
% 2.44/2.70 inference(monotonicity,[status(thm)],[13660])).
% 2.44/2.70 tff(13662,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), 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))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)))),
% 2.54/2.70 inference(transitivity,[status(thm)],[13661, 13659])).
% 2.54/2.70 tff(13663,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(13664,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[13663, 13662])).
% 2.54/2.70 tff(13665,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[13664, 453, 499, 2077, 1110, 572])).
% 2.54/2.70 tff(13666,plain,((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(13667,plain,
% 2.54/2.70 (~b(s(s(s(elem!1))), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[13666, 499, 1110, 2077])).
% 2.54/2.70 tff(13668,plain,
% 2.54/2.70 (~(s(elem!1) = s(z))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[6831, 13667, 2])).
% 2.54/2.70 tff(13669,plain,
% 2.54/2.70 (s(s(s(elem!1))) = elem!1),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[567, 13667, 563])).
% 2.54/2.70 tff(13670,plain,
% 2.54/2.70 (~(s(s(s(z))) = elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[199, 13669, 13668])).
% 2.54/2.70 tff(13671,plain,
% 2.54/2.70 (b(s(s(s(z))), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[74, 13670, 2])).
% 2.54/2.70 tff(13672,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[5511, 453, 499, 2077, 13671, 2090])).
% 2.54/2.70 tff(13673,plain,((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | r(s(s(s(z))), elem!1) | r(s(s(s(elem!1))), elem!1) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(13674,plain,
% 2.54/2.70 (~b(s(s(s(elem!1))), s(z))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[13673, 13640, 2, 13408, 13658, 9870])).
% 2.54/2.70 tff(13675,plain,
% 2.54/2.70 (r(s(s(s(elem!1))), s(z))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[856, 13674])).
% 2.54/2.70 tff(13676,plain,
% 2.54/2.70 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[13675, 13657])).
% 2.54/2.70 tff(13677,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(13678,plain,
% 2.54/2.70 (((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(13679,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[13678])).
% 2.54/2.70 tff(13680,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.54/2.70 inference(transitivity,[status(thm)],[13679, 13677])).
% 2.54/2.70 tff(13681,plain,
% 2.54/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(13682,plain,
% 2.54/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[13681, 13680])).
% 2.54/2.70 tff(13683,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[13682, 268, 13676, 13656, 13654])).
% 2.54/2.70 tff(13684,plain,(r(elem!1, s(z)) | r(s(s(s(z))), elem!1) | (~r(s(s(s(s(z)))), elem!1)) | b(s(s(s(s(z)))), s(z)) | r(s(z), elem!1) | (elem!1 = s(s(s(s(z))))) | (elem!1 = s(z)) | r(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(13685,plain,
% 2.54/2.70 (r(elem!1, s(z))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[13684, 8453, 2, 1057, 4541, 9, 1123, 1200])).
% 2.54/2.70 tff(13686,plain,
% 2.54/2.70 (~r(elem!1, s(s(s(s(z)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[12993, 13685, 1099])).
% 2.54/2.70 tff(13687,plain,
% 2.54/2.70 (b(elem!1, s(s(s(s(z)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1087, 13686, 9])).
% 2.54/2.70 tff(13688,plain,
% 2.54/2.70 (~(s(s(s(z))) = elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2080, 128, 2077])).
% 2.54/2.70 tff(13689,plain,
% 2.54/2.70 (b(s(s(s(z))), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[74, 13688, 2])).
% 2.54/2.70 tff(13690,plain,
% 2.54/2.70 (~(elem!1 = s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[4487, 13688])).
% 2.54/2.70 tff(13691,plain,
% 2.54/2.70 (b(elem!1, s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[4492, 13690, 1200])).
% 2.54/2.70 tff(13692,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[8173, 13691, 13689, 1132, 1055, 238, 3448])).
% 2.54/2.70 tff(13693,plain,(b(s(s(s(z))), s(z)) | (~r(s(s(s(s(z)))), s(z))) | (elem!1 = s(s(s(s(z))))) | (~r(elem!1, s(z))) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(13694,plain,
% 2.54/2.70 (b(s(s(s(z))), s(z))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[13693, 9, 1099, 13685, 1200, 2, 13408])).
% 2.54/2.70 tff(13695,plain,
% 2.54/2.70 (~b(s(s(s(z))), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[7149, 13694, 9870, 13687])).
% 2.54/2.70 tff(13696,plain,
% 2.54/2.70 (s(s(s(z))) = elem!1),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[74, 13695, 2])).
% 2.54/2.70 tff(13697,plain,
% 2.54/2.70 (r(s(s(s(z))), s(z))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[6652, 13696, 13685])).
% 2.54/2.70 tff(13698,plain,
% 2.54/2.70 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[4123, 13696, 249])).
% 2.54/2.70 tff(13699,plain,
% 2.54/2.70 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[518, 13698])).
% 2.54/2.70 tff(13700,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[4119, 13699, 13697, 1099])).
% 2.54/2.70 tff(13701,plain,((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(z))), elem!1) | r(elem!1, s(s(s(z)))) | b(s(s(s(s(z)))), s(z)) | r(s(z), elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(13702,plain,
% 2.54/2.70 (b(s(s(s(s(z)))), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[13701, 1123, 2, 13423, 1057, 4541, 1200])).
% 2.54/2.70 tff(13703,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[9834, 13691, 13435, 299, 13689])).
% 2.54/2.70 tff(13704,plain,(b(s(s(s(z))), s(z)) | (~b(s(s(s(s(z)))), elem!1)) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1) | (~r(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(13705,plain,
% 2.54/2.70 (b(s(s(s(z))), s(z))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[13704, 13702, 1200, 2, 1099, 13408])).
% 2.54/2.70 tff(13706,plain,
% 2.54/2.70 (b(s(z), s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[12981, 13705, 4541, 1057, 4495])).
% 2.54/2.70 tff(13707,plain,
% 2.54/2.70 (~b(elem!1, s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[10307, 13705, 9870, 13706])).
% 2.54/2.70 tff(13708,plain,
% 2.54/2.70 (elem!1 = s(s(s(z)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[4492, 13707, 1200])).
% 2.54/2.70 tff(13709,plain,
% 2.54/2.70 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[13708])).
% 2.54/2.70 tff(13710,plain,
% 2.54/2.70 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[13702, 13709])).
% 2.54/2.70 tff(13711,plain,
% 2.54/2.70 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(z))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[13708])).
% 2.54/2.70 tff(13712,plain,
% 2.54/2.70 (~b(s(s(z)), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[5574, 13702, 13408, 9870, 1099])).
% 2.54/2.70 tff(13713,plain,
% 2.54/2.70 (~b(s(z), s(s(s(s(z)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[5260, 13702, 13408, 9870])).
% 2.54/2.70 tff(13714,plain,
% 2.54/2.70 (~b(s(s(s(z))), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[5513, 13706, 13408, 9870])).
% 2.54/2.70 tff(13715,plain,
% 2.54/2.70 (s(s(s(z))) = elem!1),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[74, 13714, 2])).
% 2.54/2.70 tff(13716,plain,
% 2.54/2.70 (s(elem!1) = s(s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[81, 13715])).
% 2.54/2.70 tff(13717,plain,
% 2.54/2.70 (~b(s(z), s(elem!1))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1758, 13716, 13713])).
% 2.54/2.70 tff(13718,plain,
% 2.54/2.70 (~(s(s(z)) = elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[3644, 13717, 13706])).
% 2.54/2.70 tff(13719,plain,
% 2.54/2.70 (r(s(s(z)), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[782, 13718, 13712])).
% 2.54/2.70 tff(13720,plain,
% 2.54/2.70 (r(s(s(z)), s(s(s(z))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[13719, 13711])).
% 2.54/2.70 tff(13721,plain,
% 2.54/2.70 (~(s(z) = s(elem!1))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[171, 13716])).
% 2.54/2.70 tff(13722,plain,
% 2.54/2.70 (~(s(elem!1) = s(z))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[179, 13721])).
% 2.54/2.70 tff(13723,plain,
% 2.54/2.70 (~(s(s(s(elem!1))) = elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[199, 13722, 13715])).
% 2.54/2.70 tff(13724,plain,
% 2.54/2.70 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[13716])).
% 2.54/2.70 tff(13725,plain,
% 2.54/2.70 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[13724])).
% 2.54/2.70 tff(13726,plain,
% 2.54/2.70 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 2.54/2.70 inference(symmetry,[status(thm)],[13725])).
% 2.54/2.70 tff(13727,plain,
% 2.54/2.70 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[13726, 13716])).
% 2.54/2.70 tff(13728,plain,
% 2.54/2.70 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 2.54/2.70 inference(symmetry,[status(thm)],[13727])).
% 2.54/2.70 tff(13729,plain,
% 2.54/2.70 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(s(z)))))) = s(elem!1)))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[13728])).
% 2.54/2.70 tff(13730,plain,
% 2.54/2.70 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[6514, 13729])).
% 2.54/2.70 tff(13731,plain,
% 2.54/2.70 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[13708])).
% 2.54/2.70 tff(13732,plain,
% 2.54/2.70 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.54/2.70 inference(symmetry,[status(thm)],[13731])).
% 2.54/2.70 tff(13733,plain,
% 2.54/2.70 (b(elem!1, s(s(s(s(z)))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[13425, 13732])).
% 2.54/2.70 tff(13734,plain,
% 2.54/2.70 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2213, 13733, 1099, 13702, 13716, 13730, 9870])).
% 2.54/2.70 tff(13735,plain,
% 2.54/2.70 (~b(s(s(s(elem!1))), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[576, 13734, 13715])).
% 2.54/2.70 tff(13736,plain,
% 2.54/2.70 (r(s(s(s(elem!1))), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[567, 13735, 13723])).
% 2.54/2.70 tff(13737,plain,
% 2.54/2.70 (~b(s(elem!1), s(z))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[1062, 13716, 1057])).
% 2.54/2.70 tff(13738,plain,
% 2.54/2.70 (~(s(elem!1) = elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[11941, 13737, 13408])).
% 2.54/2.70 tff(13739,plain,
% 2.54/2.70 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[607, 13738])).
% 2.54/2.70 tff(13740,plain,
% 2.54/2.70 (r(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.70 inference(monotonicity,[status(thm)],[4485])).
% 2.54/2.70 tff(13741,plain,
% 2.54/2.70 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.54/2.70 inference(symmetry,[status(thm)],[13740])).
% 2.54/2.70 tff(13742,plain,
% 2.54/2.70 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[992, 833, 166])).
% 2.54/2.70 tff(13743,plain,
% 2.54/2.70 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[13742, 13741])).
% 2.54/2.70 tff(13744,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(13745,plain,
% 2.54/2.70 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(13746,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[13745])).
% 2.54/2.70 tff(13747,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.54/2.70 inference(transitivity,[status(thm)],[13746, 13744])).
% 2.54/2.70 tff(13748,plain,
% 2.54/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(13749,plain,
% 2.54/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[13748, 13747])).
% 2.54/2.70 tff(13750,plain,
% 2.54/2.70 ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[13749, 268, 2580])).
% 2.54/2.70 tff(13751,plain,
% 2.54/2.70 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[13750, 13743])).
% 2.54/2.70 tff(13752,plain,
% 2.54/2.70 ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[10818, 69, 13751])).
% 2.54/2.70 tff(13753,plain,
% 2.54/2.70 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[13752, 10808])).
% 2.54/2.70 tff(13754,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(13755,plain,
% 2.54/2.70 (((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(13756,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[13755])).
% 2.54/2.70 tff(13757,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.54/2.70 inference(transitivity,[status(thm)],[13756, 13754])).
% 2.54/2.70 tff(13758,plain,
% 2.54/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(13759,plain,
% 2.54/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[13758, 13757])).
% 2.54/2.70 tff(13760,plain,
% 2.54/2.70 ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[13759, 268, 2580])).
% 2.54/2.70 tff(13761,plain,
% 2.54/2.70 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[13760, 13743])).
% 2.54/2.70 tff(13762,plain,
% 2.54/2.70 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[822, 69, 2661, 13761])).
% 2.54/2.70 tff(13763,plain,
% 2.54/2.70 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2975, 268, 256, 2580])).
% 2.54/2.70 tff(13764,plain,
% 2.54/2.70 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[4081, 13763])).
% 2.54/2.70 tff(13765,plain,
% 2.54/2.70 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[610, 4484])).
% 2.54/2.70 tff(13766,plain,
% 2.54/2.70 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(elem!1)), elem!1)),
% 2.54/2.70 inference(symmetry,[status(thm)],[13765])).
% 2.54/2.70 tff(13767,plain,
% 2.54/2.70 (r(s(s(elem!1)), elem!1)),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[256, 13766])).
% 2.54/2.70 tff(13768,plain,
% 2.54/2.70 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[877, 13767, 833])).
% 2.54/2.70 tff(13769,plain,
% 2.54/2.70 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[675, 13768, 617])).
% 2.54/2.70 tff(13770,plain,
% 2.54/2.70 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[13769, 616])).
% 2.54/2.70 tff(13771,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)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(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(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(13772,plain,
% 2.54/2.70 (((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(13773,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(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[13772])).
% 2.54/2.70 tff(13774,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(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.54/2.70 inference(transitivity,[status(thm)],[13773, 13771])).
% 2.54/2.70 tff(13775,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(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(13776,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[13775, 13774])).
% 2.54/2.70 tff(13777,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[13776, 453, 13770, 13764, 13762, 13753])).
% 2.54/2.70 tff(13778,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(13779,plain,
% 2.54/2.70 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[13778, 13716, 13739, 13736, 13720, 13708])).
% 2.54/2.71 tff(13780,plain,
% 2.54/2.71 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[687, 13779])).
% 2.54/2.71 tff(13781,plain,
% 2.54/2.71 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1788, 13780, 13425, 13710])).
% 2.54/2.71 tff(13782,plain,
% 2.54/2.71 (r(s(z), s(elem!1))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[397, 13717, 13721])).
% 2.54/2.71 tff(13783,plain,
% 2.54/2.71 (r(s(z), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[392, 13782, 13715])).
% 2.54/2.71 tff(13784,plain,
% 2.54/2.71 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[5380, 13780, 13705, 13783])).
% 2.54/2.71 tff(13785,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[328, 13784, 13781])).
% 2.54/2.71 tff(13786,plain,((elem!1 = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(z))), elem!1) | r(elem!1, s(s(s(z)))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(13787,plain,
% 2.54/2.71 (r(elem!1, s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[13786, 1057, 13415, 2, 4541])).
% 2.54/2.71 tff(13788,plain,
% 2.54/2.71 (b(s(z), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12253, 13787, 4541, 13423])).
% 2.54/2.71 tff(13789,plain,
% 2.54/2.71 (~b(s(s(s(z))), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[5513, 13788, 13408, 13417])).
% 2.54/2.71 tff(13790,plain,
% 2.54/2.71 (s(s(s(z))) = elem!1),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[74, 13789, 2])).
% 2.54/2.71 tff(13791,plain,
% 2.54/2.71 (r(elem!1, s(s(s(z)))) <=> r(elem!1, elem!1)),
% 2.54/2.71 inference(monotonicity,[status(thm)],[13790])).
% 2.54/2.71 tff(13792,plain,
% 2.54/2.71 (r(elem!1, elem!1) <=> r(elem!1, s(s(s(z))))),
% 2.54/2.71 inference(symmetry,[status(thm)],[13791])).
% 2.54/2.71 tff(13793,plain,
% 2.54/2.71 ((~r(elem!1, elem!1)) <=> (~r(elem!1, s(s(s(z)))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[13792])).
% 2.54/2.71 tff(13794,plain,
% 2.54/2.71 (~r(elem!1, s(s(s(z))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[6751, 13793])).
% 2.54/2.71 tff(13795,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[13787, 13794])).
% 2.54/2.71 tff(13796,plain,(b(s(s(s(s(z)))), s(z)) | r(s(s(s(z))), elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(13797,plain,
% 2.54/2.71 (b(s(s(s(s(z)))), s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[13796, 2, 4541])).
% 2.54/2.71 tff(13798,plain,
% 2.54/2.71 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(z)))))) = s(elem!1))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[531])).
% 2.54/2.71 tff(13799,plain,
% 2.54/2.71 ((s(s(s(s(s(s(z)))))) = s(elem!1)) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 2.54/2.71 inference(symmetry,[status(thm)],[13798])).
% 2.54/2.71 tff(13800,plain,
% 2.54/2.71 ((~(s(s(s(s(s(s(z)))))) = s(elem!1))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[13799])).
% 2.54/2.71 tff(13801,plain,
% 2.54/2.71 (~(elem!1 = s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[13414, 2077])).
% 2.54/2.71 tff(13802,plain,
% 2.54/2.71 (~(s(z) = elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1125, 13801])).
% 2.54/2.71 tff(13803,plain,
% 2.54/2.71 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[547, 13802])).
% 2.54/2.71 tff(13804,plain,
% 2.54/2.71 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[557, 13803])).
% 2.54/2.71 tff(13805,plain,
% 2.54/2.71 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[13804, 540])).
% 2.54/2.71 tff(13806,plain,
% 2.54/2.71 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[13805, 13800])).
% 2.54/2.71 tff(13807,plain,
% 2.54/2.71 (b(s(z), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12720, 76, 2077])).
% 2.54/2.71 tff(13808,plain,
% 2.54/2.71 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[3782, 12715, 1764, 13807])).
% 2.54/2.71 tff(13809,plain,
% 2.54/2.71 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[518, 13808])).
% 2.54/2.71 tff(13810,plain,
% 2.54/2.71 (r(s(s(s(s(z)))), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[512, 13809, 162])).
% 2.54/2.71 tff(13811,plain,
% 2.54/2.71 (~b(elem!1, s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[11887, 1764, 2077, 499])).
% 2.54/2.71 tff(13812,plain,
% 2.54/2.71 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[136, 3609])).
% 2.54/2.71 tff(13813,plain,
% 2.54/2.71 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[13812])).
% 2.54/2.71 tff(13814,plain,
% 2.54/2.71 (~(elem!1 = s(s(s(s(z)))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[142, 13813])).
% 2.54/2.71 tff(13815,plain,
% 2.54/2.71 (r(elem!1, s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1087, 13814, 13811])).
% 2.54/2.71 tff(13816,plain,
% 2.54/2.71 (~b(elem!1, s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[10307, 12715, 499, 13807])).
% 2.54/2.71 tff(13817,plain,
% 2.54/2.71 (elem!1 = s(s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[4492, 13816, 1200])).
% 2.54/2.71 tff(13818,plain,
% 2.54/2.71 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(z))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[4484])).
% 2.54/2.71 tff(13819,plain,
% 2.54/2.71 ((s(s(z)) = elem!1) <=> (s(s(s(z))) = s(s(z)))),
% 2.54/2.71 inference(transitivity,[status(thm)],[13818, 486])).
% 2.54/2.71 tff(13820,plain,
% 2.54/2.71 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.54/2.71 inference(symmetry,[status(thm)],[13819])).
% 2.54/2.71 tff(13821,plain,
% 2.54/2.71 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[13820])).
% 2.54/2.71 tff(13822,plain,
% 2.54/2.71 (~(s(s(z)) = elem!1)),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[160, 13821])).
% 2.54/2.71 tff(13823,plain,
% 2.54/2.71 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(z))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[4484])).
% 2.54/2.71 tff(13824,plain,
% 2.54/2.71 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), elem!1)),
% 2.54/2.71 inference(symmetry,[status(thm)],[13823])).
% 2.54/2.71 tff(13825,plain,
% 2.54/2.71 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(s(z)), elem!1))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[13824])).
% 2.54/2.71 tff(13826,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[9159, 453, 1008, 120, 2090, 2957])).
% 2.54/2.71 tff(13827,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(13828,plain,
% 2.54/2.71 (~b(s(s(z)), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[13827, 1008, 120, 2090])).
% 2.54/2.71 tff(13829,plain,
% 2.54/2.71 (~b(s(s(z)), elem!1)),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[13828, 13825])).
% 2.54/2.71 tff(13830,plain,
% 2.54/2.71 (r(s(s(z)), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[782, 13829, 13822])).
% 2.54/2.71 tff(13831,plain,
% 2.54/2.71 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[6942, 13830, 419])).
% 2.54/2.71 tff(13832,plain,
% 2.54/2.71 (b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2370, 69, 13831, 2359])).
% 2.54/2.71 tff(13833,plain,
% 2.54/2.71 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[4297, 13830, 1159])).
% 2.54/2.71 tff(13834,plain,
% 2.54/2.71 (b(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[4293, 13833])).
% 2.54/2.71 tff(13835,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(s(z)))), s(s(z)))) | (~b(s(s(z)), s(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(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(13836,plain,
% 2.54/2.71 (((~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(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(13837,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)), s(s(s(s(z)))))) | (~b(s(s(z)), s(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(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[13836])).
% 2.54/2.71 tff(13838,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)), s(s(s(s(z)))))) | (~b(s(s(z)), s(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(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[13837, 13835])).
% 2.54/2.71 tff(13839,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)), s(s(s(s(z)))))) | (~b(s(s(z)), s(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))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(13840,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[13839, 13838])).
% 2.54/2.71 tff(13841,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[13840, 453, 1764, 1008, 13834, 13832])).
% 2.54/2.71 tff(13842,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~(elem!1 = s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(13843,plain,
% 2.54/2.71 (~b(s(z), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[13842, 13815, 13817, 13810, 1764, 12715, 13807])).
% 2.54/2.71 tff(13844,plain,
% 2.54/2.71 (r(s(z), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[757, 13843])).
% 2.54/2.71 tff(13845,plain,
% 2.54/2.71 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[408])).
% 2.54/2.71 tff(13846,plain,
% 2.54/2.71 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[319, 13845])).
% 2.54/2.71 tff(13847,plain,
% 2.54/2.71 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.71 inference(symmetry,[status(thm)],[8192])).
% 2.54/2.71 tff(13848,plain,
% 2.54/2.71 ((~b(elem!1, s(s(s(s(z)))))) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[13847])).
% 2.54/2.71 tff(13849,plain,
% 2.54/2.71 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[13811, 13848])).
% 2.54/2.71 tff(13850,plain,
% 2.54/2.71 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1656, 13849])).
% 2.54/2.71 tff(13851,plain,
% 2.54/2.71 (b(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[4457, 5541, 76])).
% 2.54/2.71 tff(13852,plain,
% 2.54/2.71 (~b(s(s(s(s(s(z))))), s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[5331, 13851, 2077, 499])).
% 2.54/2.71 tff(13853,plain,
% 2.54/2.71 (r(s(s(s(s(s(z))))), s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[297, 13852])).
% 2.54/2.71 tff(13854,plain,
% 2.54/2.71 (~r(s(z), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[5380, 5541, 12715, 301])).
% 2.54/2.71 tff(13855,plain,
% 2.54/2.71 (~r(s(z), s(elem!1))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[392, 13854, 76])).
% 2.54/2.71 tff(13856,plain,
% 2.54/2.71 (b(s(z), s(elem!1))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[397, 13855, 172])).
% 2.54/2.71 tff(13857,plain,
% 2.54/2.71 (b(s(z), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1758, 13856, 162])).
% 2.54/2.71 tff(13858,plain,
% 2.54/2.71 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[4817, 13857, 162, 12715, 13853, 2218, 5541])).
% 2.54/2.71 tff(13859,plain,
% 2.54/2.71 (~b(s(s(s(elem!1))), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[4409, 13858, 162])).
% 2.54/2.71 tff(13860,plain,
% 2.54/2.71 (r(s(s(s(elem!1))), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[567, 13859, 200])).
% 2.54/2.71 tff(13861,plain,
% 2.54/2.71 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[992, 13860, 162])).
% 2.54/2.71 tff(13862,plain,
% 2.54/2.71 (b(s(s(elem!1)), elem!1)),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[13851, 900])).
% 2.54/2.71 tff(13863,plain,
% 2.54/2.71 (~b(s(s(z)), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12401, 13862, 2077, 13549, 499])).
% 2.54/2.71 tff(13864,plain,
% 2.54/2.71 (r(s(s(z)), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[782, 13863, 13548])).
% 2.54/2.71 tff(13865,plain,
% 2.54/2.71 (~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[13805, 537])).
% 2.54/2.71 tff(13866,plain,
% 2.54/2.71 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[4419, 268, 1159, 13861])).
% 2.54/2.71 tff(13867,plain,
% 2.54/2.71 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[591, 69, 13866])).
% 2.54/2.71 tff(13868,plain,
% 2.54/2.71 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[13867, 13865])).
% 2.54/2.71 tff(13869,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(13870,plain,
% 2.54/2.71 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(13871,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[13870])).
% 2.54/2.71 tff(13872,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[13871, 13869])).
% 2.54/2.71 tff(13873,plain,
% 2.54/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(13874,plain,
% 2.54/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[13873, 13872])).
% 2.54/2.71 tff(13875,plain,
% 2.54/2.71 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[13874, 268, 1159, 13861])).
% 2.54/2.71 tff(13876,plain,
% 2.54/2.71 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2210, 69, 13875])).
% 2.54/2.71 tff(13877,plain,
% 2.54/2.71 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[13876, 13806])).
% 2.54/2.71 tff(13878,plain,
% 2.54/2.71 ((~r(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[6902, 2661])).
% 2.54/2.71 tff(13879,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[13878, 13877, 13868, 1159, 13864, 13861])).
% 2.54/2.71 tff(13880,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~(s(s(s(z))) = elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(13881,plain,
% 2.54/2.71 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[13880, 13810, 2077, 499, 76, 13850])).
% 2.54/2.71 tff(13882,plain,
% 2.54/2.71 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[328, 13881])).
% 2.54/2.71 tff(13883,plain,
% 2.54/2.71 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2476, 12079, 733])).
% 2.54/2.71 tff(13884,plain,
% 2.54/2.71 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[4081, 13883])).
% 2.54/2.71 tff(13885,plain,
% 2.54/2.71 (~(s(elem!1) = s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[179, 1741])).
% 2.54/2.71 tff(13886,plain,
% 2.54/2.71 (~(s(s(z)) = s(s(elem!1)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1188, 13885])).
% 2.54/2.71 tff(13887,plain,
% 2.54/2.71 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.71 inference(monotonicity,[status(thm)],[610])).
% 2.54/2.71 tff(13888,plain,
% 2.54/2.71 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.54/2.71 inference(symmetry,[status(thm)],[13887])).
% 2.54/2.71 tff(13889,plain,
% 2.54/2.71 (b(s(s(elem!1)), elem!1)),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[646, 13888])).
% 2.54/2.71 tff(13890,plain,
% 2.54/2.71 (~b(s(s(z)), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[12401, 13889, 2077, 13886, 499])).
% 2.54/2.71 tff(13891,plain,
% 2.54/2.71 (r(s(s(z)), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[782, 13890, 4060])).
% 2.54/2.71 tff(13892,plain,
% 2.54/2.71 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[6942, 13891, 419])).
% 2.54/2.71 tff(13893,plain,
% 2.54/2.71 (b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2370, 69, 13892, 2359])).
% 2.54/2.71 tff(13894,plain,
% 2.54/2.71 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[4297, 13891, 1159])).
% 2.54/2.71 tff(13895,plain,
% 2.54/2.71 (b(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[4293, 13894])).
% 2.54/2.71 tff(13896,plain,
% 2.54/2.71 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(13897,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(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[13896])).
% 2.54/2.71 tff(13898,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(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[13897, 2984])).
% 2.54/2.71 tff(13899,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(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(13900,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[13899, 13898])).
% 2.54/2.71 tff(13901,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[13900, 453, 1780, 13895, 13893, 13884])).
% 2.54/2.71 tff(13902,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (s(s(z)) = elem!1) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(13903,plain,
% 2.54/2.71 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[13902, 13882, 13815, 13810, 13548, 2077, 499, 162, 13844])).
% 2.54/2.71 tff(13904,plain,
% 2.54/2.71 (r(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[643, 13903, 6930])).
% 2.54/2.71 tff(13905,plain,
% 2.54/2.71 (r(s(s(elem!1)), elem!1)),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[13904, 866])).
% 2.54/2.71 tff(13906,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), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), 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(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(13907,plain,
% 2.54/2.71 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(13908,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[13907])).
% 2.54/2.71 tff(13909,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[13908, 13906])).
% 2.54/2.71 tff(13910,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), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(13911,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[13910, 13909])).
% 2.54/2.71 tff(13912,plain,
% 2.54/2.71 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[13911, 453, 499, 1050, 1764])).
% 2.54/2.71 tff(13913,plain,
% 2.54/2.71 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[5232, 69, 5806, 13912])).
% 2.54/2.71 tff(13914,plain,
% 2.54/2.71 (~b(s(s(s(s(z)))), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[11898, 453, 499, 2077, 1764])).
% 2.54/2.71 tff(13915,plain,
% 2.54/2.71 (r(s(s(s(s(z)))), elem!1)),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[252, 69, 3, 13914])).
% 2.54/2.71 tff(13916,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[10920, 268, 869, 13915, 13913])).
% 2.54/2.71 tff(13917,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(13918,plain,
% 2.54/2.71 (~b(s(s(elem!1)), s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[13917, 13905, 2077, 1764, 143, 499, 13846])).
% 2.54/2.71 tff(13919,plain,
% 2.54/2.71 (r(s(s(elem!1)), s(z))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1047, 13918])).
% 2.54/2.71 tff(13920,plain,
% 2.54/2.71 (r(s(s(s(s(s(z))))), s(z))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[13919, 4553])).
% 2.54/2.71 tff(13921,plain,
% 2.54/2.71 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2476, 13920, 13844])).
% 2.54/2.71 tff(13922,plain,
% 2.54/2.71 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[4081, 13921])).
% 2.54/2.71 tff(13923,plain,
% 2.54/2.71 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[4516, 268, 13904, 13810])).
% 2.54/2.71 tff(13924,plain,
% 2.54/2.71 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[10556, 13923])).
% 2.54/2.71 tff(13925,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(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(13926,plain,
% 2.54/2.71 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(13927,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)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[13926])).
% 2.54/2.71 tff(13928,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)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[13927, 13925])).
% 2.54/2.72 tff(13929,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(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(13930,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[13929, 13928])).
% 2.54/2.72 tff(13931,plain,
% 2.54/2.72 ($false),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[13930, 453, 1780, 2497, 8417, 12107, 2494])).
% 2.54/2.72 tff(13932,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.72 tff(13933,plain,
% 2.54/2.72 (~r(s(s(z)), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[13932, 13882, 13924, 13922, 13815, 13810])).
% 2.54/2.72 tff(13934,plain,
% 2.54/2.72 (b(s(s(z)), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[782, 13933, 13548])).
% 2.54/2.72 tff(13935,plain,
% 2.54/2.72 (~b(s(s(s(elem!1))), s(z))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[13673, 563, 2, 2077, 13807, 499])).
% 2.54/2.72 tff(13936,plain,
% 2.54/2.72 (r(s(s(s(elem!1))), s(z))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[856, 13935])).
% 2.54/2.72 tff(13937,plain,
% 2.54/2.72 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[13936, 4561])).
% 2.54/2.72 tff(13938,plain,
% 2.54/2.72 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[13682, 268, 13937, 5572])).
% 2.54/2.72 tff(13939,plain,
% 2.54/2.72 (b(s(s(s(elem!1))), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[567, 563, 200])).
% 2.54/2.72 tff(13940,plain,
% 2.54/2.72 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[576, 13939, 76])).
% 2.54/2.72 tff(13941,plain,
% 2.54/2.72 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[6610, 453, 2077, 922, 13940])).
% 2.54/2.72 tff(13942,plain,
% 2.54/2.72 ($false),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[822, 69, 2661, 13941, 13938])).
% 2.54/2.72 tff(13943,plain,(r(s(s(s(elem!1))), elem!1) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~(s(s(s(z))) = elem!1)) | r(s(s(s(z))), elem!1) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.72 tff(13944,plain,
% 2.54/2.72 (r(s(s(s(elem!1))), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[13943, 13934, 2077, 76, 2, 499])).
% 2.54/2.72 tff(13945,plain,
% 2.54/2.72 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[992, 13944, 162])).
% 2.54/2.72 tff(13946,plain,
% 2.54/2.72 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[13874, 268, 13810, 13945])).
% 2.54/2.72 tff(13947,plain,
% 2.54/2.72 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[2210, 69, 13946])).
% 2.54/2.72 tff(13948,plain,
% 2.54/2.72 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[13947, 13806])).
% 2.54/2.72 tff(13949,plain,
% 2.54/2.72 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[4419, 268, 13810, 13945])).
% 2.54/2.72 tff(13950,plain,
% 2.54/2.72 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[591, 69, 13949])).
% 2.54/2.72 tff(13951,plain,
% 2.54/2.72 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[13950, 13865])).
% 2.54/2.72 tff(13952,plain,
% 2.54/2.72 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[877, 13944, 13905])).
% 2.54/2.72 tff(13953,plain,
% 2.54/2.72 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[675, 13952, 2218])).
% 2.54/2.72 tff(13954,plain,
% 2.54/2.72 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[13953, 864])).
% 2.54/2.72 tff(13955,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(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(13956,plain,
% 2.54/2.72 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(13957,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(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[13956])).
% 2.54/2.72 tff(13958,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(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[13957, 13955])).
% 2.54/2.72 tff(13959,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(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(13960,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[13959, 13958])).
% 2.54/2.72 tff(13961,plain,
% 2.54/2.72 ($false),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[13960, 453, 13924, 13954, 13951, 13948])).
% 2.54/2.72 tff(13962,plain,((~(s(s(s(z))) = elem!1)) | (~b(elem!1, s(z))) | r(s(s(s(z))), elem!1) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | r(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.72 tff(13963,plain,
% 2.54/2.72 (~(s(s(s(z))) = elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[13962, 1200, 2, 13417, 13797, 13408])).
% 2.54/2.72 tff(13964,plain,
% 2.54/2.72 (b(s(s(s(z))), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[74, 13963, 2])).
% 2.54/2.72 tff(13965,plain,
% 2.54/2.72 (~b(s(z), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[5513, 13964, 13408, 13417])).
% 2.54/2.72 tff(13966,plain,
% 2.54/2.72 (r(s(z), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[227, 13965])).
% 2.54/2.72 tff(13967,plain,
% 2.54/2.72 (~b(elem!1, s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[11887, 13797, 13408, 13417])).
% 2.54/2.72 tff(13968,plain,
% 2.54/2.72 (~(elem!1 = s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[4487, 13963])).
% 2.54/2.72 tff(13969,plain,
% 2.54/2.72 (b(elem!1, s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[4492, 13968, 1200])).
% 2.54/2.72 tff(13970,plain,
% 2.54/2.72 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[5])).
% 2.54/2.72 tff(13971,plain,
% 2.54/2.72 (~b(s(z), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[5513, 1291, 2077, 499])).
% 2.54/2.72 tff(13972,plain,
% 2.54/2.72 (r(s(z), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[227, 13971])).
% 2.54/2.72 tff(13973,plain,
% 2.54/2.72 (~b(s(z), s(s(z)))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[6633, 453, 499, 2077, 922])).
% 2.54/2.72 tff(13974,plain,
% 2.54/2.72 (r(s(z), s(s(z)))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[757, 13973])).
% 2.54/2.72 tff(13975,plain,
% 2.54/2.72 (r(s(s(s(z))), s(s(z)))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[12870, 7325])).
% 2.54/2.72 tff(13976,plain,
% 2.54/2.72 ($false),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[9038, 13975, 13974, 13972])).
% 2.54/2.72 tff(13977,plain,((~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.72 tff(13978,plain,
% 2.54/2.72 (~b(s(s(z)), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[13977, 1291, 2077, 499])).
% 2.54/2.72 tff(13979,plain,
% 2.54/2.72 (s(s(s(s(z)))) = elem!1),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[8, 5])).
% 2.54/2.72 tff(13980,plain,
% 2.54/2.72 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[12577, 13979, 2077, 499, 1291, 13972])).
% 2.54/2.72 tff(13981,plain,
% 2.54/2.72 (~b(s(elem!1), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[7006, 13980, 13979])).
% 2.54/2.72 tff(13982,plain,
% 2.54/2.72 (~(s(elem!1) = s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[9377, 13981, 1291])).
% 2.54/2.72 tff(13983,plain,
% 2.54/2.72 (~(s(s(z)) = elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[9447, 13982])).
% 2.54/2.72 tff(13984,plain,
% 2.54/2.72 (r(s(s(z)), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[782, 13983, 13978])).
% 2.54/2.72 tff(13985,plain,
% 2.54/2.72 (r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[13984, 13970])).
% 2.54/2.72 tff(13986,plain,
% 2.54/2.72 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[4108, 13979])).
% 2.54/2.72 tff(13987,plain,
% 2.54/2.72 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[13986])).
% 2.54/2.72 tff(13988,plain,
% 2.54/2.72 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 2.54/2.72 inference(symmetry,[status(thm)],[13987])).
% 2.54/2.72 tff(13989,plain,
% 2.54/2.72 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[13988])).
% 2.54/2.72 tff(13990,plain,
% 2.54/2.72 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[13989])).
% 2.54/2.72 tff(13991,plain,
% 2.54/2.72 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[5])).
% 2.54/2.72 tff(13992,plain,
% 2.54/2.72 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[13991, 13990])).
% 2.54/2.72 tff(13993,plain,
% 2.54/2.72 (~(s(s(s(elem!1))) = elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[1215, 13979, 13803])).
% 2.54/2.72 tff(13994,plain,
% 2.54/2.72 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[5])).
% 2.54/2.72 tff(13995,plain,
% 2.54/2.72 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[1291, 13994])).
% 2.54/2.72 tff(13996,plain,
% 2.54/2.72 (~b(s(s(s(z))), s(z))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[5465, 1275, 499, 1291])).
% 2.54/2.72 tff(13997,plain,
% 2.54/2.72 (r(s(s(s(z))), s(z))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[134, 13996])).
% 2.54/2.72 tff(13998,plain,
% 2.54/2.72 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[5])).
% 2.54/2.72 tff(13999,plain,
% 2.54/2.72 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[1275, 13998])).
% 2.54/2.72 tff(14000,plain,
% 2.54/2.72 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[13989, 5])).
% 2.54/2.72 tff(14001,plain,
% 2.54/2.72 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[572, 14000])).
% 2.54/2.72 tff(14002,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14003,plain,
% 2.54/2.72 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14004,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[14003])).
% 2.54/2.72 tff(14005,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[14004, 14002])).
% 2.54/2.72 tff(14006,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(14007,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[14006, 14005])).
% 2.54/2.72 tff(14008,plain,
% 2.54/2.72 (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[14007, 453, 523, 1633, 14001])).
% 2.54/2.72 tff(14009,plain,
% 2.54/2.72 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[13989])).
% 2.54/2.72 tff(14010,plain,
% 2.54/2.72 (~b(s(s(s(elem!1))), s(z))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[13666, 572, 2077, 499])).
% 2.54/2.72 tff(14011,plain,
% 2.54/2.72 (r(s(s(s(elem!1))), s(z))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[856, 14010])).
% 2.54/2.72 tff(14012,plain,
% 2.54/2.72 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[14011, 14009])).
% 2.54/2.72 tff(14013,plain,
% 2.54/2.72 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[7971, 268, 233, 14012])).
% 2.54/2.72 tff(14014,plain,
% 2.54/2.72 ($false),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[12845, 14013, 14008])).
% 2.54/2.72 tff(14015,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.72 tff(14016,plain,
% 2.54/2.72 (~b(s(s(s(elem!1))), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[14015, 13999, 13997, 13995, 5, 2077, 499])).
% 2.54/2.72 tff(14017,plain,
% 2.54/2.72 (r(s(s(s(elem!1))), elem!1)),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[567, 14016, 13993])).
% 2.54/2.72 tff(14018,plain,
% 2.54/2.72 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[14017, 13992])).
% 2.54/2.72 tff(14019,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14020,plain,
% 2.54/2.72 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14021,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[14020])).
% 2.54/2.72 tff(14022,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[14021, 14019])).
% 2.54/2.72 tff(14023,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(14024,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[14023, 14022])).
% 2.54/2.72 tff(14025,plain,
% 2.54/2.72 (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[14024, 268, 14018, 13985])).
% 2.54/2.72 tff(14026,plain,
% 2.54/2.72 (~(s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[8571, 13986])).
% 2.54/2.72 tff(14027,plain,
% 2.54/2.72 (b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[8583, 69, 14026, 14025])).
% 2.54/2.72 tff(14028,plain,
% 2.54/2.72 (s(elem!1) = s(s(s(s(s(z)))))),
% 2.54/2.72 inference(symmetry,[status(thm)],[13986])).
% 2.54/2.72 tff(14029,plain,
% 2.54/2.72 ((s(s(z)) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[14028])).
% 2.54/2.72 tff(14030,plain,
% 2.54/2.72 ((s(s(z)) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.54/2.72 inference(transitivity,[status(thm)],[14029, 4133])).
% 2.54/2.72 tff(14031,plain,
% 2.54/2.72 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = s(elem!1))),
% 2.54/2.72 inference(symmetry,[status(thm)],[14030])).
% 2.54/2.72 tff(14032,plain,
% 2.54/2.72 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = s(elem!1)))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[14031])).
% 2.54/2.72 tff(14033,plain,
% 2.54/2.72 (~(s(s(z)) = s(elem!1))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[52, 14032])).
% 2.54/2.72 tff(14034,plain,
% 2.54/2.72 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[501, 13971, 499])).
% 2.54/2.72 tff(14035,plain,
% 2.54/2.72 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[5])).
% 2.54/2.72 tff(14036,plain,
% 2.54/2.72 ((~b(s(elem!1), elem!1)) <=> (~b(s(elem!1), s(s(s(s(z))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[14035])).
% 2.54/2.72 tff(14037,plain,
% 2.54/2.72 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[13981, 14036])).
% 2.54/2.72 tff(14038,plain,
% 2.54/2.72 (r(s(elem!1), s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[9382, 14037, 14034])).
% 2.54/2.72 tff(14039,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14040,plain,
% 2.54/2.72 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(14041,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1)))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[14040])).
% 2.54/2.72 tff(14042,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[14041, 14039])).
% 2.54/2.72 tff(14043,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(14044,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(z)), s(elem!1)))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14043, 14042])).
% 2.54/2.73 tff(14045,plain,
% 2.54/2.73 (~r(s(s(z)), s(elem!1))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14044, 268, 14038, 13985])).
% 2.54/2.73 tff(14046,plain,
% 2.54/2.73 ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[4261, 69, 14045])).
% 2.54/2.73 tff(14047,plain,
% 2.54/2.73 (b(s(s(z)), s(elem!1))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14046, 14033])).
% 2.54/2.73 tff(14048,plain,
% 2.54/2.73 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1273, 13979])).
% 2.54/2.73 tff(14049,plain,
% 2.54/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14050,plain,
% 2.54/2.73 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14051,plain,
% 2.54/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[14050])).
% 2.54/2.73 tff(14052,plain,
% 2.54/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.54/2.73 inference(transitivity,[status(thm)],[14051, 14049])).
% 2.54/2.73 tff(14053,plain,
% 2.54/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(14054,plain,
% 2.54/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14053, 14052])).
% 2.54/2.73 tff(14055,plain,
% 2.54/2.73 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14054, 268, 14038, 14018])).
% 2.54/2.73 tff(14056,plain,
% 2.54/2.73 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[3999, 14055, 14048])).
% 2.54/2.73 tff(14057,plain,
% 2.54/2.73 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1436, 14048])).
% 2.54/2.73 tff(14058,plain,
% 2.54/2.73 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[13220, 268, 14038, 14018])).
% 2.54/2.73 tff(14059,plain,
% 2.54/2.73 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1320, 14058, 14057])).
% 2.54/2.73 tff(14060,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(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(s(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(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14061,plain,
% 2.54/2.73 (((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14062,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(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[14061])).
% 2.54/2.73 tff(14063,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(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.54/2.73 inference(transitivity,[status(thm)],[14062, 14060])).
% 2.54/2.73 tff(14064,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(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(z)), s(elem!1))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(14065,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14064, 14063])).
% 2.54/2.73 tff(14066,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14065, 453, 14059, 14056, 14047, 14027])).
% 2.54/2.73 tff(14067,plain,((~(elem!1 = s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(14068,plain,
% 2.54/2.73 (~(elem!1 = s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14067, 13969, 13417, 13408, 13964])).
% 2.54/2.73 tff(14069,plain,
% 2.54/2.73 (r(elem!1, s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1087, 14068, 13967])).
% 2.54/2.73 tff(14070,plain,
% 2.54/2.73 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[3483])).
% 2.54/2.73 tff(14071,plain,
% 2.54/2.73 (~(s(s(s(s(z)))) = elem!1)),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14068, 14070])).
% 2.54/2.73 tff(14072,plain,
% 2.54/2.73 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[9485, 14071])).
% 2.54/2.73 tff(14073,plain,
% 2.54/2.73 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[4499, 14072])).
% 2.54/2.73 tff(14074,plain,
% 2.54/2.73 (s(s(s(s(s(z))))) = elem!1),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8839, 5529])).
% 2.54/2.73 tff(14075,plain,
% 2.54/2.73 (~(s(elem!1) = s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[5852, 14074])).
% 2.54/2.73 tff(14076,plain,
% 2.54/2.73 (~b(s(z), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[5513, 1291, 13408, 13417])).
% 2.54/2.73 tff(14077,plain,
% 2.54/2.73 (r(s(z), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[227, 14076])).
% 2.54/2.73 tff(14078,plain,
% 2.54/2.73 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[5529])).
% 2.54/2.73 tff(14079,plain,
% 2.54/2.73 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[1291, 14078])).
% 2.54/2.73 tff(14080,plain,
% 2.54/2.73 (~b(s(s(s(z))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[5465, 1275, 13417, 1291])).
% 2.54/2.73 tff(14081,plain,
% 2.54/2.73 (r(s(s(s(z))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[134, 14080])).
% 2.54/2.73 tff(14082,plain,
% 2.54/2.73 (r(elem!1, s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11061, 14074, 14077, 14081, 59])).
% 2.54/2.73 tff(14083,plain,
% 2.54/2.73 (~r(s(z), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[5592, 14074, 4541])).
% 2.54/2.73 tff(14084,plain,
% 2.54/2.73 (b(s(z), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[372, 14083])).
% 2.54/2.73 tff(14085,plain,
% 2.54/2.73 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[501, 14076, 13417])).
% 2.54/2.73 tff(14086,plain,
% 2.54/2.73 (~b(elem!1, s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[11887, 1764, 13408, 13417])).
% 2.54/2.73 tff(14087,plain,
% 2.54/2.73 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[13015, 14074, 14086])).
% 2.54/2.73 tff(14088,plain,
% 2.54/2.73 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[328, 14087])).
% 2.54/2.73 tff(14089,plain,
% 2.54/2.73 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[5786])).
% 2.54/2.73 tff(14090,plain,
% 2.54/2.73 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.54/2.73 inference(symmetry,[status(thm)],[14089])).
% 2.54/2.73 tff(14091,plain,
% 2.54/2.73 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(s(s(z))))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[14090])).
% 2.54/2.73 tff(14092,plain,
% 2.54/2.73 (~r(s(elem!1), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[9570, 1892, 238])).
% 2.54/2.73 tff(14093,plain,
% 2.54/2.73 (b(s(elem!1), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[353, 14092, 197])).
% 2.54/2.73 tff(14094,plain,
% 2.54/2.73 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14093, 10734])).
% 2.54/2.73 tff(14095,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(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14096,plain,
% 2.54/2.73 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14097,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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[14096])).
% 2.54/2.73 tff(14098,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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.73 inference(transitivity,[status(thm)],[14097, 14095])).
% 2.54/2.73 tff(14099,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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(14100,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14099, 14098])).
% 2.54/2.73 tff(14101,plain,
% 2.54/2.73 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14100, 453, 443, 1764, 14094])).
% 2.54/2.73 tff(14102,plain,
% 2.54/2.73 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14101, 14091])).
% 2.54/2.73 tff(14103,plain,
% 2.54/2.73 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(symmetry,[status(thm)],[10767])).
% 2.54/2.73 tff(14104,plain,
% 2.54/2.73 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[10773, 1892, 5529])).
% 2.54/2.73 tff(14105,plain,
% 2.54/2.73 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14104, 14103])).
% 2.54/2.73 tff(14106,plain,
% 2.54/2.73 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[10607, 14105, 301])).
% 2.54/2.73 tff(14107,plain,
% 2.54/2.73 (b(s(elem!1), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[9382, 14106, 79])).
% 2.54/2.73 tff(14108,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14107, 14102])).
% 2.54/2.73 tff(14109,plain,((~r(s(elem!1), elem!1)) | (~(elem!1 = s(s(s(s(s(z))))))) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (s(elem!1) = s(z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(14110,plain,
% 2.54/2.73 (~r(s(elem!1), elem!1)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14109, 14088, 1764, 5529, 14085, 14084, 14075, 14082])).
% 2.54/2.73 tff(14111,plain,
% 2.54/2.73 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[5529])).
% 2.54/2.73 tff(14112,plain,
% 2.54/2.73 ((s(elem!1) = elem!1) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 2.54/2.73 inference(transitivity,[status(thm)],[14111, 623])).
% 2.54/2.73 tff(14113,plain,
% 2.54/2.73 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 2.54/2.73 inference(symmetry,[status(thm)],[14112])).
% 2.54/2.73 tff(14114,plain,
% 2.54/2.73 ((~(s(s(s(s(s(z))))) = s(elem!1))) <=> (~(s(elem!1) = elem!1))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[14113])).
% 2.54/2.73 tff(14115,plain,
% 2.54/2.73 (~(s(elem!1) = elem!1)),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[4106, 14114])).
% 2.54/2.73 tff(14116,plain,
% 2.54/2.73 (b(s(elem!1), elem!1)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[2440, 14115, 14110])).
% 2.54/2.73 tff(14117,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[12771, 14116, 14079, 14077, 5529, 14075, 1275, 13417])).
% 2.54/2.73 tff(14118,plain,((~(elem!1 = s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (s(s(s(s(s(z))))) = s(elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (s(s(s(z))) = elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(14119,plain,
% 2.54/2.73 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14118, 14073, 13964, 13969, 13797, 13963, 4541])).
% 2.54/2.73 tff(14120,plain,
% 2.54/2.73 (~b(s(s(z)), elem!1)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[13977, 13964, 13408, 13417])).
% 2.54/2.73 tff(14121,plain,
% 2.54/2.73 (~b(s(s(s(s(z)))), elem!1)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[5423, 13969, 13417, 13797])).
% 2.54/2.73 tff(14122,plain,
% 2.54/2.73 (r(s(s(s(s(z)))), elem!1)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[254, 14071, 14121])).
% 2.54/2.73 tff(14123,plain,
% 2.54/2.73 (~b(s(s(s(z))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[5465, 1275, 499, 4165])).
% 2.54/2.73 tff(14124,plain,
% 2.54/2.73 (r(s(s(s(z))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[134, 14123])).
% 2.54/2.73 tff(14125,plain,
% 2.54/2.73 (~b(s(z), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[5513, 4165, 2077, 499])).
% 2.54/2.73 tff(14126,plain,
% 2.54/2.73 (r(s(z), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[227, 14125])).
% 2.54/2.73 tff(14127,plain,
% 2.54/2.73 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[3478])).
% 2.54/2.73 tff(14128,plain,
% 2.54/2.73 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 2.54/2.73 inference(symmetry,[status(thm)],[14127])).
% 2.54/2.73 tff(14129,plain,
% 2.54/2.73 (s(elem!1) = s(s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[9447, 3468])).
% 2.54/2.73 tff(14130,plain,
% 2.54/2.73 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[9847, 14129])).
% 2.54/2.73 tff(14131,plain,
% 2.54/2.73 (~(s(z) = s(elem!1))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[9855, 14130])).
% 2.54/2.73 tff(14132,plain,
% 2.54/2.73 (b(s(elem!1), elem!1)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[9377, 14129, 1291])).
% 2.54/2.73 tff(14133,plain,
% 2.54/2.73 (~b(s(z), s(elem!1))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[3403, 14132, 2077, 499])).
% 2.54/2.73 tff(14134,plain,
% 2.54/2.73 (r(s(z), s(elem!1))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[397, 14133, 14131])).
% 2.54/2.73 tff(14135,plain,
% 2.54/2.73 (r(s(s(s(s(z)))), s(elem!1))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[11, 3756])).
% 2.54/2.73 tff(14136,plain,
% 2.54/2.73 (r(s(s(elem!1)), s(elem!1))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14135, 3755])).
% 2.54/2.73 tff(14137,plain,
% 2.54/2.73 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(elem!1)))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[3477])).
% 2.54/2.73 tff(14138,plain,
% 2.54/2.73 (~r(s(z), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1692, 268, 11, 13972])).
% 2.54/2.73 tff(14139,plain,
% 2.54/2.73 (b(s(z), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1677, 69, 14138, 50])).
% 2.54/2.73 tff(14140,plain,
% 2.54/2.73 (b(s(z), s(s(elem!1)))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14139, 14137])).
% 2.54/2.73 tff(14141,plain,
% 2.54/2.73 (r(s(z), s(s(s(z)))) <=> r(s(z), s(elem!1))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[3469])).
% 2.54/2.73 tff(14142,plain,
% 2.54/2.73 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(z))))),
% 2.54/2.73 inference(symmetry,[status(thm)],[14141])).
% 2.54/2.73 tff(14143,plain,
% 2.54/2.73 (r(s(z), s(s(s(z))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[388, 14142])).
% 2.54/2.73 tff(14144,plain,
% 2.54/2.73 (~r(s(s(s(s(s(z))))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[276, 256, 14143])).
% 2.54/2.73 tff(14145,plain,
% 2.54/2.73 (b(s(s(s(s(s(z))))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[297, 14144])).
% 2.54/2.73 tff(14146,plain,
% 2.54/2.73 (r(s(s(s(s(s(z))))), s(elem!1))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[256, 3770])).
% 2.54/2.73 tff(14147,plain,
% 2.54/2.73 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
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% 2.54/2.73 tff(14148,plain,
% 2.54/2.73 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14147, 3729])).
% 2.54/2.73 tff(14149,plain,
% 2.54/2.73 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[675, 14148, 3544])).
% 2.54/2.73 tff(14150,plain,
% 2.54/2.73 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14149, 3545])).
% 2.54/2.73 tff(14151,plain,
% 2.54/2.73 (~r(s(z), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[4029, 268, 388, 14146])).
% 2.54/2.73 tff(14152,plain,
% 2.54/2.73 (b(s(z), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[372, 14151])).
% 2.54/2.73 tff(14153,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(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14154,plain,
% 2.54/2.73 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14155,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(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[14154])).
% 2.54/2.73 tff(14156,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(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.73 inference(transitivity,[status(thm)],[14155, 14153])).
% 2.54/2.73 tff(14157,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(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(elem!1)))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(14158,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14157, 14156])).
% 2.54/2.73 tff(14159,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14158, 453, 14152, 14150, 14145, 3692])).
% 2.54/2.73 tff(14160,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~(s(s(z)) = elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(14161,plain,
% 2.54/2.73 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[14160, 14140, 3468, 14136, 14134])).
% 2.54/2.73 tff(14162,plain,
% 2.54/2.73 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[687, 14161])).
% 2.54/2.73 tff(14163,plain,
% 2.54/2.73 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[14162, 3553])).
% 2.54/2.73 tff(14164,plain,
% 2.54/2.73 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[3515])).
% 2.54/2.73 tff(14165,plain,
% 2.54/2.73 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 2.54/2.73 inference(symmetry,[status(thm)],[14164])).
% 2.54/2.73 tff(14166,plain,
% 2.54/2.73 (b(elem!1, s(elem!1))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[1275, 14165])).
% 2.54/2.73 tff(14167,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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14168,plain,
% 2.54/2.73 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(14169,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[14168])).
% 2.54/2.73 tff(14170,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[14169, 14167])).
% 2.54/2.74 tff(14171,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(14172,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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[14171, 14170])).
% 2.54/2.74 tff(14173,plain,
% 2.54/2.74 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14172, 453, 14132, 14166, 14163])).
% 2.54/2.74 tff(14174,plain,
% 2.54/2.74 (r(elem!1, s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[466, 14173, 3592])).
% 2.54/2.74 tff(14175,plain,
% 2.54/2.74 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[427, 14174, 419])).
% 2.54/2.74 tff(14176,plain,
% 2.54/2.74 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[10556, 14175])).
% 2.54/2.74 tff(14177,plain,
% 2.54/2.74 (~b(s(z), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[4526, 14176, 1764, 14162])).
% 2.54/2.74 tff(14178,plain,
% 2.54/2.74 (r(s(z), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[372, 14177])).
% 2.54/2.74 tff(14179,plain,
% 2.54/2.74 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[3477])).
% 2.54/2.74 tff(14180,plain,
% 2.54/2.74 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.74 inference(symmetry,[status(thm)],[14179])).
% 2.54/2.74 tff(14181,plain,
% 2.54/2.74 ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14180])).
% 2.54/2.74 tff(14182,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(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14183,plain,
% 2.54/2.74 (((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14184,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(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14183])).
% 2.54/2.74 tff(14185,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(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.54/2.74 inference(transitivity,[status(thm)],[14184, 14182])).
% 2.54/2.74 tff(14186,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(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(14187,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(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[14186, 14185])).
% 2.54/2.74 tff(14188,plain,
% 2.54/2.74 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14187, 453, 499, 2077, 14132, 14166, 14163])).
% 2.54/2.74 tff(14189,plain,
% 2.54/2.74 (r(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[643, 14188, 7191])).
% 2.54/2.74 tff(14190,plain,
% 2.54/2.74 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 2.54/2.74 inference(monotonicity,[status(thm)],[3478])).
% 2.54/2.74 tff(14191,plain,
% 2.54/2.74 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.54/2.74 inference(symmetry,[status(thm)],[14190])).
% 2.54/2.74 tff(14192,plain,
% 2.54/2.74 (r(s(s(elem!1)), elem!1)),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[1159, 14191])).
% 2.54/2.74 tff(14193,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14194,plain,
% 2.54/2.74 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14195,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14194])).
% 2.54/2.74 tff(14196,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[14195, 14193])).
% 2.54/2.74 tff(14197,plain,
% 2.54/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(14198,plain,
% 2.54/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[14197, 14196])).
% 2.54/2.74 tff(14199,plain,
% 2.54/2.74 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14198, 268, 14192, 14189])).
% 2.54/2.74 tff(14200,plain,
% 2.54/2.74 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[14199, 14181])).
% 2.54/2.74 tff(14201,plain,
% 2.54/2.74 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[328, 14200])).
% 2.54/2.74 tff(14202,plain,
% 2.54/2.74 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11572, 14201, 1764, 14139, 14178])).
% 2.54/2.74 tff(14203,plain,
% 2.54/2.74 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2863, 14202])).
% 2.54/2.74 tff(14204,plain,
% 2.54/2.74 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[14203, 14128])).
% 2.54/2.74 tff(14205,plain,
% 2.54/2.74 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[3478])).
% 2.54/2.74 tff(14206,plain,
% 2.54/2.74 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 2.54/2.74 inference(symmetry,[status(thm)],[14205])).
% 2.54/2.74 tff(14207,plain,
% 2.54/2.74 (r(elem!1, s(s(elem!1)))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[419, 14206])).
% 2.54/2.74 tff(14208,plain,
% 2.54/2.74 ((~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[13484, 268, 14207])).
% 2.54/2.74 tff(14209,plain,
% 2.54/2.74 (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14208, 14204])).
% 2.54/2.74 tff(14210,plain,
% 2.54/2.74 (b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[5649, 14209, 5603])).
% 2.54/2.74 tff(14211,plain,
% 2.54/2.74 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(z))) <=> (s(s(s(s(s(s(s(s(z)))))))) = elem!1)),
% 2.54/2.74 inference(monotonicity,[status(thm)],[3468])).
% 2.54/2.74 tff(14212,plain,
% 2.54/2.74 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(z))) <=> (elem!1 = s(s(s(s(s(s(s(s(z)))))))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[14211, 6008])).
% 2.54/2.74 tff(14213,plain,
% 2.54/2.74 ((~(s(s(s(s(s(s(s(s(z)))))))) = s(s(z)))) <=> (~(elem!1 = s(s(s(s(s(s(s(s(z))))))))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14212])).
% 2.54/2.74 tff(14214,plain,
% 2.54/2.74 (~(elem!1 = s(s(s(s(s(s(s(s(z)))))))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[12032, 14213])).
% 2.54/2.74 tff(14215,plain,
% 2.54/2.74 ((~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[13497, 268, 14207])).
% 2.54/2.74 tff(14216,plain,
% 2.54/2.74 (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14215, 14204])).
% 2.54/2.74 tff(14217,plain,
% 2.54/2.74 (b(elem!1, s(s(s(s(s(s(s(s(z)))))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[11518, 14216, 14214])).
% 2.54/2.74 tff(14218,plain,
% 2.54/2.74 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[3477])).
% 2.54/2.74 tff(14219,plain,
% 2.54/2.74 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 2.54/2.74 inference(symmetry,[status(thm)],[14218])).
% 2.54/2.74 tff(14220,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(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14221,plain,
% 2.54/2.74 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14222,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14221])).
% 2.54/2.74 tff(14223,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.54/2.74 inference(transitivity,[status(thm)],[14222, 14220])).
% 2.54/2.74 tff(14224,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(14225,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[14224, 14223])).
% 2.54/2.74 tff(14226,plain,
% 2.54/2.74 (~b(s(s(s(z))), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14225, 453, 2077, 1291])).
% 2.54/2.74 tff(14227,plain,
% 2.54/2.74 (b(s(s(s(z))), s(s(s(z)))) <=> b(s(s(s(z))), s(elem!1))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[3469])).
% 2.54/2.74 tff(14228,plain,
% 2.54/2.74 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(z))))),
% 2.54/2.74 inference(symmetry,[status(thm)],[14227])).
% 2.54/2.74 tff(14229,plain,
% 2.54/2.74 (b(s(s(s(z))), s(s(s(z))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[11663, 14228])).
% 2.54/2.74 tff(14230,assumption,(~b(s(s(s(z))), s(s(s(z))))), introduced(assumption)).
% 2.54/2.74 tff(14231,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14230, 14229])).
% 2.54/2.74 tff(14232,plain,((~(s(s(z)) = elem!1)) | b(s(s(s(z))), s(s(s(z)))) | (~b(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(14233,plain,
% 2.54/2.74 (~b(s(s(s(z))), s(elem!1))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14232, 3468, 14226])).
% 2.54/2.74 tff(14234,plain,
% 2.54/2.74 (~(s(elem!1) = s(s(elem!1)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9349, 14233, 2, 13803])).
% 2.54/2.74 tff(14235,plain,
% 2.54/2.74 (~(s(elem!1) = elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8905, 14234])).
% 2.54/2.74 tff(14236,plain,
% 2.54/2.74 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[607, 14235])).
% 2.54/2.74 tff(14237,plain,
% 2.54/2.74 (r(s(s(s(elem!1))), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[3576, 14189, 3468])).
% 2.54/2.74 tff(14238,plain,
% 2.54/2.74 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[877, 14237, 14192])).
% 2.54/2.74 tff(14239,plain,
% 2.54/2.74 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[675, 14238, 14236])).
% 2.54/2.74 tff(14240,plain,
% 2.54/2.74 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[14239, 3545])).
% 2.54/2.74 tff(14241,plain,
% 2.54/2.74 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9017, 14178, 13972])).
% 2.54/2.74 tff(14242,plain,
% 2.54/2.74 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2570, 14241])).
% 2.54/2.74 tff(14243,plain,
% 2.54/2.74 (b(s(elem!1), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[14242, 5682])).
% 2.54/2.74 tff(14244,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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14245,plain,
% 2.54/2.74 (((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14246,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(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14245])).
% 2.54/2.74 tff(14247,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(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[14246, 14244])).
% 2.54/2.74 tff(14248,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(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(14249,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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[14248, 14247])).
% 2.54/2.74 tff(14250,plain,
% 2.54/2.74 (~b(s(elem!1), s(s(elem!1)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14249, 453, 14243, 14240, 14163])).
% 2.54/2.74 tff(14251,plain,
% 2.54/2.74 (r(s(elem!1), s(s(elem!1)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[440, 14250, 14234])).
% 2.54/2.74 tff(14252,plain,
% 2.54/2.74 (r(s(elem!1), s(s(s(s(z)))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[14251, 14219])).
% 2.54/2.74 tff(14253,plain,
% 2.54/2.74 (~r(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9796, 14203, 14252])).
% 2.54/2.74 tff(14254,plain,
% 2.54/2.74 (b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2919, 14253, 3815])).
% 2.54/2.74 tff(14255,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(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(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(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14256,plain,
% 2.54/2.74 (((~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14257,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(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z))))))))))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14256])).
% 2.54/2.74 tff(14258,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(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[14257, 14255])).
% 2.54/2.74 tff(14259,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(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(elem!1))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(14260,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(s(z))))))))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[14259, 14258])).
% 2.54/2.74 tff(14261,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14260, 453, 14166, 14254, 14217, 14210])).
% 2.54/2.74 tff(14262,plain,((~(s(s(z)) = elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | r(s(s(s(z))), elem!1) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(14263,plain,
% 2.54/2.74 (~(s(s(z)) = elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[14262, 11, 419, 499, 2077, 1159, 1275, 1764, 2, 4165])).
% 2.54/2.74 tff(14264,plain,
% 2.54/2.74 (r(s(s(z)), elem!1)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[782, 14263, 4])).
% 2.54/2.74 tff(14265,plain,
% 2.54/2.74 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[6942, 14264, 419])).
% 2.54/2.74 tff(14266,plain,
% 2.54/2.74 (b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2370, 69, 14265, 2359])).
% 2.54/2.74 tff(14267,plain,
% 2.54/2.74 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[4297, 14264, 1159])).
% 2.54/2.74 tff(14268,plain,
% 2.54/2.74 (b(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[4293, 14267])).
% 2.54/2.74 tff(14269,plain,
% 2.54/2.74 (~r(s(z), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1692, 268, 11, 14126])).
% 2.54/2.74 tff(14270,plain,
% 2.54/2.74 (b(s(z), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1677, 69, 14269, 50])).
% 2.54/2.74 tff(14271,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(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14272,plain,
% 2.54/2.74 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(14273,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(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[14272])).
% 2.54/2.74 tff(14274,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(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.54/2.75 inference(transitivity,[status(thm)],[14273, 14271])).
% 2.54/2.75 tff(14275,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(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(14276,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(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[14275, 14274])).
% 2.54/2.75 tff(14277,plain,
% 2.54/2.75 (~b(s(z), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14276, 453, 14270, 14268, 14266])).
% 2.54/2.75 tff(14278,plain,
% 2.54/2.75 (r(s(z), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[757, 14277])).
% 2.54/2.75 tff(14279,plain,
% 2.54/2.75 (~r(s(s(s(z))), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9038, 14278, 14126])).
% 2.54/2.75 tff(14280,plain,
% 2.54/2.75 (b(s(s(s(z))), s(s(z)))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12870, 14279])).
% 2.54/2.75 tff(14281,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(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(14282,plain,
% 2.54/2.75 (((~b(s(s(s(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(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(14283,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(s(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(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[14282])).
% 2.54/2.75 tff(14284,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(s(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(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.54/2.75 inference(transitivity,[status(thm)],[14283, 14281])).
% 2.54/2.75 tff(14285,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(s(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(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(14286,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(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[14285, 14284])).
% 2.54/2.75 tff(14287,plain,
% 2.54/2.75 (~b(s(s(z)), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14286, 453, 14270, 14268, 14266])).
% 2.54/2.75 tff(14288,plain,
% 2.54/2.75 (r(s(s(z)), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[720, 69, 717, 14287])).
% 2.54/2.75 tff(14289,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(14290,plain,
% 2.54/2.75 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(14291,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[14290])).
% 2.54/2.75 tff(14292,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.54/2.75 inference(transitivity,[status(thm)],[14291, 14289])).
% 2.54/2.75 tff(14293,plain,
% 2.54/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(14294,plain,
% 2.54/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[14293, 14292])).
% 2.54/2.75 tff(14295,plain,
% 2.54/2.75 (~r(s(s(z)), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14294, 268, 14124, 14288])).
% 2.54/2.75 tff(14296,plain,
% 2.54/2.75 (b(s(s(z)), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1350, 69, 14295, 12356])).
% 2.54/2.75 tff(14297,plain,
% 2.54/2.75 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[3245, 453, 14268, 14296, 14280])).
% 2.54/2.75 tff(14298,plain,
% 2.54/2.75 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1656, 14297])).
% 2.54/2.75 tff(14299,plain,
% 2.54/2.75 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[8917, 14298, 14126, 1764])).
% 2.54/2.75 tff(14300,plain,
% 2.54/2.75 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[687, 14299])).
% 2.54/2.75 tff(14301,plain,
% 2.54/2.75 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[7953, 453, 4165, 14300, 1275])).
% 2.54/2.75 tff(14302,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(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(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(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(14303,plain,
% 2.54/2.75 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(14304,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(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(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(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[14303])).
% 2.54/2.75 tff(14305,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(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(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(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.54/2.75 inference(transitivity,[status(thm)],[14304, 14302])).
% 2.54/2.75 tff(14306,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(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(14307,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(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[14306, 14305])).
% 2.54/2.75 tff(14308,plain,
% 2.54/2.75 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14307, 453, 4165, 14300, 14296])).
% 2.54/2.75 tff(14309,plain,
% 2.54/2.75 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[5711, 69, 14308, 54])).
% 2.54/2.75 tff(14310,plain,
% 2.54/2.75 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9558, 14309, 14264])).
% 2.54/2.75 tff(14311,plain,
% 2.54/2.75 (elem!1 = s(s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[466, 14310, 14301])).
% 2.54/2.75 tff(14312,plain,
% 2.54/2.75 (s(s(s(s(s(z))))) = elem!1),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[8839, 14311])).
% 2.54/2.75 tff(14313,plain,
% 2.54/2.75 (r(elem!1, s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11061, 14312, 14126, 14124, 59])).
% 2.54/2.75 tff(14314,plain,
% 2.54/2.75 (~(s(elem!1) = s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[5852, 14312])).
% 2.54/2.75 tff(14315,plain,
% 2.54/2.75 (~r(s(z), s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9047, 14309, 14278])).
% 2.54/2.75 tff(14316,plain,
% 2.54/2.75 (b(s(z), s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[372, 14315])).
% 2.54/2.75 tff(14317,plain,
% 2.54/2.75 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[501, 14125, 499])).
% 2.54/2.75 tff(14318,plain,
% 2.54/2.75 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[13015, 14312, 13811])).
% 2.54/2.75 tff(14319,plain,
% 2.54/2.75 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[328, 14318])).
% 2.54/2.75 tff(14320,plain,
% 2.54/2.75 (~r(s(elem!1), elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14109, 14319, 1764, 14311, 14317, 14316, 14314, 14313])).
% 2.54/2.75 tff(14321,plain,
% 2.54/2.75 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[4526, 14316, 1764, 14300])).
% 2.54/2.75 tff(14322,plain,
% 2.54/2.75 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[10556, 14321])).
% 2.54/2.75 tff(14323,plain,
% 2.54/2.75 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[8666, 14322, 11])).
% 2.54/2.75 tff(14324,plain,
% 2.54/2.75 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[2570, 14323])).
% 2.54/2.75 tff(14325,plain,
% 2.54/2.75 (~b(s(elem!1), elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12771, 14324, 14126, 14311, 14314, 1275, 499])).
% 2.54/2.75 tff(14326,plain,
% 2.54/2.75 (s(elem!1) = elem!1),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[2440, 14325, 14320])).
% 2.54/2.75 tff(14327,plain,
% 2.54/2.75 (elem!1 = s(elem!1)),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[14326, 1028])).
% 2.54/2.75 tff(14328,plain,
% 2.54/2.75 (elem!1 = s(s(elem!1))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[3351, 14326])).
% 2.54/2.75 tff(14329,plain,
% 2.54/2.75 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.54/2.75 inference(transitivity,[status(thm)],[5168, 3334])).
% 2.54/2.75 tff(14330,plain,
% 2.54/2.75 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[14329])).
% 2.54/2.75 tff(14331,plain,
% 2.54/2.75 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.54/2.75 inference(transitivity,[status(thm)],[284, 14330, 194, 12094, 3334])).
% 2.54/2.75 tff(14332,plain,
% 2.54/2.75 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[14331])).
% 2.54/2.75 tff(14333,plain,
% 2.54/2.75 (s(s(s(z))) = s(s(elem!1))),
% 2.54/2.75 inference(transitivity,[status(thm)],[38, 14332, 194, 12094, 3334])).
% 2.54/2.75 tff(14334,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[555, 14333])).
% 2.54/2.75 tff(14335,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~(elem!1 = s(elem!1))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(14336,plain,
% 2.54/2.75 (~(elem!1 = s(elem!1))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14335, 14328, 14312, 13803])).
% 2.54/2.75 tff(14337,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14336, 14327])).
% 2.54/2.75 tff(14338,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (s(s(s(z))) = elem!1) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | b(s(s(z)), elem!1) | (~b(elem!1, s(z))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(14339,plain,
% 2.54/2.75 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14338, 14122, 13417, 13797, 13963, 14120, 14069, 13969, 13408, 2])).
% 2.54/2.75 tff(14340,plain,
% 2.54/2.75 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[518, 14339])).
% 2.54/2.75 tff(14341,plain,
% 2.54/2.75 (r(elem!1, s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[466, 11091, 2073])).
% 2.54/2.75 tff(14342,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(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(14343,plain,
% 2.54/2.75 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(14344,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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[14343])).
% 2.54/2.75 tff(14345,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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.75 inference(transitivity,[status(thm)],[14344, 14342])).
% 2.54/2.75 tff(14346,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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(14347,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[14346, 14345])).
% 2.54/2.75 tff(14348,plain,
% 2.54/2.75 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14347, 453, 8909, 1764, 298])).
% 2.54/2.75 tff(14349,plain,
% 2.54/2.75 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[10556, 14348])).
% 2.54/2.75 tff(14350,plain,
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% 2.54/2.75 inference(unit_resolution,[status(thm)],[427, 14349, 14341, 419])).
% 2.54/2.75 tff(14351,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(14352,plain,
% 2.54/2.75 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14351, 2073, 419, 1764, 2077, 257])).
% 2.54/2.75 tff(14353,plain,
% 2.54/2.75 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[687, 14352])).
% 2.54/2.75 tff(14354,plain,
% 2.54/2.75 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[2596, 14353, 1291, 523])).
% 2.54/2.75 tff(14355,plain,
% 2.54/2.75 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[10556, 14354])).
% 2.54/2.75 tff(14356,plain,
% 2.54/2.75 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[427, 14355, 419])).
% 2.54/2.75 tff(14357,plain,
% 2.54/2.75 (b(elem!1, s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[466, 14356, 2073])).
% 2.54/2.75 tff(14358,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[7953, 453, 1291, 14357, 14353, 1275])).
% 2.54/2.75 tff(14359,plain,((elem!1 = s(s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(14360,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14359, 14340, 14119, 13969, 14069, 13964, 13797, 13408, 13966])).
% 2.54/2.75 tff(14361,plain,(r(elem!1, s(s(s(z)))) | r(s(z), elem!1) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(14362,plain,
% 2.54/2.75 (r(elem!1, s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14361, 2, 4541])).
% 2.54/2.75 tff(14363,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[8475, 13810, 13809, 1149])).
% 2.54/2.75 tff(14364,plain,((~(s(s(s(z))) = elem!1)) | (~r(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(14365,plain,
% 2.54/2.75 (~(s(s(s(z))) = elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14364, 14362, 13797, 13408])).
% 2.54/2.75 tff(14366,plain,
% 2.54/2.75 (b(s(s(s(z))), elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[74, 14365, 2])).
% 2.54/2.75 tff(14367,plain,
% 2.54/2.75 (~b(s(z), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[5513, 14366, 13408, 13417])).
% 2.54/2.75 tff(14368,plain,
% 2.54/2.75 (r(s(z), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[227, 14367])).
% 2.54/2.75 tff(14369,plain,
% 2.54/2.75 (b(elem!1, s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[12731, 14367])).
% 2.54/2.75 tff(14370,plain,
% 2.54/2.75 (~(elem!1 = s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[14067, 14369, 13417, 13408, 14366])).
% 2.54/2.75 tff(14371,plain,
% 2.54/2.75 (r(elem!1, s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1087, 14370, 13967])).
% 2.54/2.75 tff(14372,plain,
% 2.54/2.75 (~r(elem!1, s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1157, 14368, 14362])).
% 2.54/2.75 tff(14373,plain,
% 2.54/2.75 (~b(s(s(s(z))), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[5465, 14369, 13417, 14366])).
% 2.54/2.75 tff(14374,plain,
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% 2.54/2.75 inference(unit_resolution,[status(thm)],[134, 14373])).
% 2.54/2.75 tff(14375,plain,
% 2.54/2.75 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[11061, 14374, 14368, 14372, 14365])).
% 2.54/2.75 tff(14376,plain,
% 2.54/2.75 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[8839, 14375])).
% 2.54/2.75 tff(14377,plain,
% 2.54/2.75 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[13281, 14371, 14362])).
% 2.54/2.75 tff(14378,plain,
% 2.54/2.75 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[518, 14377])).
% 2.54/2.75 tff(14379,plain,
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% 2.54/2.75 inference(unit_resolution,[status(thm)],[14359, 14378, 14376, 14369, 14371, 14366, 13797, 13408, 14368])).
% 2.54/2.75 tff(14380,plain,(r(s(s(s(z))), elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(14381,plain,
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% 2.54/2.75 inference(unit_resolution,[status(thm)],[14380, 4541])).
% 2.54/2.75 tff(14382,plain,
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% 2.54/2.75 inference(unit_resolution,[status(thm)],[4961, 11, 14381])).
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% 2.54/2.75 inference(unit_resolution,[status(thm)],[547, 13416])).
% 2.54/2.75 tff(14386,plain,
% 2.54/2.75 (~(elem!1 = s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[8, 13423])).
% 2.54/2.75 tff(14387,plain,
% 2.54/2.75 (b(s(z), s(s(s(z))))),
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% 2.54/2.75 tff(14388,plain,
% 2.54/2.75 (~b(elem!1, s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[10307, 5883, 13417, 14387])).
% 2.54/2.75 tff(14389,plain,
% 2.54/2.75 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[512, 14382, 11])).
% 2.54/2.75 tff(14390,plain,
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% 2.54/2.75 tff(14391,plain,
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% 2.54/2.75 inference(unit_resolution,[status(thm)],[4492, 14391, 14388])).
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% 2.54/2.75 (~r(elem!1, s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[13281, 14392, 11])).
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% 2.54/2.75 (b(elem!1, s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1087, 14393, 14386])).
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% 2.54/2.75 tff(14398,plain,
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% 2.54/2.75 inference(unit_resolution,[status(thm)],[5538, 14398])).
% 2.54/2.75 tff(14400,plain,
% 2.54/2.75 (~r(s(s(s(s(s(z))))), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[2414, 14395, 1099])).
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% 2.54/2.75 tff(14403,plain,
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% 2.54/2.76 tff(14407,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | r(s(z), elem!1) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(14408,plain,
% 2.54/2.76 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14407, 1057, 4541])).
% 2.54/2.76 tff(14409,plain,
% 2.54/2.76 (b(s(s(s(s(z)))), s(s(s(z))))),
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% 2.54/2.76 tff(14410,plain,
% 2.54/2.76 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[7911, 1057, 13415])).
% 2.54/2.76 tff(14411,plain,
% 2.54/2.76 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1656, 14410])).
% 2.54/2.76 tff(14412,plain,
% 2.54/2.76 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[5333, 228, 13408, 14381, 637, 13417])).
% 2.54/2.76 tff(14413,plain,
% 2.54/2.76 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[687, 14412])).
% 2.54/2.76 tff(14414,plain,
% 2.54/2.76 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1788, 14413, 14411, 14409])).
% 2.54/2.76 tff(14415,plain,
% 2.54/2.76 (b(s(z), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12645, 4490, 4541])).
% 2.54/2.76 tff(14416,plain,
% 2.54/2.76 (~b(s(s(z)), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[5574, 255, 2077, 499, 1132])).
% 2.54/2.76 tff(14417,plain,
% 2.54/2.76 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2254, 11916, 1132])).
% 2.54/2.76 tff(14418,plain,
% 2.54/2.76 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[10556, 14417])).
% 2.54/2.76 tff(14419,plain,
% 2.54/2.76 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2414, 12079, 1132])).
% 2.54/2.76 tff(14420,plain,
% 2.54/2.76 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[328, 14419])).
% 2.54/2.76 tff(14421,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[6664, 14420, 14418, 1085, 3, 239, 646])).
% 2.54/2.76 tff(14422,plain,((~b(s(s(s(s(s(z))))), elem!1)) | r(elem!1, s(s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | r(s(s(s(s(z)))), elem!1) | (~r(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(14423,plain,
% 2.54/2.76 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14422, 239, 3, 1085, 1132, 2077, 499])).
% 2.54/2.76 tff(14424,plain,
% 2.54/2.76 (r(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[643, 14423, 637])).
% 2.54/2.76 tff(14425,plain,
% 2.54/2.76 (~r(s(s(z)), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[10463, 14424, 1545])).
% 2.54/2.76 tff(14426,plain,
% 2.54/2.76 (s(s(z)) = elem!1),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[782, 14425, 14416])).
% 2.54/2.76 tff(14427,plain,
% 2.54/2.76 (s(s(s(z))) = s(elem!1)),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14426])).
% 2.54/2.76 tff(14428,plain,
% 2.54/2.76 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14427])).
% 2.54/2.76 tff(14429,plain,
% 2.54/2.76 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1566, 14424, 1545])).
% 2.54/2.76 tff(14430,plain,
% 2.54/2.76 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[687, 14429])).
% 2.54/2.76 tff(14431,plain,
% 2.54/2.76 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[14430, 14428])).
% 2.54/2.76 tff(14432,plain,
% 2.54/2.76 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1788, 14430, 1633, 523])).
% 2.54/2.76 tff(14433,plain,
% 2.54/2.76 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[328, 14432])).
% 2.54/2.76 tff(14434,plain,
% 2.54/2.76 (~r(s(s(s(s(s(z))))), s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2414, 14433, 1132])).
% 2.54/2.76 tff(14435,plain,
% 2.54/2.76 (b(s(s(s(s(s(z))))), s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[297, 14434])).
% 2.54/2.76 tff(14436,plain,
% 2.54/2.76 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14427])).
% 2.54/2.76 tff(14437,plain,
% 2.54/2.76 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14436])).
% 2.54/2.76 tff(14438,plain,
% 2.54/2.76 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14427])).
% 2.54/2.76 tff(14439,plain,
% 2.54/2.76 (b(s(elem!1), s(s(s(s(z)))))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[1633, 14438])).
% 2.54/2.76 tff(14440,plain,
% 2.54/2.76 (b(s(elem!1), s(s(elem!1)))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[14439, 14437])).
% 2.54/2.76 tff(14441,plain,
% 2.54/2.76 (b(s(z), s(elem!1))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[3644, 14426, 2090])).
% 2.54/2.76 tff(14442,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(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14443,plain,
% 2.54/2.76 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14444,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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14443])).
% 2.54/2.76 tff(14445,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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[14444, 14442])).
% 2.54/2.76 tff(14446,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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(14447,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[14446, 14445])).
% 2.54/2.76 tff(14448,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14447, 453, 14441, 14440, 14435, 14431])).
% 2.54/2.76 tff(14449,plain,(r(s(s(s(s(z)))), elem!1) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (s(s(s(s(z)))) = elem!1) | r(elem!1, s(s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(14450,plain,
% 2.54/2.76 (r(s(s(s(s(z)))), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14449, 13147, 1132, 2090, 523, 1545, 1633, 3, 1085, 2077, 499])).
% 2.54/2.76 tff(14451,plain,
% 2.54/2.76 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11146, 14450, 2077, 1132, 499, 13147])).
% 2.54/2.76 tff(14452,plain,
% 2.54/2.76 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[328, 14451])).
% 2.54/2.76 tff(14453,plain,
% 2.54/2.76 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1788, 14452, 1633, 523])).
% 2.54/2.76 tff(14454,plain,
% 2.54/2.76 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[687, 14453])).
% 2.54/2.76 tff(14455,plain,
% 2.54/2.76 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1566, 14454, 1545])).
% 2.54/2.76 tff(14456,plain,
% 2.54/2.76 (b(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[643, 14455, 13147])).
% 2.54/2.76 tff(14457,plain,
% 2.54/2.76 (~b(s(s(s(s(s(z))))), s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[5331, 14456, 2077, 499])).
% 2.54/2.76 tff(14458,plain,
% 2.54/2.76 (r(s(s(s(s(s(z))))), s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[297, 14457])).
% 2.54/2.76 tff(14459,plain,
% 2.54/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14460,plain,
% 2.54/2.76 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14461,plain,
% 2.54/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14460])).
% 2.54/2.76 tff(14462,plain,
% 2.54/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[14461, 14459])).
% 2.54/2.76 tff(14463,plain,
% 2.54/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(14464,plain,
% 2.54/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[14463, 14462])).
% 2.54/2.76 tff(14465,plain,
% 2.54/2.76 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14464, 268, 14454, 1149])).
% 2.54/2.76 tff(14466,plain,
% 2.54/2.76 (b(elem!1, s(s(s(s(s(z))))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[466, 14465, 2073])).
% 2.54/2.76 tff(14467,plain,
% 2.54/2.76 (b(s(s(s(z))), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[12870, 7530])).
% 2.54/2.76 tff(14468,plain,
% 2.54/2.76 (b(s(s(z)), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1350, 69, 7165, 12356])).
% 2.54/2.76 tff(14469,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11058, 453, 523, 8417, 14468, 14467])).
% 2.54/2.76 tff(14470,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(14471,plain,
% 2.54/2.76 (~r(s(s(z)), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14470, 14450, 1545, 523])).
% 2.54/2.76 tff(14472,plain,
% 2.54/2.76 (b(elem!1, s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1087, 1085, 9])).
% 2.54/2.76 tff(14473,plain,
% 2.54/2.76 (~b(s(z), s(s(s(s(s(z))))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[11166, 14456, 2077, 499])).
% 2.54/2.76 tff(14474,plain,
% 2.54/2.76 (r(s(z), s(s(s(s(s(z))))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[372, 14473])).
% 2.54/2.76 tff(14475,plain,
% 2.54/2.76 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2254, 14474, 1132])).
% 2.54/2.76 tff(14476,plain,
% 2.54/2.76 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[10556, 14475])).
% 2.54/2.76 tff(14477,plain,
% 2.54/2.76 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[3477])).
% 2.54/2.76 tff(14478,plain,
% 2.54/2.76 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[2497, 14477])).
% 2.54/2.76 tff(14479,plain,
% 2.54/2.76 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[3478])).
% 2.54/2.76 tff(14480,plain,
% 2.54/2.76 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 2.54/2.76 inference(symmetry,[status(thm)],[14479])).
% 2.54/2.76 tff(14481,plain,
% 2.54/2.76 (b(elem!1, s(s(elem!1)))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[530, 14480])).
% 2.54/2.76 tff(14482,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[3801, 453, 14481, 923, 646, 14478])).
% 2.54/2.76 tff(14483,plain,((~(s(s(z)) = elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(14484,plain,
% 2.54/2.76 (~(s(s(z)) = elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14483, 14466, 14456, 14476, 14472])).
% 2.54/2.76 tff(14485,plain,
% 2.54/2.76 (b(s(s(z)), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[782, 14484, 14471])).
% 2.54/2.76 tff(14486,plain,
% 2.54/2.76 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[4078, 14485, 14456, 14466])).
% 2.54/2.76 tff(14487,plain,
% 2.54/2.76 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[4081, 14486])).
% 2.54/2.76 tff(14488,plain,
% 2.54/2.76 (~r(s(z), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2476, 14487, 14458])).
% 2.54/2.76 tff(14489,plain,
% 2.54/2.76 (b(s(z), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[757, 14488])).
% 2.54/2.76 tff(14490,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), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14491,plain,
% 2.54/2.76 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14492,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(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14491])).
% 2.54/2.76 tff(14493,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(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[14492, 14490])).
% 2.54/2.76 tff(14494,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(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(14495,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[14494, 14493])).
% 2.54/2.76 tff(14496,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14495, 453, 499, 14466, 14485, 14489])).
% 2.54/2.76 tff(14497,plain,((elem!1 = s(s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | r(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(14498,plain,
% 2.54/2.76 (elem!1 = s(s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14497, 1085, 1149, 1132, 2077, 1545, 1633, 523, 2090, 3, 499])).
% 2.54/2.76 tff(14499,plain,
% 2.54/2.76 (s(elem!1) = s(s(s(s(s(s(z))))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14498])).
% 2.54/2.76 tff(14500,plain,
% 2.54/2.76 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14499])).
% 2.54/2.76 tff(14501,plain,
% 2.54/2.76 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(z))))))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14500])).
% 2.54/2.76 tff(14502,plain,
% 2.54/2.76 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14501])).
% 2.54/2.76 tff(14503,plain,
% 2.54/2.76 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[14502, 5661])).
% 2.54/2.76 tff(14504,plain,
% 2.54/2.76 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14503])).
% 2.54/2.76 tff(14505,plain,
% 2.54/2.76 (s(s(s(s(s(z))))) = elem!1),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[8839, 14498])).
% 2.54/2.76 tff(14506,plain,
% 2.54/2.76 (~(s(elem!1) = s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[5852, 14505])).
% 2.54/2.76 tff(14507,plain,
% 2.54/2.76 (~(s(s(z)) = s(s(elem!1)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1188, 14506])).
% 2.54/2.76 tff(14508,plain,
% 2.54/2.76 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[4916, 14507])).
% 2.54/2.76 tff(14509,plain,
% 2.54/2.76 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[14508, 14504])).
% 2.54/2.76 tff(14510,plain,
% 2.54/2.76 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14501, 14498])).
% 2.54/2.76 tff(14511,plain,
% 2.54/2.76 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14498])).
% 2.54/2.76 tff(14512,plain,
% 2.54/2.76 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.54/2.76 inference(symmetry,[status(thm)],[14511])).
% 2.54/2.76 tff(14513,plain,
% 2.54/2.76 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(z))))))),
% 2.54/2.76 inference(commutativity,[status(thm)],[])).
% 2.54/2.76 tff(14514,plain,
% 2.54/2.76 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14501])).
% 2.54/2.76 tff(14515,plain,
% 2.54/2.76 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(z))))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[14514, 14513])).
% 2.54/2.76 tff(14516,plain,
% 2.54/2.76 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 2.54/2.76 inference(symmetry,[status(thm)],[14515])).
% 2.54/2.76 tff(14517,plain,
% 2.54/2.76 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.54/2.76 inference(transitivity,[status(thm)],[14516, 14512, 7196])).
% 2.54/2.76 tff(14518,plain,
% 2.54/2.76 ((~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14517])).
% 2.54/2.76 tff(14519,plain,
% 2.54/2.76 (~(s(s(s(elem!1))) = elem!1)),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[2688, 14518])).
% 2.54/2.76 tff(14520,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(z)))), 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(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14521,plain,
% 2.54/2.76 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14522,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(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14521])).
% 2.54/2.76 tff(14523,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(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[14522, 14520])).
% 2.54/2.76 tff(14524,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(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(14525,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(z)))), 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(s(z))))))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[14524, 14523])).
% 2.54/2.76 tff(14526,plain,
% 2.54/2.76 (~b(s(z), s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[14525, 453, 523, 1633, 2090])).
% 2.54/2.76 tff(14527,plain,
% 2.54/2.76 (r(s(z), s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1677, 69, 50, 14526])).
% 2.54/2.76 tff(14528,plain,
% 2.54/2.76 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14501])).
% 2.54/2.76 tff(14529,plain,
% 2.54/2.76 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.54/2.76 inference(symmetry,[status(thm)],[14528])).
% 2.54/2.76 tff(14530,plain,
% 2.54/2.76 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[5534, 14498, 1085])).
% 2.54/2.76 tff(14531,plain,
% 2.54/2.76 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[328, 14530])).
% 2.54/2.76 tff(14532,plain,
% 2.54/2.76 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2857, 14509, 14531, 523, 1633])).
% 2.54/2.76 tff(14533,plain,
% 2.54/2.76 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2863, 14532])).
% 2.54/2.76 tff(14534,plain,
% 2.54/2.76 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[14533, 14529])).
% 2.54/2.76 tff(14535,plain,
% 2.54/2.76 (~r(s(s(s(elem!1))), s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[6002, 14534, 14527])).
% 2.54/2.76 tff(14536,plain,
% 2.54/2.76 (b(s(s(s(elem!1))), s(z))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[856, 14535])).
% 2.54/2.76 tff(14537,plain,
% 2.54/2.76 (~b(s(s(s(elem!1))), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[13666, 14536, 2077, 499])).
% 2.54/2.76 tff(14538,plain,
% 2.54/2.76 (r(s(s(s(elem!1))), elem!1)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[567, 14537, 14519])).
% 2.54/2.76 tff(14539,plain,
% 2.54/2.76 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[14538, 14510])).
% 2.54/2.76 tff(14540,plain,
% 2.54/2.76 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[14498])).
% 2.54/2.76 tff(14541,plain,
% 2.54/2.76 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[1545, 14540])).
% 2.54/2.76 tff(14542,plain,
% 2.54/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14543,plain,
% 2.54/2.76 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(14544,plain,
% 2.54/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14543])).
% 2.54/2.77 tff(14545,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[14544, 14542])).
% 2.54/2.77 tff(14546,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(14547,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z)))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[14546, 14545])).
% 2.54/2.77 tff(14548,plain,
% 2.54/2.77 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14547, 268, 14541, 14539])).
% 2.54/2.77 tff(14549,plain,
% 2.54/2.77 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14501])).
% 2.54/2.77 tff(14550,plain,
% 2.54/2.77 (b(s(s(s(s(s(s(s(s(z)))))))), s(z))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[14536, 14549])).
% 2.54/2.77 tff(14551,plain,
% 2.54/2.77 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[10251, 14550, 2090, 1633])).
% 2.54/2.77 tff(14552,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2846, 14551, 14548, 14509])).
% 2.54/2.77 tff(14553,plain,(r(elem!1, s(s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(14554,plain,
% 2.54/2.77 (r(elem!1, s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14553, 1149, 1633, 2077, 499, 523, 1545, 2090, 1132, 3])).
% 2.54/2.77 tff(14555,plain,
% 2.54/2.77 (~b(s(s(z)), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5574, 299, 2077, 499, 1132])).
% 2.54/2.77 tff(14556,plain,
% 2.54/2.77 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1788, 1780, 1633, 523])).
% 2.54/2.77 tff(14557,plain,
% 2.54/2.77 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[687, 14556])).
% 2.54/2.77 tff(14558,plain,
% 2.54/2.77 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1566, 14557, 1545])).
% 2.54/2.77 tff(14559,plain,
% 2.54/2.77 (b(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[643, 14558, 637])).
% 2.54/2.77 tff(14560,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[6968, 453, 2077, 14559, 1780, 299])).
% 2.54/2.77 tff(14561,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(14562,plain,
% 2.54/2.77 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14561, 637, 299, 2077, 1545, 1633, 523])).
% 2.54/2.77 tff(14563,plain,
% 2.54/2.77 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[328, 14562])).
% 2.54/2.77 tff(14564,plain,
% 2.54/2.77 (~r(s(s(s(s(s(z))))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2414, 14563, 1132])).
% 2.54/2.77 tff(14565,plain,
% 2.54/2.77 (b(s(s(s(s(s(z))))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[297, 14564])).
% 2.54/2.77 tff(14566,plain,
% 2.54/2.77 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5331, 14565, 2077, 499])).
% 2.54/2.77 tff(14567,plain,
% 2.54/2.77 (r(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[643, 14566, 637])).
% 2.54/2.77 tff(14568,plain,
% 2.54/2.77 (~r(s(s(z)), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[10463, 14567, 1545])).
% 2.54/2.77 tff(14569,plain,
% 2.54/2.77 (s(s(z)) = elem!1),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[782, 14568, 14555])).
% 2.54/2.77 tff(14570,plain,
% 2.54/2.77 (s(s(s(z))) = s(elem!1)),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14569])).
% 2.54/2.77 tff(14571,plain,
% 2.54/2.77 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14570])).
% 2.54/2.77 tff(14572,plain,
% 2.54/2.77 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1566, 14567, 1545])).
% 2.54/2.77 tff(14573,plain,
% 2.54/2.77 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[687, 14572])).
% 2.54/2.77 tff(14574,plain,
% 2.54/2.77 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[14573, 14571])).
% 2.54/2.77 tff(14575,plain,
% 2.54/2.77 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14570])).
% 2.54/2.77 tff(14576,plain,
% 2.54/2.77 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14575])).
% 2.54/2.77 tff(14577,plain,
% 2.54/2.77 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14570])).
% 2.54/2.77 tff(14578,plain,
% 2.54/2.77 (b(s(elem!1), s(s(s(s(z)))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[1633, 14577])).
% 2.54/2.77 tff(14579,plain,
% 2.54/2.77 (b(s(elem!1), s(s(elem!1)))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[14578, 14576])).
% 2.54/2.77 tff(14580,plain,
% 2.54/2.77 (b(s(z), s(elem!1))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[3644, 14569, 2090])).
% 2.54/2.77 tff(14581,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14447, 453, 14580, 14579, 14565, 14574])).
% 2.54/2.77 tff(14582,plain,((s(s(s(s(s(z))))) = elem!1) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(14583,plain,
% 2.54/2.77 (s(s(s(s(s(z))))) = elem!1),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14582, 299, 2090, 1545, 2077, 499, 1132, 1633, 523])).
% 2.54/2.77 tff(14584,plain,
% 2.54/2.77 (elem!1 = s(s(s(s(s(z)))))),
% 2.54/2.77 inference(symmetry,[status(thm)],[14583])).
% 2.54/2.77 tff(14585,plain,
% 2.54/2.77 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14584])).
% 2.54/2.77 tff(14586,plain,
% 2.54/2.77 ((s(s(z)) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.54/2.77 inference(transitivity,[status(thm)],[14585, 4133])).
% 2.54/2.77 tff(14587,plain,
% 2.54/2.77 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.54/2.77 inference(symmetry,[status(thm)],[14586])).
% 2.54/2.77 tff(14588,plain,
% 2.54/2.77 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14587])).
% 2.54/2.77 tff(14589,plain,
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% 2.54/2.77 inference(modus_ponens,[status(thm)],[52, 14588])).
% 2.54/2.77 tff(14590,plain,
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% 2.54/2.77 inference(unit_resolution,[status(thm)],[782, 14589, 14555])).
% 2.54/2.77 tff(14591,plain,
% 2.54/2.77 (~r(s(s(s(z))), s(s(z)))),
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% 2.54/2.77 tff(14592,plain,
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% 2.54/2.77 inference(unit_resolution,[status(thm)],[12870, 14591])).
% 2.54/2.77 tff(14593,plain,
% 2.54/2.77 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14583])).
% 2.54/2.77 tff(14594,plain,
% 2.54/2.77 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
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% 2.54/2.77 tff(14595,plain,
% 2.54/2.77 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[1149, 14594])).
% 2.54/2.77 tff(14596,plain,
% 2.54/2.77 (elem!1 = s(s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5538, 14583])).
% 2.54/2.77 tff(14597,plain,
% 2.54/2.77 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[10851, 14590, 14596])).
% 2.54/2.77 tff(14598,plain,
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% 2.54/2.77 tff(14599,plain,
% 2.54/2.77 (b(s(s(z)), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1350, 69, 14598, 12356])).
% 2.54/2.77 tff(14600,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(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(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(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(z)), s(s(s(z))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(14601,plain,
% 2.54/2.77 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(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(z)), s(s(s(z))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(14602,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(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(z)), s(s(s(z)))))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14601])).
% 2.54/2.77 tff(14603,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(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(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(z)), s(s(s(z))))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[14602, 14600])).
% 2.54/2.77 tff(14604,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(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)))))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(14605,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[14604, 14603])).
% 2.54/2.77 tff(14606,plain,
% 2.54/2.77 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14605, 453, 523, 14599, 14592])).
% 2.54/2.77 tff(14607,plain,
% 2.54/2.77 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[6942, 14590, 419])).
% 2.54/2.77 tff(14608,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2370, 69, 14607, 2359, 14606])).
% 2.54/2.77 tff(14609,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(14610,plain,
% 2.54/2.77 (~b(s(s(s(s(z)))), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14609, 14554, 1545, 523, 1149, 2090, 2077, 499, 1132, 1633])).
% 2.54/2.77 tff(14611,plain,
% 2.54/2.77 (r(s(s(s(s(z)))), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[254, 14610, 3])).
% 2.54/2.77 tff(14612,plain,
% 2.54/2.77 (~r(s(s(z)), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14470, 1159, 1545, 523])).
% 2.54/2.77 tff(14613,plain,
% 2.54/2.77 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[11146, 637, 2077, 1132, 499, 1159])).
% 2.54/2.77 tff(14614,plain,
% 2.54/2.77 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[328, 14613])).
% 2.54/2.77 tff(14615,plain,
% 2.54/2.77 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1788, 14614, 1633, 523])).
% 2.54/2.77 tff(14616,plain,
% 2.54/2.77 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[687, 14615])).
% 2.54/2.77 tff(14617,plain,
% 2.54/2.77 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1566, 14616, 1545])).
% 2.54/2.77 tff(14618,plain,
% 2.54/2.77 (b(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[643, 14617, 637])).
% 2.54/2.77 tff(14619,plain,
% 2.54/2.77 (~b(s(z), s(s(s(s(s(z))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[11166, 14618, 2077, 499])).
% 2.54/2.77 tff(14620,plain,
% 2.54/2.77 (r(s(z), s(s(s(s(s(z))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[372, 14619])).
% 2.54/2.77 tff(14621,plain,
% 2.54/2.77 (~b(s(s(s(s(s(z))))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5331, 14618, 2077, 499])).
% 2.54/2.77 tff(14622,plain,
% 2.54/2.77 (r(s(s(s(s(s(z))))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[297, 14621])).
% 2.54/2.77 tff(14623,plain,
% 2.54/2.77 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2254, 14620, 1132])).
% 2.54/2.77 tff(14624,plain,
% 2.54/2.77 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[10556, 14623])).
% 2.54/2.77 tff(14625,plain,
% 2.54/2.77 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9047, 733, 2246])).
% 2.54/2.77 tff(14626,plain,
% 2.54/2.77 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5711, 69, 14625, 54])).
% 2.54/2.77 tff(14627,plain,
% 2.54/2.77 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[4081, 2477])).
% 2.54/2.77 tff(14628,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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(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(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(14629,plain,
% 2.54/2.77 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(14630,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(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(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(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14629])).
% 2.54/2.77 tff(14631,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(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(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(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[14630, 14628])).
% 2.54/2.77 tff(14632,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(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(14633,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[14632, 14631])).
% 2.54/2.77 tff(14634,plain,
% 2.54/2.77 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14633, 453, 2497, 14627, 14626])).
% 2.54/2.77 tff(14635,plain,
% 2.54/2.77 (r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2370, 69, 2359, 14634])).
% 2.54/2.77 tff(14636,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[7637, 268, 376, 733, 14635])).
% 2.54/2.77 tff(14637,plain,((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(14638,plain,
% 2.54/2.77 (~r(s(z), s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14637, 14624, 376, 14622, 14620])).
% 2.54/2.77 tff(14639,plain,
% 2.54/2.77 (b(s(z), s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[757, 14638])).
% 2.54/2.77 tff(14640,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[6633, 453, 499, 2077, 922, 1008])).
% 2.54/2.77 tff(14641,plain,((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(14642,plain,
% 2.54/2.77 (~b(s(s(z)), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14641, 14639, 2077, 499])).
% 2.54/2.77 tff(14643,plain,
% 2.54/2.77 (s(s(z)) = elem!1),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[782, 14642, 14612])).
% 2.54/2.77 tff(14644,plain,
% 2.54/2.77 (~(s(s(s(s(s(s(s(s(z)))))))) = elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5602, 14643])).
% 2.54/2.77 tff(14645,plain,
% 2.54/2.77 (s(s(s(z))) = s(elem!1)),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14643])).
% 2.54/2.77 tff(14646,plain,
% 2.54/2.77 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14645])).
% 2.54/2.77 tff(14647,plain,
% 2.54/2.77 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.54/2.77 inference(symmetry,[status(thm)],[14646])).
% 2.54/2.77 tff(14648,plain,
% 2.54/2.77 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14647])).
% 2.54/2.77 tff(14649,plain,
% 2.54/2.77 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 2.54/2.77 inference(symmetry,[status(thm)],[14648])).
% 2.54/2.77 tff(14650,plain,
% 2.54/2.77 ((s(s(s(z))) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14645])).
% 2.54/2.77 tff(14651,plain,
% 2.54/2.77 ((s(elem!1) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.54/2.77 inference(symmetry,[status(thm)],[14650])).
% 2.54/2.77 tff(14652,plain,
% 2.54/2.77 ((s(elem!1) = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[14651, 5661])).
% 2.54/2.77 tff(14653,plain,
% 2.54/2.77 ((~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))) <=> (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z)))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14652])).
% 2.54/2.77 tff(14654,plain,
% 2.54/2.77 (~(s(elem!1) = s(s(s(s(s(s(s(s(z)))))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[3814, 14643])).
% 2.54/2.77 tff(14655,plain,
% 2.54/2.77 (~(s(s(s(s(s(s(s(s(z)))))))) = s(s(s(z))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[14654, 14653])).
% 2.54/2.77 tff(14656,plain,
% 2.54/2.77 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2857, 14655, 14614, 523, 1633])).
% 2.54/2.77 tff(14657,plain,
% 2.54/2.77 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2863, 14656])).
% 2.54/2.77 tff(14658,plain,
% 2.54/2.77 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[14657, 14649])).
% 2.54/2.77 tff(14659,plain,
% 2.54/2.77 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14647])).
% 2.54/2.77 tff(14660,plain,
% 2.54/2.77 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 2.54/2.77 inference(symmetry,[status(thm)],[14659])).
% 2.54/2.77 tff(14661,plain,
% 2.54/2.77 (r(elem!1, s(s(elem!1)))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[419, 14660])).
% 2.54/2.77 tff(14662,plain,
% 2.54/2.77 (s(elem!1) = s(s(s(z)))),
% 2.54/2.77 inference(symmetry,[status(thm)],[14645])).
% 2.54/2.77 tff(14663,plain,
% 2.54/2.77 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14662])).
% 2.54/2.77 tff(14664,plain,
% 2.54/2.77 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 2.54/2.77 inference(symmetry,[status(thm)],[14663])).
% 2.54/2.77 tff(14665,plain,
% 2.54/2.77 (r(elem!1, s(elem!1))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[1149, 14664])).
% 2.54/2.77 tff(14666,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(14667,plain,
% 2.54/2.77 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(14668,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[14667])).
% 2.54/2.77 tff(14669,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[14668, 14666])).
% 2.54/2.77 tff(14670,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(14671,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[14670, 14669])).
% 2.54/2.77 tff(14672,plain,
% 2.54/2.77 ((~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14671, 268, 14665, 14661])).
% 2.54/2.77 tff(14673,plain,
% 2.54/2.77 (~r(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[14672, 14658])).
% 2.54/2.77 tff(14674,plain,
% 2.54/2.77 (b(s(s(s(s(s(s(s(s(z)))))))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[5649, 14673, 14644])).
% 2.54/2.78 tff(14675,plain,
% 2.54/2.78 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(z))) <=> (s(s(s(s(s(s(s(s(z)))))))) = elem!1)),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14643])).
% 2.54/2.78 tff(14676,plain,
% 2.54/2.78 ((s(s(s(s(s(s(s(s(z)))))))) = s(s(z))) <=> (elem!1 = s(s(s(s(s(s(s(s(z)))))))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[14675, 6008])).
% 2.54/2.78 tff(14677,plain,
% 2.54/2.78 ((~(s(s(s(s(s(s(s(s(z)))))))) = s(s(z)))) <=> (~(elem!1 = s(s(s(s(s(s(s(s(z))))))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14676])).
% 2.54/2.78 tff(14678,plain,
% 2.54/2.78 (~(elem!1 = s(s(s(s(s(s(s(s(z)))))))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[12032, 14677])).
% 2.54/2.78 tff(14679,plain,
% 2.54/2.78 ((~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[13497, 268, 14661])).
% 2.54/2.78 tff(14680,plain,
% 2.54/2.78 (~r(elem!1, s(s(s(s(s(s(s(s(z)))))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14679, 14658])).
% 2.54/2.78 tff(14681,plain,
% 2.54/2.78 (b(elem!1, s(s(s(s(s(s(s(s(z)))))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[11518, 14680, 14678])).
% 2.54/2.78 tff(14682,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), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(14683,plain,
% 2.54/2.78 (((~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(14684,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(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(z), s(s(s(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(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14683])).
% 2.54/2.78 tff(14685,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(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(z), s(s(s(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(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)))),
% 2.54/2.78 inference(transitivity,[status(thm)],[14684, 14682])).
% 2.54/2.78 tff(14686,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(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(14687,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), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~b(elem!1, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), elem!1))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[14686, 14685])).
% 2.54/2.78 tff(14688,plain,
% 2.54/2.78 (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14687, 453, 499, 14681, 14674])).
% 2.54/2.78 tff(14689,plain,
% 2.54/2.78 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(elem!1)))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14646])).
% 2.54/2.78 tff(14690,plain,
% 2.54/2.78 (r(s(z), s(s(elem!1)))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[376, 14689])).
% 2.54/2.78 tff(14691,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(14692,plain,
% 2.54/2.78 (((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(14693,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14692])).
% 2.54/2.78 tff(14694,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[14693, 14691])).
% 2.54/2.78 tff(14695,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(14696,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[14695, 14694])).
% 2.54/2.78 tff(14697,plain,
% 2.54/2.78 ((~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(elem!1))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14696, 268, 14690])).
% 2.54/2.78 tff(14698,plain,
% 2.54/2.78 (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14697, 14658])).
% 2.54/2.78 tff(14699,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[6101, 69, 2884, 14698, 14688])).
% 2.54/2.78 tff(14700,plain,((s(s(s(s(s(z))))) = elem!1) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(14701,plain,
% 2.54/2.78 (s(s(s(s(s(z))))) = elem!1),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14700, 14527, 523, 1633, 499, 14554, 1149, 2077, 1132, 1545, 14611])).
% 2.54/2.78 tff(14702,plain,
% 2.54/2.78 (elem!1 = s(s(s(s(s(z)))))),
% 2.54/2.78 inference(symmetry,[status(thm)],[14701])).
% 2.54/2.78 tff(14703,plain,
% 2.54/2.78 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14702])).
% 2.54/2.78 tff(14704,plain,
% 2.54/2.78 ((s(s(z)) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.54/2.78 inference(transitivity,[status(thm)],[14703, 4133])).
% 2.54/2.78 tff(14705,plain,
% 2.54/2.78 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.54/2.78 inference(symmetry,[status(thm)],[14704])).
% 2.54/2.78 tff(14706,plain,
% 2.54/2.78 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14705])).
% 2.54/2.78 tff(14707,plain,
% 2.54/2.78 (~(s(s(z)) = elem!1)),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[52, 14706])).
% 2.54/2.78 tff(14708,plain,
% 2.54/2.78 (~r(s(s(z)), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14470, 14611, 1545, 523])).
% 2.54/2.78 tff(14709,plain,
% 2.54/2.78 (~b(s(s(z)), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[11018, 14701, 2077, 499, 1545])).
% 2.54/2.78 tff(14710,plain,
% 2.54/2.78 (s(s(z)) = elem!1),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[782, 14709, 14708])).
% 2.54/2.78 tff(14711,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14710, 14707])).
% 2.54/2.78 tff(14712,plain,((~r(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(s(z)))) = elem!1) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(14713,plain,
% 2.54/2.78 (~r(elem!1, s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14712, 14415, 13417, 14381, 523, 1633, 1132, 3, 13408])).
% 2.54/2.78 tff(14714,plain,
% 2.54/2.78 (elem!1 = s(s(s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4492, 14713, 4490])).
% 2.54/2.78 tff(14715,plain,
% 2.54/2.78 (s(s(s(z))) = elem!1),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4487, 14714])).
% 2.54/2.78 tff(14716,plain,
% 2.54/2.78 (b(s(s(s(s(z)))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4123, 14715, 523])).
% 2.54/2.78 tff(14717,plain,
% 2.54/2.78 (s(s(s(s(s(z))))) = elem!1),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14582, 14716, 14415, 14381, 13408, 13417, 1132, 1633, 523])).
% 2.54/2.78 tff(14718,plain,
% 2.54/2.78 (~r(s(z), s(s(s(s(s(z))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[5592, 14717, 4541])).
% 2.54/2.78 tff(14719,plain,
% 2.54/2.78 (b(s(z), s(s(s(s(s(z))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[372, 14718])).
% 2.54/2.78 tff(14720,plain,
% 2.54/2.78 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[11166, 14719, 13408, 13417])).
% 2.54/2.78 tff(14721,plain,
% 2.54/2.78 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4457, 14720, 14715])).
% 2.54/2.78 tff(14722,plain,
% 2.54/2.78 (~b(s(s(z)), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[5574, 14716, 13408, 13417, 1132])).
% 2.54/2.78 tff(14723,plain,
% 2.54/2.78 (b(s(elem!1), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[528, 14715, 523])).
% 2.54/2.78 tff(14724,plain,
% 2.54/2.78 (~b(s(z), s(elem!1))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[3403, 14723, 13408, 13417])).
% 2.54/2.78 tff(14725,plain,
% 2.54/2.78 (~(s(s(z)) = elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[3644, 14724, 14415])).
% 2.54/2.78 tff(14726,plain,
% 2.54/2.78 (r(s(s(z)), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[782, 14725, 14722])).
% 2.54/2.78 tff(14727,plain,
% 2.54/2.78 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[10463, 14726, 14381])).
% 2.54/2.78 tff(14728,plain,
% 2.54/2.78 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4066, 14727, 14715])).
% 2.54/2.78 tff(14729,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[687, 14728, 14721])).
% 2.54/2.78 tff(14730,plain,(b(elem!1, s(s(s(z)))) | r(s(z), elem!1) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(14731,plain,
% 2.54/2.78 (b(elem!1, s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14730, 1099, 4541, 14411, 14409, 13423])).
% 2.54/2.78 tff(14732,plain,
% 2.54/2.78 (~b(s(s(s(z))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[5392, 221, 14381, 13415, 13423, 1057])).
% 2.54/2.78 tff(14733,plain,
% 2.54/2.78 (b(elem!1, s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1087, 1085, 14386])).
% 2.54/2.78 tff(14734,plain,
% 2.54/2.78 (~b(s(s(s(z))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1621, 14733, 14409, 14731])).
% 2.54/2.78 tff(14735,plain,
% 2.54/2.78 (r(s(s(s(z))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[134, 14734])).
% 2.54/2.78 tff(14736,plain,
% 2.54/2.78 (~r(elem!1, s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1586, 14735, 14381])).
% 2.54/2.78 tff(14737,plain,
% 2.54/2.78 (b(s(s(s(z))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[11883, 221, 1057, 4541, 13417, 14736, 14734, 13423, 13415])).
% 2.54/2.78 tff(14738,plain,
% 2.54/2.78 (r(s(s(s(s(z)))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12998, 14737, 14411, 13423, 1085])).
% 2.54/2.78 tff(14739,plain,
% 2.54/2.78 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[11146, 14738, 13408, 1099, 13417, 637])).
% 2.54/2.78 tff(14740,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[328, 14414, 14739])).
% 2.54/2.78 tff(14741,plain,(b(s(z), s(s(s(z)))) | (s(s(s(s(s(z))))) = elem!1) | r(elem!1, s(s(s(s(z))))) | b(s(s(s(s(z)))), s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(14742,plain,
% 2.54/2.78 (b(s(z), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14741, 1085, 637, 1057, 4541])).
% 2.54/2.78 tff(14743,plain,
% 2.54/2.78 (r(s(s(s(s(z)))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14449, 14742, 1099, 637, 14409, 14381, 14411, 13423, 1085, 13408, 13417])).
% 2.54/2.78 tff(14744,plain,
% 2.54/2.78 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[11146, 14743, 13408, 1099, 13417, 637])).
% 2.54/2.78 tff(14745,plain,
% 2.54/2.78 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[328, 14744])).
% 2.54/2.78 tff(14746,plain,
% 2.54/2.78 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1788, 14745, 14411, 14409])).
% 2.54/2.78 tff(14747,plain,
% 2.54/2.78 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[687, 14746])).
% 2.54/2.78 tff(14748,plain,
% 2.54/2.78 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1566, 14747, 14381])).
% 2.54/2.78 tff(14749,plain,
% 2.54/2.78 (b(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[643, 14748, 637])).
% 2.54/2.78 tff(14750,plain,
% 2.54/2.78 (~(elem!1 = s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[9921, 636, 258])).
% 2.54/2.78 tff(14751,plain,
% 2.54/2.78 (b(elem!1, s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1130, 14750, 2076])).
% 2.54/2.78 tff(14752,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(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(14753,plain,
% 2.54/2.78 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(14754,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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(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(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14753])).
% 2.54/2.78 tff(14755,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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(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(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[14754, 14752])).
% 2.54/2.78 tff(14756,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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(14757,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[14756, 14755])).
% 2.54/2.78 tff(14758,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14757, 453, 2077, 2611, 2090, 1275])).
% 2.54/2.78 tff(14759,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(14760,plain,
% 2.54/2.78 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14759, 14751, 2090, 1275])).
% 2.54/2.78 tff(14761,plain,
% 2.54/2.78 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2570, 14760])).
% 2.54/2.78 tff(14762,plain,
% 2.54/2.78 (b(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[643, 636, 637])).
% 2.54/2.78 tff(14763,plain,
% 2.54/2.78 (~(s(z) = elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1125, 14750])).
% 2.54/2.78 tff(14764,plain,
% 2.54/2.78 (b(s(z), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[506, 14763, 4541])).
% 2.54/2.78 tff(14765,plain,
% 2.54/2.78 (~b(s(z), s(s(s(s(s(z))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[11166, 14764, 14751, 14762])).
% 2.54/2.78 tff(14766,plain,
% 2.54/2.78 (r(s(z), s(s(s(s(s(z))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[372, 14765])).
% 2.54/2.78 tff(14767,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(14768,plain,
% 2.54/2.78 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(14769,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14768])).
% 2.54/2.78 tff(14770,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[14769, 14767])).
% 2.54/2.78 tff(14771,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(14772,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[14771, 14770])).
% 2.54/2.78 tff(14773,plain,
% 2.54/2.78 (~r(s(s(s(z))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14772, 268, 14766, 14761])).
% 2.54/2.78 tff(14774,plain,
% 2.54/2.78 (b(s(s(s(z))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[134, 14773])).
% 2.54/2.78 tff(14775,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[5523, 453, 14764, 14751, 14774, 1275])).
% 2.54/2.78 tff(14776,plain,(r(s(s(s(s(s(z))))), elem!1) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | r(s(z), elem!1) | r(elem!1, s(z)) | (~r(s(s(s(s(s(z))))), s(z))) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(14777,plain,
% 2.54/2.78 (~r(s(s(s(s(s(z))))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14776, 14748, 14731, 4541, 14736, 14742, 637])).
% 2.54/2.78 tff(14778,plain,
% 2.54/2.78 (b(s(s(s(s(s(z))))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[297, 14777])).
% 2.54/2.78 tff(14779,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[5331, 14778, 14749, 13408, 13417])).
% 2.54/2.78 tff(14780,plain,(r(elem!1, s(s(s(s(z))))) | (s(s(s(s(s(z))))) = elem!1) | r(s(z), elem!1) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(14781,plain,
% 2.54/2.78 (r(elem!1, s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14780, 637, 4541, 1057])).
% 2.54/2.78 tff(14782,plain,
% 2.54/2.78 (~r(elem!1, s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12993, 14781, 1099])).
% 2.54/2.78 tff(14783,plain,
% 2.54/2.78 (b(s(s(s(z))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[11883, 221, 1057, 4541, 13417, 14782, 14732, 13423, 13415])).
% 2.54/2.78 tff(14784,plain,
% 2.54/2.78 (~b(s(s(s(s(z)))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[9834, 14783, 14409, 14731])).
% 2.54/2.78 tff(14785,plain,
% 2.54/2.78 (r(s(s(s(s(z)))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[254, 14784, 13423])).
% 2.54/2.78 tff(14786,plain,
% 2.54/2.78 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[11146, 14785, 13408, 1099, 13417, 637])).
% 2.54/2.78 tff(14787,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[328, 14786, 14414])).
% 2.54/2.78 tff(14788,plain,(b(s(z), s(s(s(z)))) | (s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(z)))), s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(14789,plain,
% 2.54/2.78 (b(s(z), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14788, 637, 1057, 4541])).
% 2.54/2.78 tff(14790,plain,
% 2.54/2.78 (~b(s(s(s(s(z)))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14582, 14789, 637, 14381, 13408, 13417, 1099, 14411, 14409])).
% 2.54/2.78 tff(14791,plain,
% 2.54/2.78 (r(s(s(s(s(z)))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[254, 14790, 13423])).
% 2.54/2.78 tff(14792,plain,
% 2.54/2.78 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[11146, 14791, 13408, 1099, 13417, 637])).
% 2.54/2.78 tff(14793,plain,
% 2.54/2.78 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[328, 14792])).
% 2.54/2.78 tff(14794,plain,
% 2.54/2.78 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1788, 14793, 14411, 14409])).
% 2.54/2.78 tff(14795,plain,
% 2.54/2.78 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[687, 14794])).
% 2.54/2.78 tff(14796,plain,
% 2.54/2.78 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1566, 14795, 14381])).
% 2.54/2.78 tff(14797,plain,
% 2.54/2.78 (b(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[643, 14796, 637])).
% 2.54/2.78 tff(14798,plain,
% 2.54/2.78 (~r(s(s(s(s(s(z))))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14776, 14796, 14731, 4541, 14782, 14789, 637])).
% 2.54/2.78 tff(14799,plain,
% 2.54/2.78 (b(s(s(s(s(s(z))))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[297, 14798])).
% 2.54/2.78 tff(14800,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[5331, 14799, 14797, 13408, 13417])).
% 2.54/2.78 tff(14801,plain,((s(s(s(s(s(z))))) = elem!1) | r(s(z), elem!1) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(14802,plain,
% 2.54/2.78 (s(s(s(s(s(z))))) = elem!1),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14801, 1057, 4541])).
% 2.54/2.78 tff(14803,plain,
% 2.54/2.78 (elem!1 = s(s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[5538, 14802])).
% 2.54/2.78 tff(14804,plain,
% 2.54/2.78 (b(elem!1, s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14803])).
% 2.54/2.78 tff(14805,plain,
% 2.54/2.78 (b(s(s(s(s(s(z))))), s(z))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[13408, 14804])).
% 2.54/2.78 tff(14806,plain,
% 2.54/2.78 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14803])).
% 2.54/2.78 tff(14807,plain,
% 2.54/2.78 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[14731, 14806])).
% 2.54/2.78 tff(14808,plain,
% 2.54/2.78 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14803])).
% 2.54/2.78 tff(14809,plain,
% 2.54/2.78 ((s(s(s(z))) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[14808, 57])).
% 2.54/2.78 tff(14810,plain,
% 2.54/2.78 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 2.54/2.78 inference(symmetry,[status(thm)],[14809])).
% 2.54/2.78 tff(14811,plain,
% 2.54/2.78 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14810])).
% 2.54/2.78 tff(14812,plain,
% 2.54/2.78 (~(s(s(s(z))) = elem!1)),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[111, 14811])).
% 2.54/2.78 tff(14813,plain,
% 2.54/2.78 (~r(s(z), s(s(s(s(s(z))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[5592, 14802, 4541])).
% 2.54/2.78 tff(14814,plain,
% 2.54/2.78 (b(s(z), s(s(s(s(s(z))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[372, 14813])).
% 2.54/2.78 tff(14815,plain,
% 2.54/2.78 (~b(s(s(s(z))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[9007, 14805, 14807, 14814])).
% 2.54/2.78 tff(14816,plain,
% 2.54/2.78 (r(s(s(s(z))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[134, 14815])).
% 2.54/2.78 tff(14817,plain,
% 2.54/2.78 (~r(elem!1, s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1586, 14816, 14381])).
% 2.54/2.78 tff(14818,plain,
% 2.54/2.78 (~r(s(z), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[11061, 14816, 14802, 14817, 14812])).
% 2.54/2.78 tff(14819,plain,
% 2.54/2.78 (b(s(z), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[227, 14818])).
% 2.54/2.78 tff(14820,plain,
% 2.54/2.78 (~b(s(s(s(z))), s(s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[10450, 14819, 14807, 14805])).
% 2.54/2.78 tff(14821,plain,
% 2.54/2.78 (r(s(s(s(z))), s(s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[12870, 14820])).
% 2.54/2.78 tff(14822,plain,
% 2.54/2.78 (~b(s(s(z)), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[11018, 14802, 13408, 13417, 14381])).
% 2.54/2.78 tff(14823,plain,
% 2.54/2.78 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14803])).
% 2.54/2.78 tff(14824,plain,
% 2.54/2.78 ((s(s(z)) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.54/2.78 inference(transitivity,[status(thm)],[14823, 4133])).
% 2.54/2.78 tff(14825,plain,
% 2.54/2.78 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.54/2.78 inference(symmetry,[status(thm)],[14824])).
% 2.54/2.78 tff(14826,plain,
% 2.54/2.78 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14825])).
% 2.54/2.78 tff(14827,plain,
% 2.54/2.78 (~(s(s(z)) = elem!1)),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[52, 14826])).
% 2.54/2.78 tff(14828,plain,
% 2.54/2.78 (r(s(s(z)), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[782, 14827, 14822])).
% 2.54/2.78 tff(14829,plain,
% 2.54/2.78 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[10851, 14828, 14803])).
% 2.54/2.78 tff(14830,plain,
% 2.54/2.78 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14803])).
% 2.54/2.78 tff(14831,plain,
% 2.54/2.78 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[14381, 14830])).
% 2.54/2.78 tff(14832,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[3149, 268, 14831, 14829, 14821])).
% 2.54/2.78 tff(14833,plain,(b(s(s(s(s(z)))), s(z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(14834,plain,
% 2.54/2.78 (b(s(s(s(s(z)))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14833, 4541])).
% 2.54/2.78 tff(14835,plain,
% 2.54/2.78 (~b(elem!1, s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[11887, 14834, 13408, 13417])).
% 2.54/2.78 tff(14836,assumption,(~b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 2.54/2.78 tff(14837,plain,
% 2.54/2.78 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[518, 14836])).
% 2.54/2.78 tff(14838,plain,
% 2.54/2.78 (~r(s(s(s(s(z)))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4961, 14837, 14381])).
% 2.54/2.78 tff(14839,plain,
% 2.54/2.78 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[512, 14837, 14838])).
% 2.54/2.78 tff(14840,plain,
% 2.54/2.78 (~(s(s(s(z))) = elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[81, 14839])).
% 2.54/2.78 tff(14841,plain,
% 2.54/2.78 (~(elem!1 = s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4487, 14840])).
% 2.54/2.78 tff(14842,plain,
% 2.54/2.78 (~b(s(s(s(s(z)))), elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[5423, 1275, 499, 1764])).
% 2.54/2.78 tff(14843,plain,
% 2.54/2.78 (s(s(s(s(z)))) = elem!1),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[254, 14842, 239])).
% 2.54/2.78 tff(14844,plain,
% 2.54/2.78 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14843])).
% 2.54/2.78 tff(14845,plain,
% 2.54/2.78 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.78 inference(symmetry,[status(thm)],[14844])).
% 2.54/2.78 tff(14846,plain,
% 2.54/2.78 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[1275, 14845])).
% 2.54/2.78 tff(14847,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14836, 14846])).
% 2.54/2.78 tff(14848,plain,((~b(elem!1, s(s(s(z))))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), elem!1) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(14849,plain,
% 2.54/2.78 (~b(elem!1, s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[14848, 14836, 14838, 13417, 14834])).
% 2.54/2.78 tff(14850,plain,
% 2.54/2.78 (r(elem!1, s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4492, 14849, 14841])).
% 2.54/2.78 tff(14851,plain,
% 2.54/2.78 (~r(elem!1, s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[13281, 14850, 14837])).
% 2.54/2.78 tff(14852,plain,
% 2.54/2.78 (elem!1 = s(s(s(s(z))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[1087, 14851, 14835])).
% 2.54/2.78 tff(14853,plain,
% 2.54/2.78 (s(s(s(s(z)))) = elem!1),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[8, 14852])).
% 2.54/2.78 tff(14854,plain,
% 2.54/2.78 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[4108, 14853])).
% 2.54/2.78 tff(14855,plain,
% 2.54/2.78 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14854])).
% 2.54/2.78 tff(14856,plain,
% 2.54/2.78 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[14854, 14855])).
% 2.54/2.78 tff(14857,plain,
% 2.54/2.78 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.54/2.78 inference(symmetry,[status(thm)],[14856])).
% 2.54/2.78 tff(14858,plain,
% 2.54/2.78 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 2.54/2.78 inference(symmetry,[status(thm)],[14855])).
% 2.54/2.78 tff(14859,plain,
% 2.54/2.78 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14858])).
% 2.54/2.79 tff(14860,plain,
% 2.54/2.79 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14859])).
% 2.54/2.79 tff(14861,plain,
% 2.54/2.79 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[14860, 1307])).
% 2.54/2.79 tff(14862,plain,
% 2.54/2.79 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.54/2.79 inference(symmetry,[status(thm)],[14861])).
% 2.54/2.79 tff(14863,plain,
% 2.54/2.79 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14862])).
% 2.54/2.79 tff(14864,plain,
% 2.54/2.79 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1273, 14853])).
% 2.54/2.79 tff(14865,plain,
% 2.54/2.79 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1436, 14864])).
% 2.54/2.79 tff(14866,plain,
% 2.54/2.79 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[14865, 14863])).
% 2.54/2.79 tff(14867,plain,
% 2.54/2.79 (~(elem!1 = s(s(elem!1)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[4223, 14866])).
% 2.54/2.79 tff(14868,plain,
% 2.54/2.79 (~(s(elem!1) = s(s(elem!1)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1861, 14867])).
% 2.54/2.79 tff(14869,plain,
% 2.54/2.79 (~(s(s(elem!1)) = elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[3359, 14867])).
% 2.54/2.79 tff(14870,plain,
% 2.54/2.79 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14855])).
% 2.54/2.79 tff(14871,plain,
% 2.54/2.79 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14870])).
% 2.54/2.79 tff(14872,plain,
% 2.54/2.79 (~(s(s(z)) = s(s(elem!1)))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[2661, 14871])).
% 2.54/2.79 tff(14873,plain,
% 2.54/2.79 (elem!1 = s(s(s(s(z))))),
% 2.54/2.79 inference(symmetry,[status(thm)],[14853])).
% 2.54/2.79 tff(14874,plain,
% 2.54/2.79 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14873])).
% 2.54/2.79 tff(14875,plain,
% 2.54/2.79 ((s(s(z)) = elem!1) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.54/2.79 inference(transitivity,[status(thm)],[14874, 1])).
% 2.54/2.79 tff(14876,plain,
% 2.54/2.79 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.54/2.79 inference(symmetry,[status(thm)],[14875])).
% 2.54/2.79 tff(14877,plain,
% 2.54/2.79 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14876])).
% 2.54/2.79 tff(14878,plain,
% 2.54/2.79 (~(s(s(z)) = elem!1)),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[153, 14877])).
% 2.54/2.79 tff(14879,plain,
% 2.54/2.79 ((s(elem!1) = s(s(s(s(z))))) <=> (s(elem!1) = elem!1)),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14853])).
% 2.54/2.79 tff(14880,plain,
% 2.54/2.79 ((s(elem!1) = s(s(s(s(z))))) <=> (elem!1 = s(elem!1))),
% 2.54/2.79 inference(transitivity,[status(thm)],[14879, 1028])).
% 2.54/2.79 tff(14881,plain,
% 2.54/2.79 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(elem!1 = s(elem!1)))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14880])).
% 2.54/2.79 tff(14882,plain,
% 2.54/2.79 (~(elem!1 = s(elem!1))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[14839, 14881])).
% 2.54/2.79 tff(14883,plain,
% 2.54/2.79 (b(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[643, 5003, 1544])).
% 2.54/2.79 tff(14884,plain,
% 2.54/2.79 (~b(s(s(s(s(s(z))))), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5331, 14883, 2077, 499])).
% 2.54/2.79 tff(14885,plain,
% 2.54/2.79 (r(s(s(s(s(s(z))))), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[297, 14884])).
% 2.54/2.79 tff(14886,plain,
% 2.54/2.79 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(elem!1))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[8112])).
% 2.54/2.79 tff(14887,plain,
% 2.54/2.79 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.54/2.79 inference(symmetry,[status(thm)],[14886])).
% 2.54/2.79 tff(14888,plain,
% 2.54/2.79 (~r(elem!1, s(elem!1))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[8690, 268, 1149, 8114])).
% 2.54/2.79 tff(14889,plain,
% 2.54/2.79 (b(elem!1, s(elem!1))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1069, 14888, 1056])).
% 2.54/2.79 tff(14890,plain,
% 2.54/2.79 (b(elem!1, s(s(s(s(s(z))))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[14889, 14887])).
% 2.54/2.79 tff(14891,plain,
% 2.54/2.79 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[14887, 6974])).
% 2.54/2.79 tff(14892,plain,
% 2.54/2.79 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[14889, 14891])).
% 2.54/2.79 tff(14893,plain,
% 2.54/2.79 (r(s(s(elem!1)), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[6717, 14892, 499, 1170, 14883])).
% 2.54/2.79 tff(14894,plain,
% 2.54/2.79 (~b(s(s(elem!1)), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[11032, 700, 1545, 13803, 5181, 4227, 499, 2077])).
% 2.54/2.79 tff(14895,plain,
% 2.54/2.79 (r(s(s(elem!1)), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1047, 14894])).
% 2.54/2.79 tff(14896,plain,
% 2.54/2.79 (~r(s(s(z)), s(s(elem!1)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5845, 268, 14895, 869, 700])).
% 2.54/2.79 tff(14897,plain,
% 2.54/2.79 (b(s(s(z)), s(s(elem!1)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[4239, 69, 4227, 14896])).
% 2.54/2.79 tff(14898,plain,
% 2.54/2.79 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[13803, 4163])).
% 2.54/2.79 tff(14899,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(14900,plain,
% 2.54/2.79 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(14901,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14900])).
% 2.54/2.79 tff(14902,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 2.54/2.79 inference(transitivity,[status(thm)],[14901, 14899])).
% 2.54/2.79 tff(14903,plain,
% 2.54/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(14904,plain,
% 2.54/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[14903, 14902])).
% 2.54/2.79 tff(14905,plain,
% 2.54/2.79 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14904, 268, 869, 1545])).
% 2.54/2.79 tff(14906,plain,
% 2.54/2.79 ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[4175, 69, 14905])).
% 2.54/2.79 tff(14907,plain,
% 2.54/2.79 (b(s(s(elem!1)), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14906, 14898])).
% 2.54/2.79 tff(14908,plain,
% 2.54/2.79 (((~![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(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(14909,plain,
% 2.54/2.79 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(14910,plain,
% 2.54/2.79 (((~![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(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14909])).
% 2.54/2.79 tff(14911,plain,
% 2.54/2.79 (((~![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(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[14910, 14908])).
% 2.54/2.79 tff(14912,plain,
% 2.54/2.79 ((~![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(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(14913,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[14912, 14911])).
% 2.54/2.79 tff(14914,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14913, 453, 14907, 14468, 14467, 14897])).
% 2.54/2.79 tff(14915,plain,((~r(s(s(z)), elem!1)) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = elem!1) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(14916,plain,
% 2.54/2.79 (~r(s(s(z)), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14915, 14893, 1545, 8699, 8693, 499, 2077])).
% 2.54/2.79 tff(14917,plain,
% 2.54/2.79 (b(s(s(z)), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[782, 14916, 12350])).
% 2.54/2.79 tff(14918,plain,
% 2.54/2.79 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[4078, 14917, 14883, 14890])).
% 2.54/2.79 tff(14919,plain,
% 2.54/2.79 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[4081, 14918])).
% 2.54/2.79 tff(14920,plain,
% 2.54/2.79 (~b(s(z), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14641, 14917, 2077, 499])).
% 2.54/2.79 tff(14921,plain,
% 2.54/2.79 (r(s(z), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[757, 14920])).
% 2.54/2.79 tff(14922,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2476, 14921, 14919, 14885])).
% 2.54/2.79 tff(14923,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~(s(s(s(s(z)))) = elem!1)) | (elem!1 = s(elem!1)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(14924,plain,
% 2.54/2.79 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14923, 14853, 13417, 14381, 13408, 14882, 14850])).
% 2.54/2.79 tff(14925,plain,
% 2.54/2.79 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[687, 14924])).
% 2.54/2.79 tff(14926,plain,
% 2.54/2.79 (b(s(z), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[12645, 14849, 4541])).
% 2.54/2.79 tff(14927,plain,
% 2.54/2.79 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(elem!1) = elem!1))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[12327])).
% 2.54/2.79 tff(14928,plain,
% 2.54/2.79 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[512, 11, 14382])).
% 2.54/2.79 tff(14929,plain,
% 2.54/2.79 (~(s(elem!1) = elem!1)),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[14928, 14927])).
% 2.54/2.79 tff(14930,plain,
% 2.54/2.79 (~b(s(s(elem!1)), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[12401, 922, 13408, 8699, 13417])).
% 2.54/2.79 tff(14931,plain,
% 2.54/2.79 (r(s(s(elem!1)), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2240, 14930, 8693])).
% 2.54/2.79 tff(14932,plain,
% 2.54/2.79 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5213, 14931, 14381])).
% 2.54/2.79 tff(14933,plain,
% 2.54/2.79 (b(s(s(s(z))), s(s(elem!1)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5203, 14932, 14385])).
% 2.54/2.79 tff(14934,plain,
% 2.54/2.79 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[14385, 4163])).
% 2.54/2.79 tff(14935,plain,
% 2.54/2.79 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14904, 268, 14931, 14381])).
% 2.54/2.79 tff(14936,plain,
% 2.54/2.79 ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[4175, 69, 14935])).
% 2.54/2.79 tff(14937,plain,
% 2.54/2.79 (b(s(s(elem!1)), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14936, 14934])).
% 2.54/2.79 tff(14938,plain,
% 2.54/2.79 (((~![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(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(14939,plain,
% 2.54/2.79 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(14940,plain,
% 2.54/2.79 (((~![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(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z)))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14939])).
% 2.54/2.79 tff(14941,plain,
% 2.54/2.79 (((~![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(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[14940, 14938])).
% 2.54/2.79 tff(14942,plain,
% 2.54/2.79 ((~![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(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(14943,plain,
% 2.54/2.79 ((~![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(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z)))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[14942, 14941])).
% 2.54/2.79 tff(14944,plain,
% 2.54/2.79 (~b(s(elem!1), s(s(elem!1)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14943, 453, 14937, 8646, 14933])).
% 2.54/2.79 tff(14945,plain,
% 2.54/2.79 (r(s(elem!1), s(s(elem!1)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[440, 14944, 8134])).
% 2.54/2.79 tff(14946,plain,
% 2.54/2.79 (~r(s(elem!1), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[11373, 14945, 14931])).
% 2.54/2.79 tff(14947,plain,
% 2.54/2.79 (b(s(elem!1), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2440, 14946, 14929])).
% 2.54/2.79 tff(14948,plain,
% 2.54/2.79 (~b(s(z), s(elem!1))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[3403, 14947, 13408, 13417])).
% 2.54/2.79 tff(14949,plain,
% 2.54/2.79 (r(s(z), s(elem!1))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[397, 14948, 12417])).
% 2.54/2.79 tff(14950,plain,
% 2.54/2.79 (~(s(s(s(z))) = elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[81, 14928])).
% 2.54/2.79 tff(14951,plain,
% 2.54/2.79 (b(s(s(s(s(s(z))))), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[7006, 14947, 1170])).
% 2.54/2.79 tff(14952,plain,
% 2.54/2.79 (~b(s(s(s(s(s(z))))), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5331, 14951, 13408, 13417])).
% 2.54/2.79 tff(14953,plain,
% 2.54/2.79 (r(s(s(s(s(s(z))))), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[297, 14952])).
% 2.54/2.79 tff(14954,plain,
% 2.54/2.79 (~b(s(z), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14641, 922, 13408, 13417])).
% 2.54/2.79 tff(14955,plain,
% 2.54/2.79 (r(s(z), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[757, 14954])).
% 2.54/2.79 tff(14956,plain,
% 2.54/2.79 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[2476, 14953, 14955])).
% 2.54/2.79 tff(14957,plain,
% 2.54/2.79 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[4081, 14956])).
% 2.54/2.79 tff(14958,plain,
% 2.54/2.79 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[4078, 14957, 922, 14951])).
% 2.54/2.79 tff(14959,plain,
% 2.54/2.79 (r(elem!1, s(s(s(s(s(z))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[466, 14958, 6982])).
% 2.54/2.79 tff(14960,plain,
% 2.54/2.79 (~r(elem!1, s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[3465, 14959, 14953])).
% 2.54/2.79 tff(14961,plain,
% 2.54/2.79 (~b(s(s(s(z))), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5513, 4542, 5446, 2090])).
% 2.54/2.79 tff(14962,plain,
% 2.54/2.79 (r(s(s(s(z))), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[74, 14961, 59])).
% 2.54/2.79 tff(14963,plain,
% 2.54/2.79 (~r(s(s(s(s(z)))), elem!1)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[4961, 14962, 11])).
% 2.54/2.79 tff(14964,plain,
% 2.54/2.79 (s(s(s(s(z)))) = elem!1),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[254, 14963, 249])).
% 2.54/2.79 tff(14965,plain,
% 2.54/2.79 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14964])).
% 2.54/2.79 tff(14966,plain,
% 2.54/2.79 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14965])).
% 2.54/2.79 tff(14967,plain,
% 2.54/2.79 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 2.54/2.79 inference(symmetry,[status(thm)],[14966])).
% 2.54/2.79 tff(14968,plain,
% 2.54/2.79 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14967])).
% 2.54/2.79 tff(14969,plain,
% 2.54/2.79 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 2.54/2.79 inference(symmetry,[status(thm)],[14968])).
% 2.54/2.79 tff(14970,plain,
% 2.54/2.79 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (s(z) = s(s(s(elem!1))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14969])).
% 2.54/2.79 tff(14971,plain,
% 2.54/2.79 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(z))),
% 2.54/2.79 inference(transitivity,[status(thm)],[14970, 1470])).
% 2.54/2.79 tff(14972,plain,
% 2.54/2.79 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(s(s(s(s(z))))))))),
% 2.54/2.79 inference(symmetry,[status(thm)],[14971])).
% 2.54/2.79 tff(14973,plain,
% 2.54/2.79 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = s(s(s(s(s(s(s(z)))))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14972])).
% 2.54/2.79 tff(14974,plain,
% 2.54/2.79 (~(s(z) = s(s(s(s(s(s(s(z))))))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[851, 14973])).
% 2.54/2.79 tff(14975,plain,
% 2.54/2.79 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14968])).
% 2.54/2.79 tff(14976,plain,
% 2.54/2.79 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.54/2.79 inference(transitivity,[status(thm)],[14975, 8506])).
% 2.54/2.79 tff(14977,plain,
% 2.54/2.79 ((~(elem!1 = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14976])).
% 2.54/2.79 tff(14978,plain,
% 2.54/2.79 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14964])).
% 2.54/2.79 tff(14979,plain,
% 2.54/2.79 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[14978, 1391])).
% 2.54/2.79 tff(14980,plain,
% 2.54/2.79 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14979])).
% 2.54/2.79 tff(14981,plain,
% 2.54/2.79 (~(elem!1 = s(s(s(elem!1))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[6514, 14980])).
% 2.54/2.79 tff(14982,plain,
% 2.54/2.79 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[14981, 14977])).
% 2.54/2.79 tff(14983,plain,
% 2.54/2.79 ((s(elem!1) = s(s(s(s(z))))) <=> (s(elem!1) = elem!1)),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14964])).
% 2.54/2.79 tff(14984,plain,
% 2.54/2.79 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(elem!1) = elem!1))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14983])).
% 2.54/2.79 tff(14985,plain,
% 2.54/2.79 (~(s(elem!1) = elem!1)),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[79, 14984])).
% 2.54/2.79 tff(14986,plain,
% 2.54/2.79 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14965])).
% 2.54/2.79 tff(14987,plain,
% 2.54/2.79 (b(s(elem!1), s(s(s(z))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[1779, 14986])).
% 2.54/2.79 tff(14988,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(14989,plain,
% 2.54/2.79 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(14990,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[14989])).
% 2.54/2.79 tff(14991,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[14990, 14988])).
% 2.54/2.79 tff(14992,plain,
% 2.54/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(14993,plain,
% 2.54/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[14992, 14991])).
% 2.54/2.79 tff(14994,plain,
% 2.54/2.79 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[14993, 268, 233, 1545, 8292])).
% 2.54/2.79 tff(14995,plain,
% 2.54/2.79 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1191, 1170])).
% 2.54/2.79 tff(14996,plain,
% 2.54/2.79 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1238, 69, 14995, 14994])).
% 2.54/2.79 tff(14997,plain,
% 2.54/2.79 ((~r(s(s(s(z))), s(elem!1))) <=> (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[7019])).
% 2.54/2.79 tff(14998,plain,
% 2.54/2.79 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[8023, 268, 1892, 8292])).
% 2.54/2.79 tff(14999,plain,
% 2.54/2.79 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[1287, 69, 6678, 14998])).
% 2.54/2.79 tff(15000,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), introduced(assumption)).
% 2.54/2.80 tff(15001,plain,
% 2.54/2.80 (~r(s(s(s(z))), s(elem!1))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[7015, 268, 1892, 1545])).
% 2.54/2.80 tff(15002,plain,
% 2.54/2.80 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.80 inference(modus_ponens,[status(thm)],[15001, 14997])).
% 2.54/2.80 tff(15003,plain,
% 2.54/2.80 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[2570, 15002])).
% 2.54/2.80 tff(15004,plain,
% 2.54/2.80 (b(s(s(s(z))), s(elem!1))),
% 2.54/2.80 inference(modus_ponens,[status(thm)],[15003, 7045])).
% 2.54/2.80 tff(15005,plain,
% 2.54/2.80 (((~![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(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.54/2.80 inference(rewrite,[status(thm)],[])).
% 2.54/2.80 tff(15006,plain,
% 2.54/2.80 (((~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.54/2.80 inference(rewrite,[status(thm)],[])).
% 2.54/2.80 tff(15007,plain,
% 2.54/2.80 (((~![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(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 2.54/2.80 inference(monotonicity,[status(thm)],[15006])).
% 2.54/2.80 tff(15008,plain,
% 2.54/2.80 (((~![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(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.54/2.80 inference(transitivity,[status(thm)],[15007, 15005])).
% 2.54/2.80 tff(15009,plain,
% 2.54/2.80 ((~![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(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.54/2.80 inference(quant_inst,[status(thm)],[])).
% 2.54/2.80 tff(15010,plain,
% 2.54/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.54/2.80 inference(modus_ponens,[status(thm)],[15009, 15008])).
% 2.54/2.80 tff(15011,plain,
% 2.54/2.80 ($false),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[15010, 453, 15004, 8937, 15000, 14999])).
% 2.54/2.80 tff(15012,plain,((~r(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~(s(s(s(s(z)))) = elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(15013,plain,
% 2.64/2.80 (~r(s(elem!1), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[15012, 14996, 8937, 1170, 8292, 1545])).
% 2.64/2.80 tff(15014,plain,
% 2.64/2.80 (b(s(elem!1), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[2440, 15013, 605])).
% 2.64/2.80 tff(15015,plain,
% 2.64/2.80 (~b(s(elem!1), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12153, 453, 499, 2077, 15014])).
% 2.64/2.80 tff(15016,plain,
% 2.64/2.80 (r(s(elem!1), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[353, 15015, 1182])).
% 2.64/2.80 tff(15017,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(15018,plain,
% 2.64/2.80 (((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(15019,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z)))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[15018])).
% 2.64/2.80 tff(15020,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 2.64/2.80 inference(transitivity,[status(thm)],[15019, 15017])).
% 2.64/2.80 tff(15021,plain,
% 2.64/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(15022,plain,
% 2.64/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z)))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[15021, 15020])).
% 2.64/2.80 tff(15023,plain,
% 2.64/2.80 (~r(s(s(s(z))), s(elem!1))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[15022, 268, 15016, 233])).
% 2.64/2.80 tff(15024,plain,
% 2.64/2.80 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[15023, 14997])).
% 2.64/2.80 tff(15025,plain,
% 2.64/2.80 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[2570, 15024])).
% 2.64/2.80 tff(15026,plain,
% 2.64/2.80 (b(s(s(s(z))), s(elem!1))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[15025, 7045])).
% 2.64/2.80 tff(15027,plain,
% 2.64/2.80 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(15028,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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[15027])).
% 2.64/2.80 tff(15029,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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.64/2.80 inference(transitivity,[status(thm)],[15028, 15005])).
% 2.64/2.80 tff(15030,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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(15031,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(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[15030, 15029])).
% 2.64/2.80 tff(15032,plain,
% 2.64/2.80 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[15031, 453, 15026, 8937, 14996])).
% 2.64/2.80 tff(15033,plain,
% 2.64/2.80 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1287, 69, 6678, 15032])).
% 2.64/2.80 tff(15034,plain,
% 2.64/2.80 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[6673])).
% 2.64/2.80 tff(15035,plain,
% 2.64/2.80 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 2.64/2.80 inference(symmetry,[status(thm)],[6673])).
% 2.64/2.80 tff(15036,plain,
% 2.64/2.80 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[15035])).
% 2.64/2.80 tff(15037,plain,
% 2.64/2.80 ((~b(s(s(s(s(s(s(s(z))))))), s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[15036])).
% 2.64/2.80 tff(15038,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(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(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(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(15039,plain,
% 2.64/2.80 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(15040,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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(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(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[15039])).
% 2.64/2.80 tff(15041,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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(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(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.64/2.80 inference(transitivity,[status(thm)],[15040, 15038])).
% 2.64/2.80 tff(15042,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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(15043,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(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[15042, 15041])).
% 2.64/2.80 tff(15044,plain,
% 2.64/2.80 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[15043, 453, 15026, 2090, 14996])).
% 2.64/2.80 tff(15045,plain,
% 2.64/2.80 (~b(s(s(s(elem!1))), s(z))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[15044, 15037])).
% 2.64/2.80 tff(15046,plain,
% 2.64/2.80 (r(s(s(s(elem!1))), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[856, 15045])).
% 2.64/2.80 tff(15047,plain,
% 2.64/2.80 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[15046, 15034])).
% 2.64/2.80 tff(15048,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(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(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(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(15049,plain,
% 2.64/2.80 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(15050,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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(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(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[15049])).
% 2.64/2.80 tff(15051,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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(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(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.80 inference(transitivity,[status(thm)],[15050, 15048])).
% 2.64/2.80 tff(15052,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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(15053,plain,
% 2.64/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[15052, 15051])).
% 2.64/2.80 tff(15054,plain,
% 2.64/2.80 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[15053, 453, 15026, 8937, 14996])).
% 2.64/2.80 tff(15055,plain,
% 2.64/2.80 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1320, 15054, 6679])).
% 2.64/2.80 tff(15056,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[4048, 268, 15016, 15055, 15047, 15033])).
% 2.64/2.80 tff(15057,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~(s(s(s(s(z)))) = elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(elem!1) = elem!1) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(15058,plain,
% 2.64/2.80 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[15057, 14964, 14987, 2090, 233, 4542, 5446, 14985, 14962])).
% 2.64/2.80 tff(15059,plain,
% 2.64/2.80 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[3875, 15058, 14982])).
% 2.64/2.80 tff(15060,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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(15061,plain,
% 2.64/2.80 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(15062,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[15061])).
% 2.64/2.80 tff(15063,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.64/2.80 inference(transitivity,[status(thm)],[15062, 15060])).
% 2.64/2.80 tff(15064,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(15065,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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[15064, 15063])).
% 2.64/2.80 tff(15066,plain,
% 2.64/2.80 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[15065, 453, 4542, 5446, 15059])).
% 2.64/2.80 tff(15067,plain,
% 2.64/2.80 ((s(z) = s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1485, 69, 15066])).
% 2.64/2.80 tff(15068,plain,
% 2.64/2.80 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[15067, 14974])).
% 2.64/2.80 tff(15069,plain,
% 2.64/2.80 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1273, 14964])).
% 2.64/2.80 tff(15070,plain,
% 2.64/2.80 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1436, 15069])).
% 2.64/2.80 tff(15071,plain,
% 2.64/2.80 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[14968])).
% 2.64/2.80 tff(15072,plain,
% 2.64/2.80 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.64/2.80 inference(monotonicity,[status(thm)],[14968])).
% 2.64/2.80 tff(15073,plain,
% 2.64/2.80 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.64/2.80 inference(symmetry,[status(thm)],[15072])).
% 2.64/2.80 tff(15074,plain,
% 2.64/2.80 (b(s(s(s(elem!1))), elem!1)),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[15059, 15073])).
% 2.64/2.80 tff(15075,plain,
% 2.64/2.80 (~b(s(s(s(elem!1))), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[13666, 15074, 5446, 4542])).
% 2.64/2.80 tff(15076,plain,
% 2.64/2.80 (r(s(s(s(elem!1))), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[856, 15075])).
% 2.64/2.80 tff(15077,plain,
% 2.64/2.80 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[15076, 15071])).
% 2.64/2.80 tff(15078,plain,
% 2.64/2.80 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1535, 268, 233, 15077])).
% 2.64/2.80 tff(15079,plain,
% 2.64/2.80 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1191, 14964])).
% 2.64/2.80 tff(15080,plain,
% 2.64/2.80 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[1238, 69, 15079, 15078])).
% 2.64/2.80 tff(15081,plain,
% 2.64/2.80 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(elem!1))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[14965])).
% 2.64/2.80 tff(15082,plain,
% 2.64/2.80 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[14965])).
% 2.64/2.80 tff(15083,plain,
% 2.64/2.80 ((s(z) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(z))),
% 2.64/2.80 inference(transitivity,[status(thm)],[15082, 173])).
% 2.64/2.80 tff(15084,plain,
% 2.64/2.80 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 2.64/2.80 inference(transitivity,[status(thm)],[15083, 174])).
% 2.64/2.80 tff(15085,plain,
% 2.64/2.80 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(z) = s(elem!1)))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[15084])).
% 2.64/2.80 tff(15086,plain,
% 2.64/2.80 (~(s(z) = s(elem!1))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[289, 15085])).
% 2.64/2.80 tff(15087,plain,
% 2.64/2.80 (~r(s(elem!1), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[7017, 7009, 1545])).
% 2.64/2.80 tff(15088,plain,
% 2.64/2.80 (b(s(elem!1), elem!1)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[2440, 15087, 605])).
% 2.64/2.80 tff(15089,plain,
% 2.64/2.80 (~b(s(z), s(elem!1))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[12588, 15088, 1123, 2076, 4541])).
% 2.64/2.81 tff(15090,plain,
% 2.64/2.81 (r(s(z), s(elem!1))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[397, 15089, 177])).
% 2.64/2.81 tff(15091,plain,
% 2.64/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15092,plain,
% 2.64/2.81 (((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15093,plain,
% 2.64/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z)))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[15092])).
% 2.64/2.81 tff(15094,plain,
% 2.64/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[15093, 15091])).
% 2.64/2.81 tff(15095,plain,
% 2.64/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(15096,plain,
% 2.64/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z)))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[15095, 15094])).
% 2.64/2.81 tff(15097,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15096, 268, 15090, 233, 7009])).
% 2.64/2.81 tff(15098,plain,((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (s(z) = s(elem!1)) | (elem!1 = s(z)) | r(elem!1, s(z)) | r(s(z), elem!1) | (s(elem!1) = elem!1) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(15099,plain,
% 2.64/2.81 (~r(s(s(s(z))), s(elem!1))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15098, 15086, 233, 1123, 2076, 4541, 14985, 14962])).
% 2.64/2.81 tff(15100,plain,
% 2.64/2.81 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[7024, 15099, 14964])).
% 2.64/2.81 tff(15101,plain,
% 2.64/2.81 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2570, 15100])).
% 2.64/2.81 tff(15102,plain,
% 2.64/2.81 (b(s(s(s(z))), s(elem!1))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[15101, 15081])).
% 2.64/2.81 tff(15103,plain,
% 2.64/2.81 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15053, 453, 15102, 14987, 15080])).
% 2.64/2.81 tff(15104,plain,
% 2.64/2.81 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1320, 15103, 15070])).
% 2.64/2.81 tff(15105,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), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), 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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15106,plain,
% 2.64/2.81 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15107,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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(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(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[15106])).
% 2.64/2.81 tff(15108,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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(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(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[15107, 15105])).
% 2.64/2.81 tff(15109,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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(elem!1))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(15110,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), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[15109, 15108])).
% 2.64/2.81 tff(15111,plain,
% 2.64/2.81 (~b(s(z), s(elem!1))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15110, 453, 15102, 14987, 2090])).
% 2.64/2.81 tff(15112,plain,
% 2.64/2.81 (r(s(z), s(elem!1))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[397, 15111, 15086])).
% 2.64/2.81 tff(15113,plain,
% 2.64/2.81 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(elem!1) = s(z)))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[15083])).
% 2.64/2.81 tff(15114,plain,
% 2.64/2.81 (~(s(elem!1) = s(z))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[289, 15113])).
% 2.64/2.81 tff(15115,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(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), 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(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15116,plain,
% 2.64/2.81 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15117,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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[15116])).
% 2.64/2.81 tff(15118,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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[15117, 15115])).
% 2.64/2.81 tff(15119,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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(z))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(15120,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(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[15119, 15118])).
% 2.64/2.81 tff(15121,plain,
% 2.64/2.81 (~b(s(elem!1), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15120, 453, 15102, 14987, 2090])).
% 2.64/2.81 tff(15122,plain,
% 2.64/2.81 (r(s(elem!1), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[353, 15121, 15114])).
% 2.64/2.81 tff(15123,plain,
% 2.64/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15124,plain,
% 2.64/2.81 (((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15125,plain,
% 2.64/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[15124])).
% 2.64/2.81 tff(15126,plain,
% 2.64/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[15125, 15123])).
% 2.64/2.81 tff(15127,plain,
% 2.64/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(15128,plain,
% 2.64/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[15127, 15126])).
% 2.64/2.81 tff(15129,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15128, 268, 15122, 15112, 15104, 15068])).
% 2.64/2.81 tff(15130,plain,(r(s(z), elem!1) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (elem!1 = s(z)) | r(elem!1, s(z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (s(elem!1) = s(s(s(s(z))))) | b(s(s(s(s(z)))), elem!1) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(15131,plain,
% 2.64/2.81 (~r(s(s(s(z))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15130, 14960, 13415, 14928, 2090, 4541, 12405, 1779, 11, 14950])).
% 2.64/2.81 tff(15132,plain,
% 2.64/2.81 (b(s(s(s(z))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[134, 15131])).
% 2.64/2.81 tff(15133,plain,
% 2.64/2.81 (~b(s(s(elem!1)), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5215, 15132, 13408, 14385, 14381, 8693, 13417])).
% 2.64/2.81 tff(15134,plain,
% 2.64/2.81 (r(s(s(elem!1)), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1047, 15133])).
% 2.64/2.81 tff(15135,plain,
% 2.64/2.81 (~r(s(s(elem!1)), s(elem!1))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[3414, 15134, 14949])).
% 2.64/2.81 tff(15136,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15137,plain,
% 2.64/2.81 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15138,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[15137])).
% 2.64/2.81 tff(15139,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[15138, 15136])).
% 2.64/2.81 tff(15140,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(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(15141,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[15140, 15139])).
% 2.64/2.81 tff(15142,plain,
% 2.64/2.81 (~b(s(s(elem!1)), s(elem!1))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15141, 453, 14937, 8646, 14933])).
% 2.64/2.81 tff(15143,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1874, 69, 15142, 15135, 12404])).
% 2.64/2.81 tff(15144,plain,((~b(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | r(s(z), elem!1) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(15145,plain,
% 2.64/2.81 (~b(s(s(z)), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15144, 14926, 4541, 14925, 14837, 14853])).
% 2.64/2.81 tff(15146,plain,
% 2.64/2.81 (r(s(s(z)), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[782, 15145, 14878])).
% 2.64/2.81 tff(15147,plain,
% 2.64/2.81 (~r(s(s(elem!1)), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[14915, 15146, 14381, 14872, 14869, 13417, 13408])).
% 2.64/2.81 tff(15148,plain,
% 2.64/2.81 (b(s(s(elem!1)), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2240, 15147, 14869])).
% 2.64/2.81 tff(15149,plain,
% 2.64/2.81 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.64/2.81 inference(monotonicity,[status(thm)],[14853])).
% 2.64/2.81 tff(15150,plain,
% 2.64/2.81 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[15149, 55])).
% 2.64/2.81 tff(15151,plain,
% 2.64/2.81 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.64/2.81 inference(transitivity,[status(thm)],[15150, 56])).
% 2.64/2.81 tff(15152,plain,
% 2.64/2.81 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[15151])).
% 2.64/2.81 tff(15153,plain,
% 2.64/2.81 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[319, 15152])).
% 2.64/2.81 tff(15154,plain,
% 2.64/2.81 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[10463, 15146, 14381])).
% 2.64/2.81 tff(15155,plain,
% 2.64/2.81 (b(s(s(s(s(s(z))))), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[643, 15154, 15153])).
% 2.64/2.81 tff(15156,plain,
% 2.64/2.81 (b(s(elem!1), elem!1)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1336, 15155, 14853])).
% 2.64/2.81 tff(15157,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(elem!1, s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), 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(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15158,plain,
% 2.64/2.81 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(elem!1, s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15159,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[15158])).
% 2.64/2.81 tff(15160,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 2.64/2.81 inference(transitivity,[status(thm)],[15159, 15157])).
% 2.64/2.81 tff(15161,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(15162,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[15161, 15160])).
% 2.64/2.81 tff(15163,plain,
% 2.64/2.81 (~b(s(elem!1), s(s(elem!1)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15162, 453, 13408, 15156, 15148])).
% 2.64/2.81 tff(15164,plain,
% 2.64/2.81 (r(s(elem!1), s(s(elem!1)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[440, 15163, 14868])).
% 2.64/2.81 tff(15165,plain,
% 2.64/2.81 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[15164, 14857])).
% 2.64/2.81 tff(15166,plain,
% 2.64/2.81 (~b(s(s(s(s(s(z))))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5331, 15155, 13408, 13417])).
% 2.64/2.81 tff(15167,plain,
% 2.64/2.81 (r(s(s(s(s(s(z))))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[297, 15166])).
% 2.64/2.81 tff(15168,plain,
% 2.64/2.81 (r(s(s(s(s(s(s(z)))))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[14855])).
% 2.64/2.81 tff(15169,plain,
% 2.64/2.81 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.81 inference(symmetry,[status(thm)],[15168])).
% 2.64/2.81 tff(15170,plain,
% 2.64/2.81 (~b(s(s(elem!1)), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[11032, 15146, 14381, 14385, 14869, 14872, 13417, 13408])).
% 2.64/2.81 tff(15171,plain,
% 2.64/2.81 (r(s(s(elem!1)), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1047, 15170])).
% 2.64/2.81 tff(15172,plain,
% 2.64/2.81 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[15171, 15169])).
% 2.64/2.81 tff(15173,plain,
% 2.64/2.81 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[4805, 15172, 15167])).
% 2.64/2.81 tff(15174,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15173, 15165])).
% 2.64/2.81 tff(15175,plain,(b(s(s(s(s(z)))), s(s(s(z)))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(15176,plain,
% 2.64/2.81 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[15175, 4541])).
% 2.64/2.81 tff(15177,plain,
% 2.64/2.81 (r(elem!1, s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1087, 9, 14835])).
% 2.64/2.81 tff(15178,plain,
% 2.64/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15179,plain,
% 2.64/2.81 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(15180,plain,
% 2.64/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[15179])).
% 2.64/2.81 tff(15181,plain,
% 2.64/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[15180, 15178])).
% 2.64/2.82 tff(15182,plain,
% 2.64/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(15183,plain,
% 2.64/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[15182, 15181])).
% 2.64/2.82 tff(15184,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15183, 268, 1545, 300, 419])).
% 2.64/2.82 tff(15185,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(15186,plain,
% 2.64/2.82 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15185, 15177, 14381])).
% 2.64/2.82 tff(15187,plain,
% 2.64/2.82 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1656, 15186])).
% 2.64/2.82 tff(15188,plain,
% 2.64/2.82 (~b(s(z), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2102, 15187, 14834, 15176])).
% 2.64/2.82 tff(15189,plain,
% 2.64/2.82 (~(s(s(s(z))) = elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12720, 15188, 13408])).
% 2.64/2.82 tff(15190,plain,
% 2.64/2.82 (b(elem!1, s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12731, 15188])).
% 2.64/2.82 tff(15191,plain,
% 2.64/2.82 (r(s(z), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[227, 15188])).
% 2.64/2.82 tff(15192,plain,
% 2.64/2.82 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[5333, 637, 2077, 1545, 257, 499])).
% 2.64/2.82 tff(15193,plain,
% 2.64/2.82 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15185, 419, 1545])).
% 2.64/2.82 tff(15194,plain,
% 2.64/2.82 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1656, 15193])).
% 2.64/2.82 tff(15195,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(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(15196,plain,
% 2.64/2.82 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(15197,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15196])).
% 2.64/2.82 tff(15198,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[15197, 15195])).
% 2.64/2.82 tff(15199,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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(15200,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[15199, 15198])).
% 2.64/2.82 tff(15201,plain,
% 2.64/2.82 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15200, 453, 1633, 1779, 1275])).
% 2.64/2.82 tff(15202,plain,
% 2.64/2.82 (r(elem!1, s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[466, 15201, 2073])).
% 2.64/2.82 tff(15203,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[427, 15202, 11914, 419])).
% 2.64/2.82 tff(15204,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(15205,plain,
% 2.64/2.82 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15204, 8840, 15194, 419, 1275, 523])).
% 2.64/2.82 tff(15206,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[687, 15205, 15192])).
% 2.64/2.82 tff(15207,plain,((s(s(s(s(s(z))))) = elem!1) | (~r(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(15208,plain,
% 2.64/2.82 (s(s(s(s(s(z))))) = elem!1),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15207, 15177, 15190, 15176, 13408, 14381, 15191, 13417])).
% 2.64/2.82 tff(15209,plain,
% 2.64/2.82 (elem!1 = s(s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[5538, 15208])).
% 2.64/2.82 tff(15210,plain,
% 2.64/2.82 (~b(s(s(s(z))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[14118, 15209, 14834, 10372, 15190, 15189, 4541])).
% 2.64/2.82 tff(15211,plain,
% 2.64/2.82 (~b(s(s(s(z))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[5444, 15210, 15188, 3])).
% 2.64/2.82 tff(15212,plain,
% 2.64/2.82 (~r(elem!1, s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[10359, 15210, 3, 15188, 15189])).
% 2.64/2.82 tff(15213,plain,
% 2.64/2.82 (~r(s(s(s(z))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[11061, 15212, 15191, 15208, 15189])).
% 2.64/2.82 tff(15214,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[134, 15213, 15211])).
% 2.64/2.82 tff(15215,plain,((s(s(s(s(z)))) = elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(15216,plain,
% 2.64/2.82 (s(s(s(s(z)))) = elem!1),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15215, 4541])).
% 2.64/2.82 tff(15217,plain,
% 2.64/2.82 (b(elem!1, s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12270, 15216, 15176])).
% 2.64/2.82 tff(15218,plain,
% 2.64/2.82 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[4108, 15216])).
% 2.64/2.82 tff(15219,plain,
% 2.64/2.82 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15218])).
% 2.64/2.82 tff(15220,plain,
% 2.64/2.82 ((elem!1 = s(s(s(s(s(z)))))) <=> (elem!1 = s(elem!1))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15218])).
% 2.64/2.82 tff(15221,plain,
% 2.64/2.82 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(elem!1) = elem!1)),
% 2.64/2.82 inference(transitivity,[status(thm)],[15220, 1027])).
% 2.64/2.82 tff(15222,plain,
% 2.64/2.82 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.64/2.82 inference(symmetry,[status(thm)],[15221])).
% 2.64/2.82 tff(15223,plain,
% 2.64/2.82 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15218])).
% 2.64/2.82 tff(15224,plain,
% 2.64/2.82 (s(s(s(s(z)))) = elem!1),
% 2.64/2.82 inference(transitivity,[status(thm)],[284, 15223, 85])).
% 2.64/2.82 tff(15225,plain,
% 2.64/2.82 ((s(elem!1) = s(s(s(s(z))))) <=> (s(elem!1) = elem!1)),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15224])).
% 2.64/2.82 tff(15226,plain,
% 2.64/2.82 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.64/2.82 inference(transitivity,[status(thm)],[15225, 15222, 56])).
% 2.64/2.82 tff(15227,plain,
% 2.64/2.82 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15226])).
% 2.64/2.82 tff(15228,plain,
% 2.64/2.82 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15218])).
% 2.64/2.82 tff(15229,plain,
% 2.64/2.82 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15228])).
% 2.64/2.82 tff(15230,plain,
% 2.64/2.82 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[319, 15229])).
% 2.64/2.82 tff(15231,plain,
% 2.64/2.82 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[15230, 15227])).
% 2.64/2.82 tff(15232,plain,
% 2.64/2.82 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[14759, 2090, 13408, 15217])).
% 2.64/2.82 tff(15233,plain,
% 2.64/2.82 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2570, 15232])).
% 2.64/2.82 tff(15234,plain,
% 2.64/2.82 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15218])).
% 2.64/2.82 tff(15235,plain,
% 2.64/2.82 ((s(z) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(z))),
% 2.64/2.82 inference(transitivity,[status(thm)],[15234, 173])).
% 2.64/2.82 tff(15236,plain,
% 2.64/2.82 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 2.64/2.82 inference(transitivity,[status(thm)],[15235, 174])).
% 2.64/2.82 tff(15237,plain,
% 2.64/2.82 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(z) = s(elem!1)))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15236])).
% 2.64/2.82 tff(15238,plain,
% 2.64/2.82 (~(s(z) = s(elem!1))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[289, 15237])).
% 2.64/2.82 tff(15239,plain,
% 2.64/2.82 (~b(s(s(s(z))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[3782, 2090, 14834, 15176])).
% 2.64/2.82 tff(15240,plain,
% 2.64/2.82 (r(s(s(s(z))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[134, 15239])).
% 2.64/2.82 tff(15241,plain,
% 2.64/2.82 (~r(elem!1, s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1586, 15240, 14381])).
% 2.64/2.82 tff(15242,plain,
% 2.64/2.82 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(elem!1) = elem!1))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15225])).
% 2.64/2.82 tff(15243,plain,
% 2.64/2.82 (~(s(elem!1) = elem!1)),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[15230, 15242])).
% 2.64/2.82 tff(15244,plain,
% 2.64/2.82 (~r(s(s(s(z))), s(elem!1))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15098, 15240, 4541, 13415, 14381, 15243, 15241, 15238])).
% 2.64/2.82 tff(15245,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[7024, 15244, 15233, 15216])).
% 2.64/2.82 tff(15246,plain,((~b(s(z), s(s(s(z))))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(15247,plain,
% 2.64/2.82 (~b(s(z), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15246, 4541])).
% 2.64/2.82 tff(15248,plain,
% 2.64/2.82 (r(s(z), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[227, 15247])).
% 2.64/2.82 tff(15249,plain,
% 2.64/2.82 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[5333, 15248, 13408, 14381, 15231, 13417])).
% 2.64/2.82 tff(15250,plain,
% 2.64/2.82 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[687, 15249])).
% 2.64/2.82 tff(15251,plain,
% 2.64/2.82 (b(s(elem!1), s(s(s(z))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[15250, 15219])).
% 2.64/2.82 tff(15252,plain,
% 2.64/2.82 ((s(elem!1) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[15225, 15222])).
% 2.64/2.82 tff(15253,plain,
% 2.64/2.82 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15252])).
% 2.64/2.82 tff(15254,plain,
% 2.64/2.82 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[15230, 15253])).
% 2.64/2.82 tff(15255,plain,
% 2.64/2.82 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[8112])).
% 2.64/2.82 tff(15256,plain,
% 2.64/2.82 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(z))))))),
% 2.64/2.82 inference(symmetry,[status(thm)],[15255])).
% 2.64/2.82 tff(15257,plain,
% 2.64/2.82 (elem!1 = s(s(s(s(z))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[86, 15256, 23])).
% 2.64/2.82 tff(15258,plain,
% 2.64/2.82 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15257])).
% 2.64/2.82 tff(15259,plain,
% 2.64/2.82 ((s(s(z)) = elem!1) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.64/2.82 inference(transitivity,[status(thm)],[15258, 1])).
% 2.64/2.82 tff(15260,plain,
% 2.64/2.82 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.64/2.82 inference(symmetry,[status(thm)],[15259])).
% 2.64/2.82 tff(15261,plain,
% 2.64/2.82 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15260])).
% 2.64/2.82 tff(15262,plain,
% 2.64/2.82 (~(s(s(z)) = elem!1)),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[153, 15261])).
% 2.64/2.82 tff(15263,plain,
% 2.64/2.82 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.64/2.82 inference(symmetry,[status(thm)],[8641])).
% 2.64/2.82 tff(15264,plain,
% 2.64/2.82 (s(s(s(s(z)))) = elem!1),
% 2.64/2.82 inference(transitivity,[status(thm)],[284, 15255, 85])).
% 2.64/2.82 tff(15265,plain,
% 2.64/2.82 ((s(elem!1) = s(s(s(s(z))))) <=> (s(elem!1) = elem!1)),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15264])).
% 2.64/2.82 tff(15266,plain,
% 2.64/2.82 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.64/2.82 inference(transitivity,[status(thm)],[15265, 15263, 56])).
% 2.64/2.82 tff(15267,plain,
% 2.64/2.82 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15266])).
% 2.64/2.82 tff(15268,plain,
% 2.64/2.82 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[8112])).
% 2.64/2.82 tff(15269,plain,
% 2.64/2.82 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15268])).
% 2.64/2.82 tff(15270,plain,
% 2.64/2.82 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[319, 15269])).
% 2.64/2.82 tff(15271,plain,
% 2.64/2.82 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[15270, 15267])).
% 2.64/2.82 tff(15272,plain,
% 2.64/2.82 (r(s(s(s(s(s(z))))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[643, 638, 15271])).
% 2.64/2.82 tff(15273,plain,
% 2.64/2.82 (~r(s(s(z)), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[10463, 15272, 1545])).
% 2.64/2.82 tff(15274,plain,
% 2.64/2.82 (b(s(s(z)), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[782, 15273, 15262])).
% 2.64/2.82 tff(15275,plain,
% 2.64/2.82 (~b(s(s(elem!1)), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12401, 15274, 2077, 8699, 499])).
% 2.64/2.82 tff(15276,plain,
% 2.64/2.82 (r(s(s(elem!1)), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2240, 15275, 8693])).
% 2.64/2.82 tff(15277,plain,
% 2.64/2.82 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(elem!1) = elem!1))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15265])).
% 2.64/2.82 tff(15278,plain,
% 2.64/2.82 (~(s(elem!1) = elem!1)),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[15270, 15277])).
% 2.64/2.82 tff(15279,plain,
% 2.64/2.82 (r(s(elem!1), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2440, 7007, 15278])).
% 2.64/2.82 tff(15280,plain,
% 2.64/2.82 (~r(s(s(elem!1)), s(elem!1))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[11304, 268, 15279, 15276])).
% 2.64/2.82 tff(15281,plain,
% 2.64/2.82 (b(s(s(elem!1)), s(elem!1))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1874, 69, 15280, 12404])).
% 2.64/2.82 tff(15282,plain,
% 2.64/2.82 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[5213, 15276, 1545])).
% 2.64/2.82 tff(15283,plain,
% 2.64/2.82 (b(s(s(s(z))), s(s(elem!1)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[5203, 15282, 13803])).
% 2.64/2.82 tff(15284,plain,
% 2.64/2.82 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[8112])).
% 2.64/2.82 tff(15285,plain,
% 2.64/2.82 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.64/2.82 inference(transitivity,[status(thm)],[15284, 10379])).
% 2.64/2.82 tff(15286,plain,
% 2.64/2.82 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15285])).
% 2.64/2.82 tff(15287,plain,
% 2.64/2.82 (~(s(s(s(z))) = s(elem!1))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[111, 15286])).
% 2.64/2.82 tff(15288,plain,
% 2.64/2.82 (~r(s(s(s(z))), s(elem!1))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[7017, 15279, 1545])).
% 2.64/2.82 tff(15289,plain,
% 2.64/2.82 (b(s(s(s(z))), s(elem!1))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9480, 15288, 15287])).
% 2.64/2.82 tff(15290,plain,
% 2.64/2.82 (~r(s(elem!1), s(s(elem!1)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[11373, 15276, 15279])).
% 2.64/2.82 tff(15291,plain,
% 2.64/2.82 (b(s(elem!1), s(s(elem!1)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[440, 15290, 8134])).
% 2.64/2.82 tff(15292,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[12485, 453, 15291, 15289, 15283, 15281])).
% 2.64/2.82 tff(15293,plain,(b(s(s(s(s(s(z))))), elem!1) | (~r(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(15294,plain,
% 2.64/2.82 (b(s(s(s(s(s(z))))), elem!1)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15293, 14381, 13408, 13417, 15216])).
% 2.64/2.82 tff(15295,plain,
% 2.64/2.82 (~b(s(z), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[11166, 15294, 13408, 13417])).
% 2.64/2.82 tff(15296,plain,
% 2.64/2.82 (r(s(z), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[372, 15295])).
% 2.64/2.82 tff(15297,plain,
% 2.64/2.82 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9017, 15296, 15248])).
% 2.64/2.82 tff(15298,plain,
% 2.64/2.82 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2570, 15297])).
% 2.64/2.82 tff(15299,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(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, 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(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(15300,plain,
% 2.64/2.82 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(15301,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15300])).
% 2.64/2.82 tff(15302,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[15301, 15299])).
% 2.64/2.82 tff(15303,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(15304,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[15303, 15302])).
% 2.64/2.82 tff(15305,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15304, 453, 923, 1779, 2611, 1275])).
% 2.64/2.82 tff(15306,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(15307,plain,
% 2.64/2.82 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[15306, 15298, 15217, 15250])).
% 2.64/2.82 tff(15308,plain,
% 2.64/2.82 (r(elem!1, s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[466, 15307, 15254])).
% 2.64/2.82 tff(15309,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(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(15310,plain,
% 2.64/2.82 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(15311,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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[15310])).
% 2.64/2.82 tff(15312,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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[15311, 15309])).
% 2.64/2.82 tff(15313,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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(15314,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(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[15313, 15312])).
% 2.64/2.83 tff(15315,plain,
% 2.64/2.83 (~b(elem!1, s(s(s(s(z)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15314, 453, 523, 2611, 1275])).
% 2.64/2.83 tff(15316,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15317,plain,
% 2.64/2.83 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15318,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[15317])).
% 2.64/2.83 tff(15319,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.64/2.83 inference(transitivity,[status(thm)],[15318, 15316])).
% 2.64/2.83 tff(15320,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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(15321,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[15320, 15319])).
% 2.64/2.83 tff(15322,plain,
% 2.64/2.83 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15321, 453, 523, 1779, 2611])).
% 2.64/2.83 tff(15323,plain,
% 2.64/2.83 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[2463, 69, 15322, 2453])).
% 2.64/2.83 tff(15324,plain,
% 2.64/2.83 (~r(elem!1, s(s(s(s(z)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[427, 15323, 412])).
% 2.64/2.83 tff(15325,plain,
% 2.64/2.83 (elem!1 = s(s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[1087, 15324, 15315])).
% 2.64/2.83 tff(15326,plain,
% 2.64/2.83 (s(s(s(s(z)))) = elem!1),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[8, 15325])).
% 2.64/2.83 tff(15327,plain,
% 2.64/2.83 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[4108, 15326])).
% 2.64/2.83 tff(15328,plain,
% 2.64/2.83 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(elem!1))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[15327])).
% 2.64/2.83 tff(15329,plain,
% 2.64/2.83 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.83 inference(symmetry,[status(thm)],[15328])).
% 2.64/2.83 tff(15330,plain,
% 2.64/2.83 ((~b(s(s(s(z))), s(elem!1))) <=> (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[15329])).
% 2.64/2.83 tff(15331,plain,
% 2.64/2.83 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[6845, 15330])).
% 2.64/2.83 tff(15332,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[2611, 15331])).
% 2.64/2.83 tff(15333,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | b(s(s(s(z))), s(elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(15334,plain,
% 2.64/2.83 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15333, 412, 6845, 523, 1779, 1275])).
% 2.64/2.83 tff(15335,plain,
% 2.64/2.83 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[2570, 15334])).
% 2.64/2.83 tff(15336,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15337,plain,
% 2.64/2.83 (((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15338,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[15337])).
% 2.64/2.83 tff(15339,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.64/2.83 inference(transitivity,[status(thm)],[15338, 15336])).
% 2.64/2.83 tff(15340,plain,
% 2.64/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(15341,plain,
% 2.64/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[15340, 15339])).
% 2.64/2.83 tff(15342,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15341, 268, 412, 1545, 15335])).
% 2.64/2.83 tff(15343,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)) | b(s(s(s(z))), s(elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(15344,plain,
% 2.64/2.83 (b(s(s(s(z))), s(elem!1))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15343, 15308, 14381, 15176, 15217, 15250])).
% 2.64/2.83 tff(15345,plain,
% 2.64/2.83 (b(s(elem!1), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[1336, 15294, 15216])).
% 2.64/2.83 tff(15346,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(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15347,plain,
% 2.64/2.83 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15348,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(z))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[15347])).
% 2.64/2.83 tff(15349,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(z))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.83 inference(transitivity,[status(thm)],[15348, 15346])).
% 2.64/2.83 tff(15350,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(z))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(15351,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[15350, 15349])).
% 2.64/2.83 tff(15352,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15351, 453, 15345, 15344, 15251, 15217])).
% 2.64/2.83 tff(15353,plain,(r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(15354,plain,
% 2.64/2.83 (~(elem!1 = s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12708, 15353])).
% 2.64/2.83 tff(15355,plain,
% 2.64/2.83 (b(elem!1, s(z)) | r(elem!1, s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[1130, 15354])).
% 2.64/2.83 tff(15356,plain,
% 2.64/2.83 (r(elem!1, s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15355, 10])).
% 2.64/2.83 tff(15357,plain,
% 2.64/2.83 (~(s(z) = elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[1125, 15354])).
% 2.64/2.83 tff(15358,plain,
% 2.64/2.83 ((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (~r(elem!1, s(z)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13157, 15357])).
% 2.64/2.83 tff(15359,plain,
% 2.64/2.83 (~r(s(s(s(s(s(z))))), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15358, 8837, 8836, 637, 15356])).
% 2.64/2.83 tff(15360,plain,
% 2.64/2.83 (b(s(s(s(s(s(z))))), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[297, 15359])).
% 2.64/2.83 tff(15361,plain,
% 2.64/2.83 (~b(s(s(z)), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9620, 1275, 1291, 299])).
% 2.64/2.83 tff(15362,plain,
% 2.64/2.83 (b(s(s(s(s(z)))), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[7911, 9618, 1123])).
% 2.64/2.83 tff(15363,plain,
% 2.64/2.83 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9834, 1275, 1291, 299])).
% 2.64/2.83 tff(15364,plain,
% 2.64/2.83 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[518, 15363])).
% 2.64/2.83 tff(15365,plain,
% 2.64/2.83 (~b(s(z), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[5423, 15362, 299, 1275])).
% 2.64/2.83 tff(15366,plain,
% 2.64/2.83 (r(s(z), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[506, 15365, 4495])).
% 2.64/2.83 tff(15367,plain,
% 2.64/2.83 (~r(s(s(z)), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9644, 15366, 1291, 15364, 1275, 374, 637, 15362])).
% 2.64/2.83 tff(15368,plain,
% 2.64/2.83 (s(s(z)) = elem!1),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[782, 15367, 15361])).
% 2.64/2.83 tff(15369,plain,
% 2.64/2.83 (s(s(s(z))) = s(elem!1)),
% 2.64/2.83 inference(monotonicity,[status(thm)],[15368])).
% 2.64/2.83 tff(15370,plain,
% 2.64/2.83 (b(s(s(s(z))), s(s(s(z)))) <=> b(s(s(s(z))), s(elem!1))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[15369])).
% 2.64/2.83 tff(15371,plain,
% 2.64/2.83 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(z))))),
% 2.64/2.83 inference(symmetry,[status(thm)],[15370])).
% 2.64/2.83 tff(15372,plain,
% 2.64/2.83 (b(s(s(s(z))), s(s(s(z))))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[11663, 15371])).
% 2.64/2.83 tff(15373,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(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15374,plain,
% 2.64/2.83 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15375,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[15374])).
% 2.64/2.83 tff(15376,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.83 inference(transitivity,[status(thm)],[15375, 15373])).
% 2.64/2.83 tff(15377,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(15378,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[15377, 15376])).
% 2.64/2.83 tff(15379,plain,
% 2.64/2.83 (~b(s(s(s(z))), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15378, 453, 1291, 1275])).
% 2.64/2.83 tff(15380,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15379, 15372])).
% 2.64/2.83 tff(15381,plain,((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (s(s(s(s(s(z))))) = elem!1) | (~b(s(s(s(s(z)))), elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(15382,plain,
% 2.64/2.83 ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (s(s(s(s(s(z))))) = elem!1) | (~b(s(s(s(s(z)))), elem!1))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15381, 15354])).
% 2.64/2.83 tff(15383,plain,
% 2.64/2.83 (~b(elem!1, s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15382, 15360, 8836, 8837, 637, 9869])).
% 2.64/2.83 tff(15384,plain,
% 2.64/2.83 (r(elem!1, s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[4492, 15383, 8842])).
% 2.64/2.83 tff(15385,plain,
% 2.64/2.83 (~r(elem!1, s(s(s(s(z)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13281, 15384, 11])).
% 2.64/2.83 tff(15386,plain,
% 2.64/2.83 (b(elem!1, s(s(s(s(z)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[1087, 15385, 9])).
% 2.64/2.83 tff(15387,plain,
% 2.64/2.83 (~b(s(s(z)), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[6077, 15386, 8837, 8836, 11])).
% 2.64/2.83 tff(15388,plain,
% 2.64/2.83 (b(s(z), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12713, 15383, 10])).
% 2.64/2.83 tff(15389,plain,
% 2.64/2.83 (~r(s(s(s(s(z)))), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[8475, 15384, 11])).
% 2.64/2.83 tff(15390,plain,
% 2.64/2.83 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12998, 15385, 8836, 3, 15389])).
% 2.64/2.83 tff(15391,plain,
% 2.64/2.83 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[1656, 15390])).
% 2.64/2.83 tff(15392,plain,
% 2.64/2.83 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[10556, 5910])).
% 2.64/2.83 tff(15393,plain,
% 2.64/2.83 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[6664, 15392, 3, 1085, 5914, 239])).
% 2.64/2.83 tff(15394,plain,
% 2.64/2.83 (r(s(s(s(s(s(z))))), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[643, 15393, 637])).
% 2.64/2.83 tff(15395,plain,
% 2.64/2.83 (b(s(s(s(s(z)))), s(z)) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[7911, 15354])).
% 2.64/2.83 tff(15396,plain,
% 2.64/2.83 (b(s(s(s(s(z)))), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15395, 300])).
% 2.64/2.83 tff(15397,plain,
% 2.64/2.83 (~b(s(z), s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[8186, 15392, 15396, 5914])).
% 2.64/2.83 tff(15398,plain,
% 2.64/2.83 (r(s(z), s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[372, 15397])).
% 2.64/2.83 tff(15399,plain,
% 2.64/2.83 ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[4530, 15353])).
% 2.64/2.83 tff(15400,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15399, 15398, 15394])).
% 2.64/2.83 tff(15401,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (s(s(s(s(s(z))))) = elem!1) | (s(s(s(s(z)))) = elem!1) | r(elem!1, s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(15402,plain,
% 2.64/2.83 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15401, 637, 3, 15385, 15389, 11, 15391])).
% 2.64/2.83 tff(15403,plain,
% 2.64/2.83 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[687, 15402])).
% 2.64/2.83 tff(15404,plain,
% 2.64/2.83 (~r(s(z), s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15399, 722])).
% 2.64/2.83 tff(15405,plain,
% 2.64/2.83 (b(s(z), s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[372, 15404])).
% 2.64/2.83 tff(15406,plain,
% 2.64/2.83 (~b(s(s(s(z))), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9007, 15405, 374, 1779])).
% 2.64/2.83 tff(15407,plain,
% 2.64/2.83 ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[777, 15353])).
% 2.64/2.83 tff(15408,plain,
% 2.64/2.83 (~r(s(s(z)), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15407, 722])).
% 2.64/2.83 tff(15409,plain,
% 2.64/2.83 (s(s(z)) = elem!1),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[782, 15408, 4])).
% 2.64/2.83 tff(15410,plain,
% 2.64/2.83 (s(elem!1) = s(s(s(z)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9447, 15409])).
% 2.64/2.83 tff(15411,plain,
% 2.64/2.83 (~r(s(s(s(z))), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9427, 15410, 238, 1149])).
% 2.64/2.83 tff(15412,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[134, 15411, 15406])).
% 2.64/2.83 tff(15413,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(15414,plain,
% 2.64/2.83 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15413, 15384, 15356, 15360, 15403, 15387])).
% 2.64/2.83 tff(15415,plain,
% 2.64/2.83 (b(s(s(s(s(s(z))))), elem!1)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[643, 15414, 637])).
% 2.64/2.83 tff(15416,plain,
% 2.64/2.83 (~r(elem!1, s(s(s(s(z)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[13281, 1149, 11])).
% 2.64/2.83 tff(15417,plain,
% 2.64/2.83 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[12998, 15416, 1291, 3, 9691])).
% 2.64/2.83 tff(15418,plain,
% 2.64/2.83 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[1656, 15417])).
% 2.64/2.83 tff(15419,plain,
% 2.64/2.83 (b(s(s(s(s(z)))), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15395, 15418])).
% 2.64/2.83 tff(15420,plain,
% 2.64/2.83 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[3942, 14132, 15419, 2090, 3468, 374])).
% 2.64/2.83 tff(15421,plain,
% 2.64/2.83 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[328, 15420])).
% 2.64/2.83 tff(15422,plain,
% 2.64/2.83 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[6664, 15421, 3, 15416, 646, 9691])).
% 2.64/2.83 tff(15423,plain,
% 2.64/2.83 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[10556, 15422])).
% 2.64/2.83 tff(15424,plain,
% 2.64/2.83 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[8666, 15423, 11])).
% 2.64/2.83 tff(15425,plain,
% 2.64/2.83 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[2570, 15424])).
% 2.64/2.83 tff(15426,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(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15427,plain,
% 2.64/2.83 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(15428,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(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[15427])).
% 2.64/2.83 tff(15429,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(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.64/2.83 inference(transitivity,[status(thm)],[15428, 15426])).
% 2.64/2.83 tff(15430,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(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(15431,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[15430, 15429])).
% 2.64/2.83 tff(15432,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15431, 453, 1291, 923, 374, 2611])).
% 2.64/2.83 tff(15433,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(15434,plain,
% 2.64/2.83 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15433, 15425, 374, 1291])).
% 2.64/2.83 tff(15435,plain,
% 2.64/2.83 (r(elem!1, s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[466, 15434, 2073])).
% 2.64/2.83 tff(15436,plain,
% 2.64/2.83 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[15435, 11097])).
% 2.64/2.83 tff(15437,plain,
% 2.64/2.83 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[9372])).
% 2.64/2.83 tff(15438,plain,
% 2.64/2.83 (elem!1 = s(s(z))),
% 2.64/2.83 inference(transitivity,[status(thm)],[86, 15437, 97])).
% 2.64/2.83 tff(15439,plain,
% 2.64/2.83 (r(elem!1, s(z)) <=> r(s(s(z)), s(z))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[15438])).
% 2.64/2.83 tff(15440,plain,
% 2.64/2.83 (r(s(s(z)), s(z)) <=> r(elem!1, s(z))),
% 2.64/2.83 inference(symmetry,[status(thm)],[15439])).
% 2.64/2.83 tff(15441,plain,
% 2.64/2.83 ((~r(s(s(z)), s(z))) <=> (~r(elem!1, s(z)))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[15440])).
% 2.64/2.83 tff(15442,assumption,(~r(s(s(z)), s(z))), introduced(assumption)).
% 2.64/2.83 tff(15443,plain,
% 2.64/2.83 (~r(elem!1, s(z))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[15442, 15441])).
% 2.64/2.83 tff(15444,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[238, 15443])).
% 2.64/2.83 tff(15445,plain,((~(s(elem!1) = s(s(s(z))))) | (~r(elem!1, s(z))) | r(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(15446,plain,
% 2.64/2.83 (r(s(s(z)), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15445, 14129, 238])).
% 2.64/2.83 tff(15447,plain,
% 2.64/2.83 (~r(s(s(s(z))), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9427, 14129, 238, 1149])).
% 2.64/2.83 tff(15448,plain,
% 2.64/2.83 (b(s(s(s(z))), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[134, 15447])).
% 2.64/2.83 tff(15449,plain,
% 2.64/2.83 (~b(s(z), s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9007, 15448, 374, 1779])).
% 2.64/2.83 tff(15450,plain,
% 2.64/2.83 (r(s(z), s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[372, 15449])).
% 2.64/2.83 tff(15451,plain,
% 2.64/2.83 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9113, 15450, 15446])).
% 2.64/2.83 tff(15452,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[15451, 15436])).
% 2.64/2.83 tff(15453,plain,((~(s(s(z)) = elem!1)) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(15454,plain,
% 2.64/2.83 (~(s(s(z)) = elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15453, 8840, 15360, 8836, 11, 3, 15415, 15403, 15388, 15356, 15384])).
% 2.64/2.84 tff(15455,plain,
% 2.64/2.84 (r(s(s(z)), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[782, 15454, 15387])).
% 2.64/2.84 tff(15456,plain,
% 2.64/2.84 (~r(s(s(z)), s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[707, 268, 15353, 15455])).
% 2.64/2.84 tff(15457,plain,
% 2.64/2.84 (b(s(s(z)), s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[720, 69, 717, 15456])).
% 2.64/2.84 tff(15458,plain,
% 2.64/2.84 ((~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[741, 15353])).
% 2.64/2.84 tff(15459,plain,
% 2.64/2.84 (~r(s(z), s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15458, 15455])).
% 2.64/2.84 tff(15460,plain,
% 2.64/2.84 (b(s(z), s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[757, 15459])).
% 2.64/2.84 tff(15461,plain,
% 2.64/2.84 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9547, 453, 15460, 15360, 15457])).
% 2.64/2.84 tff(15462,plain,
% 2.64/2.84 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9547, 453, 758, 374, 721])).
% 2.64/2.84 tff(15463,plain,
% 2.64/2.84 ((s(s(z)) = s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[5711, 69, 15462])).
% 2.64/2.84 tff(15464,plain,
% 2.64/2.84 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15463, 5578])).
% 2.64/2.84 tff(15465,plain,
% 2.64/2.84 (~r(s(s(s(z))), s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[3149, 268, 4621, 15464])).
% 2.64/2.84 tff(15466,plain,
% 2.64/2.84 (b(s(s(s(z))), s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[2534, 69, 160, 15465])).
% 2.64/2.84 tff(15467,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[7537, 453, 758, 2090, 15466, 721])).
% 2.64/2.84 tff(15468,plain,((~r(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(15469,plain,
% 2.64/2.84 ((~r(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15468, 15353])).
% 2.64/2.84 tff(15470,plain,
% 2.64/2.84 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15469, 15455, 15360, 15388])).
% 2.64/2.84 tff(15471,plain,
% 2.64/2.84 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[2570, 15470])).
% 2.64/2.84 tff(15472,plain,
% 2.64/2.84 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15433, 15471, 15360, 8836])).
% 2.64/2.84 tff(15473,plain,
% 2.64/2.84 (r(elem!1, s(s(s(s(s(z))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[466, 15472, 8840])).
% 2.64/2.84 tff(15474,plain,
% 2.64/2.84 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9558, 15473, 15455])).
% 2.64/2.84 tff(15475,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[5711, 69, 15474, 15461, 54])).
% 2.64/2.84 tff(15476,plain,((s(s(s(s(s(z))))) = elem!1) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | b(elem!1, s(z)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(15477,plain,
% 2.64/2.84 (s(s(s(s(s(z))))) = elem!1),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15476, 3, 11, 10, 2])).
% 2.64/2.84 tff(15478,plain,
% 2.64/2.84 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15477])).
% 2.64/2.84 tff(15479,plain,
% 2.64/2.84 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15478])).
% 2.64/2.84 tff(15480,plain,
% 2.64/2.84 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.64/2.84 inference(symmetry,[status(thm)],[15479])).
% 2.64/2.84 tff(15481,plain,
% 2.64/2.84 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15480])).
% 2.64/2.84 tff(15482,plain,
% 2.64/2.84 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.64/2.84 inference(symmetry,[status(thm)],[15481])).
% 2.64/2.84 tff(15483,plain,
% 2.64/2.84 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15477])).
% 2.64/2.84 tff(15484,plain,
% 2.64/2.84 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[15483, 3858])).
% 2.64/2.84 tff(15485,plain,
% 2.64/2.84 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.64/2.84 inference(transitivity,[status(thm)],[15484, 8506])).
% 2.64/2.84 tff(15486,plain,
% 2.64/2.84 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15485])).
% 2.64/2.84 tff(15487,plain,
% 2.64/2.84 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[2729, 15486])).
% 2.64/2.84 tff(15488,plain,
% 2.64/2.84 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15479])).
% 2.64/2.84 tff(15489,plain,
% 2.64/2.84 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.84 inference(symmetry,[status(thm)],[15488])).
% 2.64/2.84 tff(15490,plain,
% 2.64/2.84 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(z)) = s(s(s(s(s(s(s(z)))))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15489])).
% 2.64/2.84 tff(15491,plain,
% 2.64/2.84 (~(s(elem!1) = s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[5852, 15477])).
% 2.64/2.84 tff(15492,plain,
% 2.64/2.84 (~(s(s(z)) = s(s(elem!1)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1188, 15491])).
% 2.64/2.84 tff(15493,plain,
% 2.64/2.84 (~(s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[15492, 15490])).
% 2.64/2.84 tff(15494,plain,
% 2.64/2.84 (elem!1 = s(s(s(s(s(z)))))),
% 2.64/2.84 inference(symmetry,[status(thm)],[15477])).
% 2.64/2.84 tff(15495,plain,
% 2.64/2.84 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15494])).
% 2.64/2.84 tff(15496,plain,
% 2.64/2.84 ((s(s(z)) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.64/2.84 inference(transitivity,[status(thm)],[15495, 4133])).
% 2.64/2.84 tff(15497,plain,
% 2.64/2.84 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.64/2.84 inference(symmetry,[status(thm)],[15496])).
% 2.64/2.84 tff(15498,plain,
% 2.64/2.84 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15497])).
% 2.64/2.84 tff(15499,plain,
% 2.64/2.84 (~(s(s(z)) = elem!1)),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[52, 15498])).
% 2.64/2.84 tff(15500,plain,
% 2.64/2.84 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15477])).
% 2.64/2.84 tff(15501,plain,
% 2.64/2.84 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 2.64/2.84 inference(transitivity,[status(thm)],[15500, 1027])).
% 2.64/2.84 tff(15502,plain,
% 2.64/2.84 ((~(s(s(s(s(s(z))))) = s(elem!1))) <=> (~(s(elem!1) = elem!1))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15501])).
% 2.64/2.84 tff(15503,plain,
% 2.64/2.84 (~(s(elem!1) = elem!1)),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[10372, 15502])).
% 2.64/2.84 tff(15504,plain,
% 2.64/2.84 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15477])).
% 2.64/2.84 tff(15505,plain,
% 2.64/2.84 (elem!1 = s(s(s(s(s(z)))))),
% 2.64/2.84 inference(symmetry,[status(thm)],[5168])).
% 2.64/2.84 tff(15506,plain,
% 2.64/2.84 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15505])).
% 2.64/2.84 tff(15507,plain,
% 2.64/2.84 ((s(s(z)) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.64/2.84 inference(transitivity,[status(thm)],[15506, 4133])).
% 2.64/2.84 tff(15508,plain,
% 2.64/2.84 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.64/2.84 inference(symmetry,[status(thm)],[15507])).
% 2.64/2.84 tff(15509,plain,
% 2.64/2.84 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15508])).
% 2.64/2.84 tff(15510,plain,
% 2.64/2.84 (~(s(s(z)) = elem!1)),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[52, 15509])).
% 2.64/2.84 tff(15511,plain,
% 2.64/2.84 (~(s(s(s(z))) = s(elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[11953, 15510])).
% 2.64/2.84 tff(15512,plain,
% 2.64/2.84 (b(elem!1, s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[13015, 1984, 5168])).
% 2.64/2.84 tff(15513,plain,
% 2.64/2.84 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[5168])).
% 2.64/2.84 tff(15514,plain,
% 2.64/2.84 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 2.64/2.84 inference(transitivity,[status(thm)],[15513, 1027])).
% 2.64/2.84 tff(15515,plain,
% 2.64/2.84 ((~(s(s(s(s(s(z))))) = s(elem!1))) <=> (~(s(elem!1) = elem!1))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15514])).
% 2.64/2.84 tff(15516,plain,
% 2.64/2.84 (~(s(elem!1) = elem!1)),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[10372, 15515])).
% 2.64/2.84 tff(15517,plain,
% 2.64/2.84 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[5168])).
% 2.64/2.84 tff(15518,plain,
% 2.64/2.84 (r(elem!1, s(s(s(z))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[256, 15517])).
% 2.64/2.84 tff(15519,plain,
% 2.64/2.84 (~r(s(s(s(s(z)))), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[8473, 268, 11, 15518])).
% 2.64/2.84 tff(15520,plain,
% 2.64/2.84 (b(s(s(s(s(z)))), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[254, 15519, 3])).
% 2.64/2.84 tff(15521,plain,
% 2.64/2.84 (~b(s(s(z)), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[6077, 15520, 15512, 1291, 11])).
% 2.64/2.84 tff(15522,plain,
% 2.64/2.84 (r(s(s(z)), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[782, 15521, 15510])).
% 2.64/2.84 tff(15523,plain,
% 2.64/2.84 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.64/2.84 inference(monotonicity,[status(thm)],[5169])).
% 2.64/2.84 tff(15524,plain,
% 2.64/2.84 (r(s(elem!1), elem!1) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.84 inference(symmetry,[status(thm)],[15523])).
% 2.64/2.84 tff(15525,plain,
% 2.64/2.84 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[1892, 15524])).
% 2.64/2.84 tff(15526,plain,
% 2.64/2.84 (b(s(s(s(s(s(s(z)))))), s(z)) <=> b(s(elem!1), s(z))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[5169])).
% 2.64/2.84 tff(15527,plain,
% 2.64/2.84 (b(s(elem!1), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.84 inference(symmetry,[status(thm)],[15526])).
% 2.64/2.84 tff(15528,plain,
% 2.64/2.84 (b(s(elem!1), s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[353, 14092, 6231])).
% 2.64/2.84 tff(15529,plain,
% 2.64/2.84 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[15528, 15527])).
% 2.64/2.84 tff(15530,plain,
% 2.64/2.84 ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1719, 2661])).
% 2.64/2.84 tff(15531,plain,
% 2.64/2.84 ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15530, 15353])).
% 2.64/2.84 tff(15532,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15531, 15529, 15525, 700])).
% 2.64/2.84 tff(15533,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~(s(s(s(s(s(z))))) = elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(15534,plain,
% 2.64/2.84 (~r(s(elem!1), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15533, 15522, 5168, 238])).
% 2.64/2.84 tff(15535,plain,
% 2.64/2.84 (b(s(elem!1), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[2440, 15534, 15516])).
% 2.64/2.84 tff(15536,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(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(15537,plain,
% 2.64/2.84 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(15538,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15537])).
% 2.64/2.84 tff(15539,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[15538, 15536])).
% 2.64/2.84 tff(15540,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(15541,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(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[15540, 15539])).
% 2.64/2.84 tff(15542,plain,
% 2.64/2.84 (~b(s(s(s(z))), s(elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15541, 453, 15535, 1291, 15512])).
% 2.64/2.84 tff(15543,plain,
% 2.64/2.84 (r(s(s(s(z))), s(elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9480, 15542, 15511])).
% 2.64/2.84 tff(15544,plain,
% 2.64/2.84 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[512, 15519, 11])).
% 2.64/2.84 tff(15545,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(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(15546,plain,
% 2.64/2.84 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(15547,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15546])).
% 2.64/2.84 tff(15548,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.64/2.84 inference(transitivity,[status(thm)],[15547, 15545])).
% 2.64/2.84 tff(15549,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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(15550,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[15549, 15548])).
% 2.64/2.84 tff(15551,plain,
% 2.64/2.84 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15550, 453, 15535, 15512, 15520])).
% 2.64/2.84 tff(15552,plain,
% 2.64/2.84 (r(s(elem!1), s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9382, 15551, 15544])).
% 2.64/2.84 tff(15553,plain,
% 2.64/2.84 (~r(elem!1, s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9400, 268, 11, 15518])).
% 2.64/2.84 tff(15554,plain,
% 2.64/2.84 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[12998, 15553, 1291, 3, 15519])).
% 2.64/2.84 tff(15555,plain,
% 2.64/2.84 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1656, 15554])).
% 2.64/2.84 tff(15556,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9715, 268, 15555, 15552, 15543])).
% 2.64/2.84 tff(15557,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~(s(s(s(s(s(z))))) = elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(15558,plain,
% 2.64/2.84 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15557, 15477, 8836, 15356, 11, 3])).
% 2.64/2.84 tff(15559,plain,
% 2.64/2.84 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[687, 15558])).
% 2.64/2.84 tff(15560,plain,
% 2.64/2.84 (b(elem!1, s(s(s(z))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[15559, 15504])).
% 2.64/2.84 tff(15561,plain,
% 2.64/2.84 (~(s(elem!1) = s(s(s(z))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9847, 5229])).
% 2.64/2.84 tff(15562,plain,
% 2.64/2.84 (r(s(elem!1), s(s(s(z))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[1305, 1298, 15561])).
% 2.64/2.84 tff(15563,plain,
% 2.64/2.84 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[5171])).
% 2.64/2.84 tff(15564,plain,
% 2.64/2.84 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(elem!1)))),
% 2.64/2.84 inference(symmetry,[status(thm)],[15563])).
% 2.64/2.84 tff(15565,plain,
% 2.64/2.84 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15564])).
% 2.64/2.84 tff(15566,plain,
% 2.64/2.84 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[5169])).
% 2.64/2.84 tff(15567,plain,
% 2.64/2.84 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[15566, 1307])).
% 2.64/2.84 tff(15568,plain,
% 2.64/2.84 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z)))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15567])).
% 2.64/2.84 tff(15569,plain,
% 2.64/2.84 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z)))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[10799, 5965])).
% 2.64/2.84 tff(15570,plain,
% 2.64/2.84 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[15569, 15568])).
% 2.64/2.84 tff(15571,plain,
% 2.64/2.84 (~(s(elem!1) = s(s(elem!1)))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[15570, 15565])).
% 2.64/2.84 tff(15572,plain,
% 2.64/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(15573,plain,
% 2.64/2.84 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(15574,plain,
% 2.64/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[15573])).
% 2.64/2.84 tff(15575,plain,
% 2.64/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[15574, 15572])).
% 2.64/2.84 tff(15576,plain,
% 2.64/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(15577,plain,
% 2.64/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[15576, 15575])).
% 2.64/2.84 tff(15578,plain,
% 2.64/2.84 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15577, 268, 11, 15562])).
% 2.64/2.84 tff(15579,plain,
% 2.64/2.84 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[512, 239, 11])).
% 2.64/2.84 tff(15580,plain,
% 2.64/2.84 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9392, 255, 1275, 629])).
% 2.64/2.84 tff(15581,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9382, 15580, 15579, 9362])).
% 2.64/2.84 tff(15582,plain,(r(s(s(s(s(z)))), elem!1) | r(s(elem!1), s(s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(15583,plain,
% 2.64/2.84 (r(s(s(s(s(z)))), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15582, 15578, 1275, 629, 11, 3])).
% 2.64/2.84 tff(15584,plain,
% 2.64/2.84 ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~(s(s(s(s(s(z))))) = elem!1))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[10922, 15353])).
% 2.64/2.84 tff(15585,plain,
% 2.64/2.84 (~r(s(s(elem!1)), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[15584, 15583, 5168])).
% 2.64/2.84 tff(15586,plain,
% 2.64/2.84 (b(s(s(elem!1)), elem!1)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[2240, 15585, 5180])).
% 2.64/2.84 tff(15587,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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(15588,plain,
% 2.64/2.84 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(15589,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15588])).
% 2.64/2.85 tff(15590,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15589, 15587])).
% 2.64/2.85 tff(15591,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(15592,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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15591, 15590])).
% 2.64/2.85 tff(15593,plain,
% 2.64/2.85 (~b(s(elem!1), s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15592, 453, 629, 15586, 1275])).
% 2.64/2.85 tff(15594,plain,
% 2.64/2.85 (r(s(elem!1), s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[440, 15593, 15571])).
% 2.64/2.85 tff(15595,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(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(15596,plain,
% 2.64/2.85 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(15597,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15596])).
% 2.64/2.85 tff(15598,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15597, 15595])).
% 2.64/2.85 tff(15599,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(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(15600,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15599, 15598])).
% 2.64/2.85 tff(15601,plain,
% 2.64/2.85 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15600, 453, 15586, 1291, 1275])).
% 2.64/2.85 tff(15602,plain,
% 2.64/2.85 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[547, 15357])).
% 2.64/2.85 tff(15603,plain,
% 2.64/2.85 (r(s(s(s(z))), s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[5203, 15602])).
% 2.64/2.85 tff(15604,plain,
% 2.64/2.85 (r(s(s(s(z))), s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15603, 15601])).
% 2.64/2.85 tff(15605,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[7130, 15604, 15594, 15562])).
% 2.64/2.85 tff(15606,plain,((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~(s(s(s(s(s(z))))) = elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(15607,plain,
% 2.64/2.85 (~b(s(elem!1), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15606, 15560, 8836, 15477, 11, 3])).
% 2.64/2.85 tff(15608,plain,
% 2.64/2.85 (r(s(elem!1), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2440, 15607, 15503])).
% 2.64/2.85 tff(15609,plain,
% 2.64/2.85 (~r(s(s(z)), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15533, 15608, 15477, 15356])).
% 2.64/2.85 tff(15610,plain,
% 2.64/2.85 (b(s(s(z)), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[782, 15609, 15499])).
% 2.64/2.85 tff(15611,plain,
% 2.64/2.85 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15480])).
% 2.64/2.85 tff(15612,plain,
% 2.64/2.85 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(s(elem!1)))),
% 2.64/2.85 inference(symmetry,[status(thm)],[15611])).
% 2.64/2.85 tff(15613,plain,
% 2.64/2.85 ((~(elem!1 = s(s(s(s(s(s(s(z))))))))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15612])).
% 2.64/2.85 tff(15614,plain,
% 2.64/2.85 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15484])).
% 2.64/2.85 tff(15615,plain,
% 2.64/2.85 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[2729, 15614])).
% 2.64/2.85 tff(15616,plain,
% 2.64/2.85 (~(elem!1 = s(s(elem!1)))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15615, 15613])).
% 2.64/2.85 tff(15617,plain,
% 2.64/2.85 (~r(s(elem!1), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9570, 15608, 15356])).
% 2.64/2.85 tff(15618,plain,
% 2.64/2.85 (b(s(elem!1), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[353, 15617, 15491])).
% 2.64/2.85 tff(15619,plain,
% 2.64/2.85 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15480])).
% 2.64/2.85 tff(15620,plain,
% 2.64/2.85 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(elem!1) = s(s(elem!1)))),
% 2.64/2.85 inference(symmetry,[status(thm)],[15619])).
% 2.64/2.85 tff(15621,plain,
% 2.64/2.85 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15620])).
% 2.64/2.85 tff(15622,plain,
% 2.64/2.85 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15478])).
% 2.64/2.85 tff(15623,plain,
% 2.64/2.85 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15622, 1307])).
% 2.64/2.85 tff(15624,plain,
% 2.64/2.85 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z)))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15623])).
% 2.64/2.85 tff(15625,plain,
% 2.64/2.85 (elem!1 = s(s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[5538, 15477])).
% 2.64/2.85 tff(15626,plain,
% 2.64/2.85 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z)))))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[10799, 15625])).
% 2.64/2.85 tff(15627,plain,
% 2.64/2.85 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15626, 15624])).
% 2.64/2.85 tff(15628,plain,
% 2.64/2.85 (~(s(elem!1) = s(s(elem!1)))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15627, 15621])).
% 2.64/2.85 tff(15629,plain,
% 2.64/2.85 (~(s(z) = s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[5029, 15491])).
% 2.64/2.85 tff(15630,plain,
% 2.64/2.85 ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1912, 15353])).
% 2.64/2.85 tff(15631,plain,
% 2.64/2.85 (~r(s(z), s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15630, 15608])).
% 2.64/2.85 tff(15632,plain,
% 2.64/2.85 (b(s(z), s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[397, 15631, 15629])).
% 2.64/2.85 tff(15633,plain,
% 2.64/2.85 (~r(elem!1, s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2017, 15632, 15356, 15628, 15608, 15618])).
% 2.64/2.85 tff(15634,plain,
% 2.64/2.85 (b(elem!1, s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1024, 15633, 15616])).
% 2.64/2.85 tff(15635,plain,
% 2.64/2.85 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[8609, 15634, 8836, 15610, 15493])).
% 2.64/2.85 tff(15636,plain,
% 2.64/2.85 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[3875, 15635, 15487])).
% 2.64/2.85 tff(15637,plain,
% 2.64/2.85 (r(s(s(elem!1)), elem!1)),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15636, 15482])).
% 2.64/2.85 tff(15638,plain,
% 2.64/2.85 (~b(s(s(s(s(z)))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9620, 15610, 15560, 8836])).
% 2.64/2.85 tff(15639,plain,
% 2.64/2.85 (r(s(s(s(s(z)))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[254, 15638, 3])).
% 2.64/2.85 tff(15640,plain,
% 2.64/2.85 (~r(s(s(elem!1)), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15584, 15639, 15477])).
% 2.64/2.85 tff(15641,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15640, 15637])).
% 2.64/2.85 tff(15642,plain,((s(s(s(s(z)))) = elem!1) | (~r(s(s(s(s(z)))), s(s(s(z))))) | b(elem!1, s(z)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(15643,plain,
% 2.64/2.85 (s(s(s(s(z)))) = elem!1),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15642, 11, 10, 2])).
% 2.64/2.85 tff(15644,plain,
% 2.64/2.85 ((s(elem!1) = s(s(s(s(z))))) <=> (s(elem!1) = elem!1)),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15643])).
% 2.64/2.85 tff(15645,plain,
% 2.64/2.85 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.64/2.85 inference(symmetry,[status(thm)],[15644])).
% 2.64/2.85 tff(15646,plain,
% 2.64/2.85 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4108, 15643])).
% 2.64/2.85 tff(15647,plain,
% 2.64/2.85 (~b(s(s(s(s(z)))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9368, 15646])).
% 2.64/2.85 tff(15648,plain,
% 2.64/2.85 (s(s(s(s(s(z))))) = elem!1),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[8833, 15647, 10, 2])).
% 2.64/2.85 tff(15649,plain,
% 2.64/2.85 (elem!1 = s(s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[5538, 15648])).
% 2.64/2.85 tff(15650,plain,
% 2.64/2.85 (s(s(s(s(s(z))))) = elem!1),
% 2.64/2.85 inference(symmetry,[status(thm)],[15649])).
% 2.64/2.85 tff(15651,plain,
% 2.64/2.85 (s(elem!1) = s(s(s(s(s(z)))))),
% 2.64/2.85 inference(symmetry,[status(thm)],[15646])).
% 2.64/2.85 tff(15652,plain,
% 2.64/2.85 (s(elem!1) = elem!1),
% 2.64/2.85 inference(transitivity,[status(thm)],[15651, 15650])).
% 2.64/2.85 tff(15653,plain,
% 2.64/2.85 (s(elem!1) = s(s(s(s(z))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15652, 15645])).
% 2.64/2.85 tff(15654,plain,
% 2.64/2.85 (s(elem!1) = s(s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4499, 15646])).
% 2.64/2.85 tff(15655,plain,
% 2.64/2.85 (~b(s(s(s(s(z)))), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4309, 15654, 10])).
% 2.64/2.85 tff(15656,plain,
% 2.64/2.85 (r(s(s(s(s(z)))), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1098, 15655])).
% 2.64/2.85 tff(15657,plain,
% 2.64/2.85 ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1167, 15353])).
% 2.64/2.85 tff(15658,plain,
% 2.64/2.85 (~r(s(s(s(s(z)))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15657, 15656])).
% 2.64/2.85 tff(15659,plain,
% 2.64/2.85 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[512, 15658, 11])).
% 2.64/2.85 tff(15660,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15659, 15653])).
% 2.64/2.85 tff(15661,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | b(elem!1, s(z)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(15662,plain,
% 2.64/2.85 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15661, 2, 10])).
% 2.64/2.85 tff(15663,plain,
% 2.64/2.85 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[518, 15662])).
% 2.64/2.85 tff(15664,plain,
% 2.64/2.85 (~b(elem!1, s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9834, 8837, 8836, 15663])).
% 2.64/2.85 tff(15665,plain,
% 2.64/2.85 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | r(s(s(s(z))), elem!1) | (~b(s(s(s(s(s(z))))), s(z))) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[13277, 15602])).
% 2.64/2.85 tff(15666,plain,
% 2.64/2.85 (~r(elem!1, s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15665, 15360, 2, 15663, 8840, 8837, 9869, 8836])).
% 2.64/2.85 tff(15667,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4492, 15666, 8842, 15664])).
% 2.64/2.85 tff(15668,plain,((s(s(s(s(s(z))))) = elem!1) | r(s(s(s(z))), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(15669,plain,
% 2.64/2.85 (s(s(s(s(s(z))))) = elem!1),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15668, 2, 10])).
% 2.64/2.85 tff(15670,plain,
% 2.64/2.85 (elem!1 = s(s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[5538, 15669])).
% 2.64/2.85 tff(15671,plain,
% 2.64/2.85 (s(s(s(s(s(z))))) = elem!1),
% 2.64/2.85 inference(symmetry,[status(thm)],[15670])).
% 2.64/2.85 tff(15672,plain,
% 2.64/2.85 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15671])).
% 2.64/2.85 tff(15673,plain,
% 2.64/2.85 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(symmetry,[status(thm)],[15672])).
% 2.64/2.85 tff(15674,plain,
% 2.64/2.85 (s(elem!1) = s(s(s(s(s(s(z))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15670])).
% 2.64/2.85 tff(15675,plain,
% 2.64/2.85 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15674])).
% 2.64/2.85 tff(15676,plain,
% 2.64/2.85 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 2.64/2.85 inference(symmetry,[status(thm)],[15675])).
% 2.64/2.85 tff(15677,plain,
% 2.64/2.85 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15670, 15676])).
% 2.64/2.85 tff(15678,plain,
% 2.64/2.85 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(symmetry,[status(thm)],[15677])).
% 2.64/2.85 tff(15679,plain,
% 2.64/2.85 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15670])).
% 2.64/2.85 tff(15680,plain,
% 2.64/2.85 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15679, 15678])).
% 2.64/2.85 tff(15681,plain,
% 2.64/2.85 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15670, 15675])).
% 2.64/2.85 tff(15682,plain,
% 2.64/2.85 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15681, 5915])).
% 2.64/2.85 tff(15683,plain,
% 2.64/2.85 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(elem!1)))),
% 2.64/2.85 inference(symmetry,[status(thm)],[15682])).
% 2.64/2.85 tff(15684,plain,
% 2.64/2.85 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15683])).
% 2.64/2.85 tff(15685,plain,
% 2.64/2.85 (~(elem!1 = s(s(elem!1)))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[2729, 15684])).
% 2.64/2.85 tff(15686,plain,
% 2.64/2.85 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15675])).
% 2.64/2.85 tff(15687,plain,
% 2.64/2.85 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(z)) = s(s(s(s(s(s(s(z)))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15686])).
% 2.64/2.85 tff(15688,plain,
% 2.64/2.85 (~(s(elem!1) = s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[5852, 15669])).
% 2.64/2.85 tff(15689,plain,
% 2.64/2.85 (~(s(s(z)) = s(s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1188, 15688])).
% 2.64/2.85 tff(15690,plain,
% 2.64/2.85 (~(s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15689, 15687])).
% 2.64/2.85 tff(15691,plain,
% 2.64/2.85 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15670])).
% 2.64/2.85 tff(15692,plain,
% 2.64/2.85 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.64/2.85 inference(symmetry,[status(thm)],[15691])).
% 2.64/2.85 tff(15693,plain,
% 2.64/2.85 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15675])).
% 2.64/2.85 tff(15694,plain,
% 2.64/2.85 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15670])).
% 2.64/2.85 tff(15695,plain,
% 2.64/2.85 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.64/2.85 inference(transitivity,[status(thm)],[15694, 15693, 15692])).
% 2.64/2.85 tff(15696,plain,
% 2.64/2.85 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (s(s(elem!1)) = elem!1)),
% 2.64/2.85 inference(transitivity,[status(thm)],[15683, 2170])).
% 2.64/2.85 tff(15697,plain,
% 2.64/2.85 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15696])).
% 2.64/2.85 tff(15698,plain,
% 2.64/2.85 (~(s(s(elem!1)) = elem!1)),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[2729, 15697])).
% 2.64/2.85 tff(15699,plain,
% 2.64/2.85 (~(s(z) = s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[5029, 15688])).
% 2.64/2.85 tff(15700,plain,
% 2.64/2.85 (b(elem!1, s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[5529])).
% 2.64/2.85 tff(15701,plain,
% 2.64/2.85 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.64/2.85 inference(monotonicity,[status(thm)],[5821])).
% 2.64/2.85 tff(15702,plain,
% 2.64/2.85 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15701, 3858])).
% 2.64/2.85 tff(15703,plain,
% 2.64/2.85 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15702])).
% 2.64/2.85 tff(15704,plain,
% 2.64/2.85 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[2729, 15703])).
% 2.64/2.85 tff(15705,plain,
% 2.64/2.85 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[10791])).
% 2.64/2.85 tff(15706,plain,
% 2.64/2.85 (r(s(elem!1), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(symmetry,[status(thm)],[15705])).
% 2.64/2.85 tff(15707,plain,
% 2.64/2.85 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z)))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[10793])).
% 2.64/2.85 tff(15708,plain,
% 2.64/2.85 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[10800, 15707])).
% 2.64/2.85 tff(15709,plain,
% 2.64/2.85 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[5529])).
% 2.64/2.85 tff(15710,plain,
% 2.64/2.85 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15709, 3539])).
% 2.64/2.85 tff(15711,plain,
% 2.64/2.85 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.64/2.85 inference(symmetry,[status(thm)],[15710])).
% 2.64/2.85 tff(15712,plain,
% 2.64/2.85 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15711])).
% 2.64/2.85 tff(15713,plain,
% 2.64/2.85 (~(s(s(s(s(z)))) = elem!1)),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[319, 15712])).
% 2.64/2.85 tff(15714,plain,
% 2.64/2.85 (b(s(s(s(s(z)))), elem!1)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[254, 239, 15713])).
% 2.64/2.85 tff(15715,plain,
% 2.64/2.85 (~b(elem!1, s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9834, 15714, 1291, 523])).
% 2.64/2.85 tff(15716,plain,
% 2.64/2.85 (b(s(z), s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[12713, 15715, 10])).
% 2.64/2.85 tff(15717,plain,
% 2.64/2.85 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[5529])).
% 2.64/2.85 tff(15718,plain,
% 2.64/2.85 ((s(s(z)) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15717, 4133])).
% 2.64/2.85 tff(15719,plain,
% 2.64/2.85 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.64/2.85 inference(symmetry,[status(thm)],[15718])).
% 2.64/2.85 tff(15720,plain,
% 2.64/2.85 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15719])).
% 2.64/2.85 tff(15721,plain,
% 2.64/2.85 (~(s(s(z)) = elem!1)),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[52, 15720])).
% 2.64/2.85 tff(15722,plain,
% 2.64/2.85 (~(s(s(s(z))) = s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[11953, 15721])).
% 2.64/2.85 tff(15723,plain,
% 2.64/2.85 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[5529])).
% 2.64/2.85 tff(15724,plain,
% 2.64/2.85 ((s(s(s(z))) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15723, 57])).
% 2.64/2.85 tff(15725,plain,
% 2.64/2.85 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 2.64/2.85 inference(symmetry,[status(thm)],[15724])).
% 2.64/2.85 tff(15726,plain,
% 2.64/2.85 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15725, 1194])).
% 2.64/2.85 tff(15727,plain,
% 2.64/2.85 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15726])).
% 2.64/2.85 tff(15728,plain,
% 2.64/2.85 (~(elem!1 = s(s(s(z))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[111, 15727])).
% 2.64/2.85 tff(15729,plain,
% 2.64/2.85 (r(elem!1, s(s(s(z))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4492, 15715, 15728])).
% 2.64/2.85 tff(15730,plain,
% 2.64/2.85 (~(elem!1 = s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[8957, 6036])).
% 2.64/2.85 tff(15731,plain,
% 2.64/2.85 (~b(elem!1, s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9830, 15714, 1291, 523])).
% 2.64/2.85 tff(15732,plain,
% 2.64/2.85 (r(elem!1, s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1069, 15731, 15730])).
% 2.64/2.85 tff(15733,plain,
% 2.64/2.85 (~r(s(s(s(z))), s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9495, 15732, 15729])).
% 2.64/2.85 tff(15734,plain,
% 2.64/2.85 (b(s(s(s(z))), s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9480, 15733, 15722])).
% 2.64/2.85 tff(15735,plain,
% 2.64/2.85 ((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1751, 15353])).
% 2.64/2.85 tff(15736,plain,
% 2.64/2.85 (~r(s(z), s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15735, 15732])).
% 2.64/2.85 tff(15737,plain,
% 2.64/2.85 (b(s(z), s(elem!1))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[397, 15736, 177])).
% 2.64/2.85 tff(15738,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), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(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(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(15739,plain,
% 2.64/2.85 (((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(15740,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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), 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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[15739])).
% 2.64/2.85 tff(15741,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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), 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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15740, 15738])).
% 2.64/2.85 tff(15742,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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(15743,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15742, 15741])).
% 2.64/2.85 tff(15744,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15743, 453, 1549, 11663, 2090, 1446])).
% 2.64/2.85 tff(15745,plain,((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(15746,plain,
% 2.64/2.85 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[15745, 15737, 15734, 15716])).
% 2.64/2.85 tff(15747,plain,
% 2.64/2.85 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[1320, 15746, 15708])).
% 2.64/2.85 tff(15748,plain,
% 2.64/2.85 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15747, 15706])).
% 2.64/2.85 tff(15749,plain,
% 2.64/2.85 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[10791])).
% 2.64/2.85 tff(15750,plain,
% 2.64/2.85 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.64/2.85 inference(symmetry,[status(thm)],[15749])).
% 2.64/2.85 tff(15751,plain,
% 2.64/2.85 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[5529])).
% 2.64/2.85 tff(15752,plain,
% 2.64/2.85 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[15751, 15750])).
% 2.64/2.85 tff(15753,plain,
% 2.64/2.85 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15732, 15752])).
% 2.64/2.85 tff(15754,plain,
% 2.64/2.85 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[5821])).
% 2.64/2.85 tff(15755,plain,
% 2.64/2.85 (r(elem!1, s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(symmetry,[status(thm)],[15754])).
% 2.64/2.85 tff(15756,assumption,(r(elem!1, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.64/2.85 tff(15757,plain,
% 2.64/2.85 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[15756, 15755])).
% 2.64/2.85 tff(15758,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.64/2.85 tff(15759,plain,
% 2.64/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(15760,plain,
% 2.64/2.85 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(15761,plain,
% 2.64/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15760])).
% 2.64/2.86 tff(15762,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[15761, 15759])).
% 2.64/2.86 tff(15763,plain,
% 2.64/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(15764,plain,
% 2.64/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15763, 15762])).
% 2.64/2.86 tff(15765,plain,
% 2.64/2.86 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15764, 268, 2040, 15758])).
% 2.64/2.86 tff(15766,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15765, 15757])).
% 2.64/2.86 tff(15767,plain,((~r(elem!1, s(s(s(s(s(s(s(z))))))))) | (~(elem!1 = s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(15768,plain,
% 2.64/2.86 (~r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15767, 15753, 5529, 15748])).
% 2.64/2.86 tff(15769,plain,
% 2.64/2.86 (b(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[3856, 15768, 15704])).
% 2.64/2.86 tff(15770,plain,
% 2.64/2.86 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15769, 15700])).
% 2.64/2.86 tff(15771,plain,
% 2.64/2.86 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[5529])).
% 2.64/2.86 tff(15772,plain,
% 2.64/2.86 ((~r(s(s(s(s(z)))), elem!1)) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15771])).
% 2.64/2.86 tff(15773,plain,
% 2.64/2.86 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[239, 15772])).
% 2.64/2.86 tff(15774,plain,
% 2.64/2.86 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2463, 69, 15773, 2453])).
% 2.64/2.86 tff(15775,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(15776,plain,
% 2.64/2.86 (((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(15777,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(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15776])).
% 2.64/2.86 tff(15778,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(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[15777, 15775])).
% 2.64/2.86 tff(15779,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(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(15780,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15779, 15778])).
% 2.64/2.86 tff(15781,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15780, 453, 523, 15774, 14079, 15770])).
% 2.64/2.86 tff(15782,plain,(r(s(s(s(s(z)))), elem!1) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~(elem!1 = s(s(s(s(s(z))))))) | (s(z) = s(elem!1)) | b(elem!1, s(z)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(15783,plain,
% 2.64/2.86 (r(s(s(s(s(z)))), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15782, 15663, 15670, 15699, 10, 8836])).
% 2.64/2.86 tff(15784,plain,
% 2.64/2.86 (~r(s(s(elem!1)), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15584, 15783, 15669])).
% 2.64/2.86 tff(15785,plain,
% 2.64/2.86 (b(s(s(elem!1)), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2240, 15784, 15698])).
% 2.64/2.86 tff(15786,plain,
% 2.64/2.86 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15785, 15695])).
% 2.64/2.86 tff(15787,plain,
% 2.64/2.86 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15670])).
% 2.64/2.86 tff(15788,plain,
% 2.64/2.86 ((s(s(z)) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.64/2.86 inference(transitivity,[status(thm)],[15787, 4133])).
% 2.64/2.86 tff(15789,plain,
% 2.64/2.86 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.64/2.86 inference(symmetry,[status(thm)],[15788])).
% 2.64/2.86 tff(15790,plain,
% 2.64/2.86 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15789])).
% 2.64/2.86 tff(15791,plain,
% 2.64/2.86 (~(s(s(z)) = elem!1)),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[52, 15790])).
% 2.64/2.86 tff(15792,plain,
% 2.64/2.86 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15670])).
% 2.64/2.86 tff(15793,plain,
% 2.64/2.86 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15783, 15792])).
% 2.64/2.86 tff(15794,plain,
% 2.64/2.86 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(s(z))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15670])).
% 2.64/2.86 tff(15795,plain,
% 2.64/2.86 (r(s(z), s(s(s(s(s(z))))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15353, 15794])).
% 2.64/2.86 tff(15796,plain,
% 2.64/2.86 (~r(s(z), s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[4686, 268, 15795, 15793])).
% 2.64/2.86 tff(15797,plain,
% 2.64/2.86 (b(s(z), s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1677, 69, 15796, 50])).
% 2.64/2.86 tff(15798,plain,
% 2.64/2.86 ((~r(s(s(z)), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[8427, 15353])).
% 2.64/2.86 tff(15799,plain,
% 2.64/2.86 (~r(s(s(z)), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15798, 15797, 15783])).
% 2.64/2.86 tff(15800,plain,
% 2.64/2.86 (b(s(s(z)), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[782, 15799, 15791])).
% 2.64/2.86 tff(15801,plain,
% 2.64/2.86 (~b(elem!1, s(s(elem!1)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[8609, 15800, 8836, 15786, 15690])).
% 2.64/2.86 tff(15802,plain,
% 2.64/2.86 (r(elem!1, s(s(elem!1)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1024, 15801, 15685])).
% 2.64/2.86 tff(15803,plain,
% 2.64/2.86 (r(elem!1, s(s(s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15802, 15680])).
% 2.64/2.86 tff(15804,plain,
% 2.64/2.86 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15803, 15673])).
% 2.64/2.86 tff(15805,plain,
% 2.64/2.86 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15675])).
% 2.64/2.86 tff(15806,plain,
% 2.64/2.86 (~r(s(s(elem!1)), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1041, 15802, 15356])).
% 2.64/2.86 tff(15807,plain,
% 2.64/2.86 (b(s(s(elem!1)), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1047, 15806])).
% 2.64/2.86 tff(15808,plain,
% 2.64/2.86 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15807, 15805])).
% 2.64/2.86 tff(15809,plain,
% 2.64/2.86 (~r(s(s(s(s(z)))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15657, 15783])).
% 2.64/2.86 tff(15810,plain,
% 2.64/2.86 (b(s(s(s(s(z)))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1098, 15809])).
% 2.64/2.86 tff(15811,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(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(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(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(15812,plain,
% 2.64/2.86 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(15813,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), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(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(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15812])).
% 2.64/2.86 tff(15814,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), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(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(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[15813, 15811])).
% 2.64/2.86 tff(15815,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), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(15816,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(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15815, 15814])).
% 2.64/2.86 tff(15817,plain,
% 2.64/2.86 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15816, 453, 15810, 15797, 15808])).
% 2.64/2.86 tff(15818,plain,
% 2.64/2.86 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[6308, 15817])).
% 2.64/2.86 tff(15819,plain,
% 2.64/2.86 (r(elem!1, s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15670])).
% 2.64/2.86 tff(15820,plain,
% 2.64/2.86 (r(s(s(s(s(s(z))))), s(z))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15356, 15819])).
% 2.64/2.86 tff(15821,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(15822,plain,
% 2.64/2.86 (((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(15823,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15822])).
% 2.64/2.86 tff(15824,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[15823, 15821])).
% 2.64/2.86 tff(15825,plain,
% 2.64/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(15826,plain,
% 2.64/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15825, 15824])).
% 2.64/2.86 tff(15827,plain,
% 2.64/2.86 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15826, 268, 15820, 15793, 15818])).
% 2.64/2.86 tff(15828,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15827, 15804])).
% 2.64/2.86 tff(15829,plain,(r(s(s(s(z))), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(15830,plain,
% 2.64/2.86 (r(s(s(s(z))), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15829, 10])).
% 2.64/2.86 tff(15831,plain,
% 2.64/2.86 (~r(s(s(s(z))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1586, 15830, 15356])).
% 2.64/2.86 tff(15832,plain,
% 2.64/2.86 (b(s(s(s(z))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[134, 15831])).
% 2.64/2.86 tff(15833,plain,
% 2.64/2.86 ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[4885, 15353])).
% 2.64/2.86 tff(15834,plain,
% 2.64/2.86 (~r(s(z), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15833, 1545])).
% 2.64/2.86 tff(15835,plain,
% 2.64/2.86 (b(s(z), s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[227, 15834])).
% 2.64/2.86 tff(15836,plain,
% 2.64/2.86 (~r(s(s(s(s(z)))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15657, 1159])).
% 2.64/2.86 tff(15837,plain,
% 2.64/2.86 (b(s(s(s(s(z)))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1098, 15836])).
% 2.64/2.86 tff(15838,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[3782, 5340, 15837, 15835, 120])).
% 2.64/2.86 tff(15839,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(15840,plain,
% 2.64/2.86 (~r(s(s(s(s(z)))), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15839, 15832, 15830])).
% 2.64/2.86 tff(15841,plain,
% 2.64/2.86 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.86 inference(symmetry,[status(thm)],[6987])).
% 2.64/2.86 tff(15842,plain,
% 2.64/2.86 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15830, 15841])).
% 2.64/2.86 tff(15843,plain,
% 2.64/2.86 (~b(s(s(s(s(z)))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[4309, 12410, 10])).
% 2.64/2.86 tff(15844,plain,
% 2.64/2.86 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15395, 15843])).
% 2.64/2.86 tff(15845,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15844, 15842])).
% 2.64/2.86 tff(15846,plain,((~(s(s(s(s(z)))) = elem!1)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(15847,plain,
% 2.64/2.86 (~(s(s(s(s(z)))) = elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15846, 10])).
% 2.64/2.86 tff(15848,plain,
% 2.64/2.86 (r(s(z), s(s(s(z)))) | (~(s(s(s(z))) = elem!1))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[6774, 15353])).
% 2.64/2.86 tff(15849,plain,
% 2.64/2.86 (~(s(s(s(z))) = elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15848, 15834])).
% 2.64/2.86 tff(15850,plain,
% 2.64/2.86 (~(elem!1 = s(s(s(z))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[4487, 15849])).
% 2.64/2.86 tff(15851,plain,
% 2.64/2.86 (~r(s(s(s(z))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1586, 1545, 238])).
% 2.64/2.86 tff(15852,plain,
% 2.64/2.86 (b(s(s(s(z))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[134, 15851])).
% 2.64/2.86 tff(15853,plain,
% 2.64/2.86 (~b(s(s(s(s(z)))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[3782, 523, 15835, 15852])).
% 2.64/2.86 tff(15854,plain,
% 2.64/2.86 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15395, 15853])).
% 2.64/2.86 tff(15855,plain,
% 2.64/2.86 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1656, 15854])).
% 2.64/2.86 tff(15856,plain,
% 2.64/2.86 (~b(s(z), s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2894, 15855, 15852, 523])).
% 2.64/2.86 tff(15857,plain,
% 2.64/2.86 (r(s(z), s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1677, 69, 50, 15856])).
% 2.64/2.86 tff(15858,plain,
% 2.64/2.86 (r(s(s(s(s(z)))), s(z))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1098, 15853])).
% 2.64/2.86 tff(15859,plain,
% 2.64/2.86 (~r(elem!1, s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[12993, 15858, 238])).
% 2.64/2.86 tff(15860,plain,
% 2.64/2.86 (b(elem!1, s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1087, 15859, 1055])).
% 2.64/2.86 tff(15861,plain,
% 2.64/2.86 ((~r(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[7539, 15353])).
% 2.64/2.86 tff(15862,plain,
% 2.64/2.86 (~r(s(s(z)), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15861, 15835, 1545])).
% 2.64/2.86 tff(15863,plain,
% 2.64/2.86 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.86 inference(symmetry,[status(thm)],[14477])).
% 2.64/2.86 tff(15864,plain,
% 2.64/2.86 ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) <=> (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15863])).
% 2.64/2.86 tff(15865,plain,
% 2.64/2.86 (b(s(s(s(s(s(z))))), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[7218, 3468, 238, 1545, 15835, 15852])).
% 2.64/2.86 tff(15866,plain,
% 2.64/2.86 ((~r(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[7866, 15602])).
% 2.64/2.86 tff(15867,plain,
% 2.64/2.86 (~r(s(s(elem!1)), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15866, 15852, 238, 1545, 15835])).
% 2.64/2.86 tff(15868,plain,
% 2.64/2.86 (b(s(s(elem!1)), elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2240, 3502, 15867])).
% 2.64/2.86 tff(15869,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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(15870,plain,
% 2.64/2.86 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(15871,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $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(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), 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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[15870])).
% 2.64/2.86 tff(15872,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), 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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.64/2.86 inference(transitivity,[status(thm)],[15871, 15869])).
% 2.64/2.86 tff(15873,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(15874,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15873, 15872])).
% 2.64/2.86 tff(15875,plain,
% 2.64/2.86 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[15874, 453, 14481, 15868, 15865])).
% 2.64/2.86 tff(15876,plain,
% 2.64/2.86 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15875, 15864])).
% 2.64/2.86 tff(15877,plain,
% 2.64/2.86 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[10556, 15876])).
% 2.64/2.86 tff(15878,plain,
% 2.64/2.86 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15877, 3536])).
% 2.64/2.86 tff(15879,plain,
% 2.64/2.86 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[3477])).
% 2.64/2.86 tff(15880,plain,
% 2.64/2.86 ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) <=> (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[3479])).
% 2.64/2.86 tff(15881,plain,
% 2.64/2.86 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[3862, 3823])).
% 2.64/2.86 tff(15882,plain,
% 2.64/2.86 (r(s(elem!1), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.64/2.86 inference(monotonicity,[status(thm)],[3515])).
% 2.64/2.86 tff(15883,plain,
% 2.64/2.86 (r(s(s(s(z))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.64/2.86 inference(symmetry,[status(thm)],[15882])).
% 2.64/2.86 tff(15884,plain,
% 2.64/2.86 (r(s(elem!1), elem!1)),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[1545, 15883])).
% 2.64/2.86 tff(15885,plain,
% 2.64/2.86 (b(s(z), s(elem!1))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[3644, 3468, 15835])).
% 2.64/2.86 tff(15886,plain,
% 2.64/2.86 (b(s(elem!1), s(z))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[15852, 5605])).
% 2.64/2.86 tff(15887,assumption,(s(z) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.64/2.86 tff(15888,plain,
% 2.64/2.86 (s(s(s(s(s(s(s(z))))))) = s(z)),
% 2.64/2.86 inference(symmetry,[status(thm)],[15887])).
% 2.64/2.86 tff(15889,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2636, 15888])).
% 2.64/2.86 tff(15890,plain,(~(s(z) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(15891,plain,
% 2.64/2.86 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[8298, 268, 15353, 8292])).
% 2.64/2.86 tff(15892,plain,
% 2.64/2.86 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1485, 69, 15891, 15890])).
% 2.64/2.86 tff(15893,plain,
% 2.64/2.86 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[3999, 14998, 1284])).
% 2.64/2.86 tff(15894,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(15895,plain,
% 2.64/2.86 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(15896,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15895])).
% 2.64/2.87 tff(15897,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[15896, 15894])).
% 2.64/2.87 tff(15898,plain,
% 2.64/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(15899,plain,
% 2.64/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[15898, 15897])).
% 2.64/2.87 tff(15900,plain,
% 2.64/2.87 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15899, 268, 1892, 8292])).
% 2.64/2.87 tff(15901,plain,
% 2.64/2.87 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[1320, 15900, 1442])).
% 2.64/2.87 tff(15902,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(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(15903,plain,
% 2.64/2.87 (((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(15904,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(s(s(s(z))))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15903])).
% 2.64/2.87 tff(15905,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(s(s(s(z))))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[15904, 15902])).
% 2.64/2.87 tff(15906,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(s(s(s(z))))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(15907,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[15906, 15905])).
% 2.64/2.87 tff(15908,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15907, 453, 1059, 1549, 15901, 15893, 15892])).
% 2.64/2.87 tff(15909,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(15910,plain,
% 2.64/2.87 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15909, 15886, 15885, 3476, 3825, 15884])).
% 2.64/2.87 tff(15911,plain,
% 2.64/2.87 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[3875, 15910, 15881])).
% 2.64/2.87 tff(15912,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(15913,plain,
% 2.64/2.87 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(15914,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15913])).
% 2.64/2.87 tff(15915,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[15914, 15912])).
% 2.64/2.87 tff(15916,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(15917,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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[15916, 15915])).
% 2.64/2.87 tff(15918,plain,
% 2.64/2.87 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15917, 453, 14481, 15868, 15911])).
% 2.64/2.87 tff(15919,plain,
% 2.64/2.87 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[15918, 15880])).
% 2.64/2.87 tff(15920,plain,
% 2.64/2.87 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[2696, 15919])).
% 2.64/2.87 tff(15921,plain,
% 2.64/2.87 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[15920, 15879])).
% 2.64/2.87 tff(15922,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(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(15923,plain,
% 2.64/2.87 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(15924,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15923])).
% 2.64/2.87 tff(15925,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[15924, 15922])).
% 2.64/2.87 tff(15926,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(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(15927,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(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[15926, 15925])).
% 2.64/2.87 tff(15928,plain,
% 2.64/2.87 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15927, 453, 14481, 15865, 15911])).
% 2.64/2.87 tff(15929,plain,
% 2.64/2.87 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[11422, 15928])).
% 2.64/2.87 tff(15930,plain,
% 2.64/2.87 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[3477])).
% 2.64/2.87 tff(15931,plain,
% 2.64/2.87 (r(s(s(elem!1)), s(z))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[1132, 15930])).
% 2.64/2.87 tff(15932,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(15933,plain,
% 2.64/2.87 (((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(15934,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15933])).
% 2.64/2.87 tff(15935,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[15934, 15932])).
% 2.64/2.87 tff(15936,plain,
% 2.64/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(15937,plain,
% 2.64/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[15936, 15935])).
% 2.64/2.87 tff(15938,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15937, 268, 15931, 15929, 15921, 15878])).
% 2.64/2.87 tff(15939,plain,((~(s(s(z)) = elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(15940,plain,
% 2.64/2.87 (~(s(s(z)) = elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15939, 15860, 15858, 1545, 238])).
% 2.64/2.87 tff(15941,plain,
% 2.64/2.87 (b(s(s(z)), elem!1)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[782, 15940, 15862])).
% 2.64/2.87 tff(15942,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(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(15943,plain,
% 2.64/2.87 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(15944,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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[15943])).
% 2.64/2.87 tff(15945,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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.64/2.87 inference(transitivity,[status(thm)],[15944, 15942])).
% 2.64/2.87 tff(15946,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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(15947,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[15946, 15945])).
% 2.64/2.87 tff(15948,plain,
% 2.64/2.87 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[15947, 453, 523, 15941, 15855, 15860, 299])).
% 2.64/2.87 tff(15949,plain,
% 2.64/2.87 (r(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[2370, 69, 2359, 15948])).
% 2.64/2.87 tff(15950,plain,
% 2.64/2.87 (~r(s(z), s(s(z)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[7637, 268, 15857, 15949])).
% 2.64/2.87 tff(15951,plain,
% 2.64/2.88 (b(s(z), s(s(z)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[757, 15950])).
% 2.64/2.88 tff(15952,plain,
% 2.64/2.88 (~b(s(s(z)), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13827, 15951, 15852, 15835])).
% 2.64/2.88 tff(15953,plain,
% 2.64/2.88 (r(s(s(z)), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1350, 69, 15952, 12356])).
% 2.64/2.88 tff(15954,plain,
% 2.64/2.88 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[14464, 268, 256, 1149])).
% 2.64/2.88 tff(15955,plain,
% 2.64/2.88 (b(elem!1, s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[466, 15954, 8840])).
% 2.64/2.88 tff(15956,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[4078, 13764, 15955, 922, 5323])).
% 2.64/2.88 tff(15957,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(15958,plain,
% 2.64/2.88 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[15957, 15941, 15953, 1149, 637, 1545])).
% 2.64/2.88 tff(15959,plain,
% 2.64/2.88 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[687, 15958])).
% 2.64/2.88 tff(15960,plain,
% 2.64/2.88 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[5380, 15959, 15857, 15852])).
% 2.64/2.88 tff(15961,plain,
% 2.64/2.88 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1788, 15959, 523, 15855])).
% 2.64/2.88 tff(15962,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[328, 15961, 15960])).
% 2.64/2.88 tff(15963,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(z))) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(15964,plain,
% 2.64/2.88 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[15963, 1149, 637, 1545, 255, 238, 9])).
% 2.64/2.88 tff(15965,plain,
% 2.64/2.88 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[518, 15964])).
% 2.64/2.88 tff(15966,plain,
% 2.64/2.88 (~r(elem!1, s(s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[13281, 15965, 1149])).
% 2.64/2.88 tff(15967,plain,
% 2.64/2.88 (b(elem!1, s(s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1087, 15966, 9])).
% 2.64/2.88 tff(15968,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(15969,plain,
% 2.64/2.88 (((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(15970,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[15969])).
% 2.64/2.88 tff(15971,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.64/2.88 inference(transitivity,[status(thm)],[15970, 15968])).
% 2.64/2.88 tff(15972,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(15973,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[15972, 15971])).
% 2.64/2.88 tff(15974,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[15973, 268, 14136, 15929, 15921, 15878])).
% 2.64/2.88 tff(15975,plain,((~(s(s(z)) = elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(15976,plain,
% 2.64/2.88 (~(s(s(z)) = elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[15975, 15967, 1545, 15965, 238])).
% 2.64/2.88 tff(15977,plain,
% 2.64/2.88 (b(s(s(z)), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[782, 15976, 15862])).
% 2.64/2.88 tff(15978,plain,
% 2.64/2.88 ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[730, 15353])).
% 2.64/2.88 tff(15979,plain,
% 2.64/2.88 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[15978, 258])).
% 2.64/2.88 tff(15980,plain,
% 2.64/2.88 (b(s(s(s(s(s(z))))), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[643, 15979, 637])).
% 2.64/2.88 tff(15981,plain,
% 2.64/2.88 (b(elem!1, s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[466, 4103, 8840])).
% 2.64/2.88 tff(15982,plain,
% 2.64/2.88 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[947, 15981, 299, 922, 15980])).
% 2.64/2.88 tff(15983,plain,
% 2.64/2.88 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10556, 15982])).
% 2.64/2.88 tff(15984,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[11247, 453, 15981, 15980, 299, 15983])).
% 2.64/2.88 tff(15985,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(15986,plain,
% 2.64/2.88 (~r(s(s(s(s(s(z))))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[15985, 15977, 255, 637, 238])).
% 2.64/2.88 tff(15987,plain,
% 2.64/2.88 (b(s(s(s(s(s(z))))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[297, 15986])).
% 2.64/2.88 tff(15988,plain,
% 2.64/2.88 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[3300, 453, 15987, 15852, 15835])).
% 2.64/2.88 tff(15989,plain,
% 2.64/2.88 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[687, 15988])).
% 2.64/2.88 tff(15990,plain,
% 2.64/2.88 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1566, 15989, 1545])).
% 2.64/2.88 tff(15991,plain,
% 2.64/2.88 (b(s(s(s(s(s(z))))), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[643, 15990, 637])).
% 2.64/2.88 tff(15992,plain,
% 2.64/2.88 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1982, 15989, 15965])).
% 2.64/2.88 tff(15993,plain,
% 2.64/2.88 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[328, 15992])).
% 2.64/2.88 tff(15994,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(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(15995,plain,
% 2.64/2.88 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(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(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(15996,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), s(s(s(z))))) | (~b(s(z), s(s(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(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[15995])).
% 2.64/2.88 tff(15997,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), s(s(s(z))))) | (~b(s(z), s(s(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(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.88 inference(transitivity,[status(thm)],[15996, 15994])).
% 2.64/2.88 tff(15998,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), s(s(s(z))))) | (~b(s(z), s(s(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(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(15999,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[15998, 15997])).
% 2.64/2.88 tff(16000,plain,
% 2.64/2.88 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[15999, 453, 15987, 15852, 15835])).
% 2.64/2.88 tff(16001,plain,
% 2.64/2.88 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[2570, 16000])).
% 2.64/2.88 tff(16002,plain,
% 2.64/2.88 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[8666, 16001, 15965])).
% 2.64/2.88 tff(16003,plain,
% 2.64/2.88 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10556, 16002])).
% 2.64/2.88 tff(16004,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[6664, 16003, 15993, 3, 15991, 15966, 239])).
% 2.64/2.88 tff(16005,plain,((~r(elem!1, s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | r(s(s(s(s(z)))), elem!1) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(16006,plain,
% 2.64/2.88 (~r(elem!1, s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16005, 239, 3, 637, 1545, 238])).
% 2.64/2.88 tff(16007,plain,
% 2.64/2.88 (b(elem!1, s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[4492, 16006, 15850])).
% 2.64/2.88 tff(16008,plain,
% 2.64/2.88 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[3468])).
% 2.64/2.88 tff(16009,plain,
% 2.64/2.88 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(elem!1, s(s(s(z)))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16008])).
% 2.64/2.88 tff(16010,plain,
% 2.64/2.88 (~b(elem!1, s(s(s(z))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[8939, 16009])).
% 2.64/2.88 tff(16011,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1275, 16010])).
% 2.64/2.88 tff(16012,plain,(b(s(s(z)), s(s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(16013,plain,
% 2.64/2.88 (b(s(s(z)), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16012, 3468, 1275])).
% 2.64/2.88 tff(16014,plain,
% 2.64/2.88 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[3468])).
% 2.64/2.88 tff(16015,plain,
% 2.64/2.88 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.88 inference(symmetry,[status(thm)],[16014])).
% 2.64/2.88 tff(16016,plain,
% 2.64/2.88 (b(elem!1, s(s(elem!1))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.88 inference(transitivity,[status(thm)],[14479, 16015])).
% 2.64/2.88 tff(16017,plain,
% 2.64/2.88 ((s(s(z)) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[3468])).
% 2.64/2.88 tff(16018,plain,
% 2.64/2.88 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16017])).
% 2.64/2.88 tff(16019,plain,
% 2.64/2.88 (~(s(elem!1) = s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[179, 14131])).
% 2.64/2.88 tff(16020,plain,
% 2.64/2.88 (~(s(s(z)) = s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1188, 16019])).
% 2.64/2.88 tff(16021,plain,
% 2.64/2.88 (~(elem!1 = s(s(elem!1)))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[16020, 16018])).
% 2.64/2.88 tff(16022,plain,
% 2.64/2.88 (~(s(elem!1) = s(s(elem!1)))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[15602, 11781])).
% 2.64/2.88 tff(16023,plain,
% 2.64/2.88 (~r(elem!1, s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[2017, 16022, 238, 15885, 15884, 15886])).
% 2.64/2.88 tff(16024,plain,
% 2.64/2.88 (b(elem!1, s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1024, 16023, 16021])).
% 2.64/2.88 tff(16025,plain,
% 2.64/2.88 (b(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[16024, 16016])).
% 2.64/2.88 tff(16026,plain,
% 2.64/2.88 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[2965, 16025, 15852, 16013])).
% 2.64/2.88 tff(16027,plain,
% 2.64/2.88 (b(elem!1, s(s(s(s(z)))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[16024, 14479])).
% 2.64/2.88 tff(16028,plain,
% 2.64/2.88 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[15975, 16027, 1545, 3468, 238])).
% 2.64/2.88 tff(16029,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[518, 16028, 16026])).
% 2.64/2.88 tff(16030,plain,((~(s(s(z)) = elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(z))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(16031,plain,
% 2.64/2.88 (~(s(s(z)) = elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16030, 16007, 238, 1545])).
% 2.64/2.88 tff(16032,plain,
% 2.64/2.88 (b(s(s(z)), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[782, 16031, 15862])).
% 2.64/2.88 tff(16033,plain,
% 2.64/2.88 (~r(s(s(s(s(s(z))))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[15985, 16032, 255, 637, 238])).
% 2.64/2.88 tff(16034,plain,
% 2.64/2.88 (b(s(s(s(s(s(z))))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[297, 16033])).
% 2.64/2.88 tff(16035,plain,
% 2.64/2.88 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[15999, 453, 16034, 15852, 15835])).
% 2.64/2.88 tff(16036,plain,
% 2.64/2.88 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[2570, 16035])).
% 2.64/2.88 tff(16037,plain,
% 2.64/2.88 (~b(s(s(s(s(z)))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[3782, 523, 2090, 120])).
% 2.64/2.88 tff(16038,plain,
% 2.64/2.88 (r(s(s(s(s(z)))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1098, 16037])).
% 2.64/2.88 tff(16039,plain,
% 2.64/2.88 (~b(elem!1, s(s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1621, 523, 120, 1275])).
% 2.64/2.88 tff(16040,plain,
% 2.64/2.88 (r(elem!1, s(s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1087, 16039, 1055])).
% 2.64/2.88 tff(16041,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[12993, 16040, 16038, 238])).
% 2.64/2.88 tff(16042,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(z))) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(16043,plain,
% 2.64/2.88 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16042, 16007, 9, 15852, 238, 15835])).
% 2.64/2.88 tff(16044,plain,
% 2.64/2.88 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[518, 16043])).
% 2.64/2.88 tff(16045,plain,
% 2.64/2.88 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[8666, 16044, 16036])).
% 2.64/2.88 tff(16046,plain,
% 2.64/2.88 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10556, 16045])).
% 2.64/2.88 tff(16047,plain,
% 2.64/2.88 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[3300, 453, 16034, 15852, 15835])).
% 2.64/2.88 tff(16048,plain,
% 2.64/2.88 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[687, 16047])).
% 2.64/2.88 tff(16049,plain,
% 2.64/2.88 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1982, 16044, 16048])).
% 2.64/2.88 tff(16050,plain,
% 2.64/2.88 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[328, 16049])).
% 2.64/2.88 tff(16051,plain,
% 2.64/2.88 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1566, 16048, 1545])).
% 2.64/2.88 tff(16052,plain,
% 2.64/2.88 (b(s(s(s(s(s(z))))), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[643, 16051, 637])).
% 2.64/2.88 tff(16053,plain,
% 2.64/2.88 (r(elem!1, s(s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[6664, 16046, 3, 16052, 16050, 239])).
% 2.64/2.88 tff(16054,plain,
% 2.64/2.88 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[15185, 16053, 1545])).
% 2.64/2.88 tff(16055,plain,
% 2.64/2.88 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1656, 16054])).
% 2.64/2.88 tff(16056,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[15341, 268, 412, 1545, 4621])).
% 2.64/2.88 tff(16057,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(16058,plain,
% 2.64/2.88 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16057, 16036, 1545])).
% 2.64/2.88 tff(16059,plain,
% 2.64/2.88 (b(elem!1, s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[466, 16058, 8840])).
% 2.64/2.88 tff(16060,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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(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(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(16061,plain,
% 2.64/2.88 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(16062,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16061])).
% 2.64/2.88 tff(16063,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, 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(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.64/2.88 inference(transitivity,[status(thm)],[16062, 16060])).
% 2.64/2.88 tff(16064,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(16065,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[16064, 16063])).
% 2.64/2.88 tff(16066,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16065, 453, 16059, 16055, 16050, 255, 16046, 16007])).
% 2.64/2.88 tff(16067,plain,(r(s(s(s(s(z)))), elem!1) | (~r(s(s(s(z))), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, s(z))) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(16068,plain,
% 2.64/2.88 (s(s(s(s(s(z))))) = elem!1),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[16067, 15847, 15830, 15356, 15840])).
% 2.64/2.88 tff(16069,plain,
% 2.64/2.88 (elem!1 = s(s(s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[5538, 16068])).
% 2.64/2.88 tff(16070,plain,
% 2.64/2.88 (~r(s(z), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[15833, 15830])).
% 2.64/2.88 tff(16071,plain,
% 2.64/2.88 (b(s(z), s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[227, 16070])).
% 2.64/2.88 tff(16072,plain,
% 2.64/2.88 (~r(s(s(z)), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[15861, 16071, 15830])).
% 2.64/2.88 tff(16073,plain,
% 2.64/2.88 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16069])).
% 2.64/2.88 tff(16074,plain,
% 2.64/2.88 ((s(s(z)) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.64/2.88 inference(transitivity,[status(thm)],[16073, 4133])).
% 2.64/2.88 tff(16075,plain,
% 2.64/2.88 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.64/2.88 inference(symmetry,[status(thm)],[16074])).
% 2.64/2.88 tff(16076,plain,
% 2.64/2.88 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16075])).
% 2.64/2.88 tff(16077,plain,
% 2.64/2.88 (~(s(s(z)) = elem!1)),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[52, 16076])).
% 2.64/2.88 tff(16078,plain,
% 2.64/2.88 (b(s(s(z)), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[782, 16077, 16072])).
% 2.64/2.88 tff(16079,plain,
% 2.64/2.88 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[12865, 16078, 16069])).
% 2.64/2.88 tff(16080,plain,
% 2.64/2.88 (s(elem!1) = s(s(s(s(s(s(z))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16069])).
% 2.64/2.88 tff(16081,plain,
% 2.64/2.88 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16080])).
% 2.64/2.88 tff(16082,plain,
% 2.64/2.88 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16081, 16069])).
% 2.64/2.88 tff(16083,plain,
% 2.64/2.88 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16082])).
% 2.64/2.88 tff(16084,plain,
% 2.64/2.88 (~r(s(s(elem!1)), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[15866, 15832, 15356, 15830, 16071])).
% 2.64/2.88 tff(16085,plain,
% 2.64/2.88 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[16084, 16083])).
% 2.64/2.88 tff(16086,plain,
% 2.64/2.88 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[11422, 16085])).
% 2.64/2.88 tff(16087,plain,
% 2.64/2.88 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16069])).
% 2.64/2.88 tff(16088,plain,
% 2.64/2.88 (b(s(s(s(s(z)))), elem!1)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[254, 15847, 15840])).
% 2.64/2.88 tff(16089,plain,
% 2.64/2.88 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[16088, 16087])).
% 2.64/2.88 tff(16090,plain,
% 2.64/2.88 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16081])).
% 2.64/2.88 tff(16091,plain,
% 2.64/2.88 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(z)) = s(s(s(s(s(s(s(z)))))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16090])).
% 2.64/2.88 tff(16092,plain,
% 2.64/2.88 (~(s(elem!1) = s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[5852, 16068])).
% 2.64/2.88 tff(16093,plain,
% 2.64/2.88 (~(s(s(z)) = s(s(elem!1)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1188, 16092])).
% 2.64/2.88 tff(16094,plain,
% 2.64/2.88 (~(s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[16093, 16091])).
% 2.64/2.88 tff(16095,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(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(16096,plain,
% 2.64/2.88 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(16097,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[16096])).
% 2.64/2.88 tff(16098,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.64/2.88 inference(transitivity,[status(thm)],[16097, 16095])).
% 2.64/2.88 tff(16099,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(16100,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(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[16099, 16098])).
% 2.64/2.89 tff(16101,plain,
% 2.64/2.89 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[16100, 453, 1780, 10689, 8943])).
% 2.64/2.89 tff(16102,plain,
% 2.64/2.89 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[8583, 69, 8580, 16101])).
% 2.64/2.89 tff(16103,plain,
% 2.64/2.89 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[6600, 453, 1780, 2497, 8943])).
% 2.64/2.89 tff(16104,plain,
% 2.64/2.89 (r(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[2370, 69, 2359, 16103])).
% 2.64/2.89 tff(16105,plain,
% 2.64/2.89 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[9136, 453, 1780, 2497, 8943])).
% 2.64/2.89 tff(16106,plain,
% 2.64/2.89 (r(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[4293, 16105])).
% 2.64/2.89 tff(16107,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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16108,plain,
% 2.64/2.89 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16109,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(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(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[16108])).
% 2.64/2.89 tff(16110,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(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(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[16109, 16107])).
% 2.64/2.89 tff(16111,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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(16112,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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[16111, 16110])).
% 2.64/2.89 tff(16113,plain,
% 2.64/2.89 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[16112, 453, 1780, 2497, 10689])).
% 2.64/2.89 tff(16114,plain,
% 2.64/2.89 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[6308, 16113])).
% 2.64/2.89 tff(16115,plain,
% 2.64/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16116,plain,
% 2.64/2.89 (((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16117,plain,
% 2.64/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[16116])).
% 2.64/2.89 tff(16118,plain,
% 2.64/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[16117, 16115])).
% 2.64/2.89 tff(16119,plain,
% 2.64/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(16120,plain,
% 2.64/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[16119, 16118])).
% 2.64/2.89 tff(16121,plain,
% 2.64/2.89 ($false),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[16120, 268, 16114, 16106, 16104, 16102])).
% 2.64/2.89 tff(16122,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (s(s(z)) = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.89 tff(16123,plain,
% 2.64/2.89 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[16122, 16094, 16089, 16079, 16086])).
% 2.64/2.89 tff(16124,plain,
% 2.64/2.89 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[328, 16123])).
% 2.64/2.89 tff(16125,plain,
% 2.64/2.89 (r(elem!1, s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[16069])).
% 2.64/2.89 tff(16126,plain,
% 2.64/2.89 (r(s(s(s(s(s(z))))), s(z))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[15356, 16125])).
% 2.64/2.89 tff(16127,plain,
% 2.64/2.89 (~r(s(s(s(s(z)))), s(z))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[2414, 16124, 16126])).
% 2.64/2.89 tff(16128,plain,
% 2.64/2.89 (b(s(s(s(s(z)))), s(z))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1098, 16127])).
% 2.64/2.89 tff(16129,plain,
% 2.64/2.89 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1982, 256, 301])).
% 2.64/2.89 tff(16130,plain,
% 2.64/2.89 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[518, 16129])).
% 2.64/2.89 tff(16131,plain,
% 2.64/2.89 (r(elem!1, s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[5534, 5965, 301])).
% 2.64/2.89 tff(16132,plain,
% 2.64/2.89 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[5432, 15518, 1545, 16131])).
% 2.64/2.89 tff(16133,plain,
% 2.64/2.89 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1656, 16132])).
% 2.64/2.89 tff(16134,plain,
% 2.64/2.89 (~b(s(z), s(s(s(z))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[2102, 16133, 16130, 1764])).
% 2.64/2.89 tff(16135,plain,
% 2.64/2.89 (r(s(z), s(s(s(z))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[225, 69, 109, 16134])).
% 2.64/2.89 tff(16136,plain,
% 2.64/2.89 ($false),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1155, 268, 238, 15518, 16135])).
% 2.64/2.89 tff(16137,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~r(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.89 tff(16138,plain,
% 2.64/2.89 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[16137, 16128, 15356, 15830, 16068, 16124])).
% 2.64/2.89 tff(16139,plain,
% 2.64/2.89 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[687, 16138])).
% 2.64/2.89 tff(16140,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(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16141,plain,
% 2.64/2.89 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16142,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[16141])).
% 2.64/2.89 tff(16143,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[16142, 16140])).
% 2.64/2.89 tff(16144,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(16145,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(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[16144, 16143])).
% 2.64/2.89 tff(16146,plain,
% 2.64/2.89 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[16145, 453, 16139, 16086, 16079])).
% 2.64/2.89 tff(16147,plain,
% 2.64/2.89 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[8583, 69, 16094, 16146])).
% 2.64/2.89 tff(16148,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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(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(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16149,plain,
% 2.64/2.89 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16150,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(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(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[16149])).
% 2.64/2.89 tff(16151,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(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(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[16150, 16148])).
% 2.64/2.89 tff(16152,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(16153,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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[16152, 16151])).
% 2.64/2.89 tff(16154,plain,
% 2.64/2.89 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[16153, 453, 16139, 16089, 16079])).
% 2.64/2.89 tff(16155,plain,
% 2.64/2.89 (r(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[2370, 69, 2359, 16154])).
% 2.64/2.89 tff(16156,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(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(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(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16157,plain,
% 2.64/2.89 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(16158,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[16157])).
% 2.64/2.89 tff(16159,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[16158, 16156])).
% 2.64/2.89 tff(16160,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.64/2.90 inference(quant_inst,[status(thm)],[])).
% 2.64/2.90 tff(16161,plain,
% 2.64/2.90 ((~![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(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.64/2.90 inference(modus_ponens,[status(thm)],[16160, 16159])).
% 2.64/2.90 tff(16162,plain,
% 2.64/2.90 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[16161, 453, 16139, 16089, 16079])).
% 2.64/2.90 tff(16163,plain,
% 2.64/2.90 (r(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[4293, 16162])).
% 2.64/2.90 tff(16164,plain,
% 2.64/2.90 (((~![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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.64/2.90 inference(rewrite,[status(thm)],[])).
% 2.64/2.90 tff(16165,plain,
% 2.64/2.90 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.64/2.90 inference(rewrite,[status(thm)],[])).
% 2.64/2.90 tff(16166,plain,
% 2.64/2.90 (((~![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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(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(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 2.64/2.90 inference(monotonicity,[status(thm)],[16165])).
% 2.64/2.90 tff(16167,plain,
% 2.64/2.90 (((~![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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(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(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.64/2.90 inference(transitivity,[status(thm)],[16166, 16164])).
% 2.64/2.90 tff(16168,plain,
% 2.64/2.90 ((~![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(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.64/2.90 inference(quant_inst,[status(thm)],[])).
% 2.64/2.90 tff(16169,plain,
% 2.64/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[16168, 16167])).
% 2.74/2.90 tff(16170,plain,
% 2.74/2.90 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16169, 453, 16139, 16089, 16086])).
% 2.74/2.90 tff(16171,plain,
% 2.74/2.90 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[6308, 16170])).
% 2.74/2.90 tff(16172,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16120, 268, 16171, 16163, 16155, 16147])).
% 2.74/2.90 tff(16173,plain,(b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(16174,plain,
% 2.74/2.90 (~(s(s(s(z))) = elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[12720, 221, 16173])).
% 2.74/2.90 tff(16175,plain,
% 2.74/2.90 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[15407, 700])).
% 2.74/2.90 tff(16176,plain,
% 2.74/2.90 (b(s(s(s(z))), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[74, 16174, 2])).
% 2.74/2.90 tff(16177,plain,
% 2.74/2.90 (~b(s(s(z)), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[10938, 453, 2077, 1291, 922])).
% 2.74/2.90 tff(16178,plain,
% 2.74/2.90 (r(s(s(z)), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1350, 69, 16177, 12356])).
% 2.74/2.90 tff(16179,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(16180,plain,
% 2.74/2.90 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(16181,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16180])).
% 2.74/2.90 tff(16182,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.74/2.90 inference(transitivity,[status(thm)],[16181, 16179])).
% 2.74/2.90 tff(16183,plain,
% 2.74/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(16184,plain,
% 2.74/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[16183, 16182])).
% 2.74/2.90 tff(16185,plain,
% 2.74/2.90 (~r(s(s(z)), s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16184, 268, 701, 257, 16178])).
% 2.74/2.90 tff(16186,plain,
% 2.74/2.90 (b(s(s(z)), s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[720, 69, 717, 16185])).
% 2.74/2.90 tff(16187,plain,
% 2.74/2.90 (~r(s(z), s(s(z)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[9038, 7326, 257])).
% 2.74/2.90 tff(16188,plain,
% 2.74/2.90 (b(s(z), s(s(z)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[757, 16187])).
% 2.74/2.90 tff(16189,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(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(16190,plain,
% 2.74/2.90 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(16191,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), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16190])).
% 2.74/2.90 tff(16192,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), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 2.74/2.90 inference(transitivity,[status(thm)],[16191, 16189])).
% 2.74/2.90 tff(16193,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), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(16194,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[16193, 16192])).
% 2.74/2.90 tff(16195,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16194, 453, 2077, 922, 16188, 16186])).
% 2.74/2.90 tff(16196,plain,((~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(16197,plain,
% 2.74/2.90 ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16196, 15353])).
% 2.74/2.90 tff(16198,plain,
% 2.74/2.90 (~b(s(s(z)), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16197, 1291, 16173, 257])).
% 2.74/2.90 tff(16199,plain,
% 2.74/2.90 ((~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)))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1611, 15353])).
% 2.74/2.90 tff(16200,plain,
% 2.74/2.90 (~r(s(s(s(s(z)))), s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16199, 11, 257])).
% 2.74/2.90 tff(16201,plain,
% 2.74/2.90 (b(s(s(s(s(z)))), s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1098, 16200])).
% 2.74/2.90 tff(16202,plain,
% 2.74/2.90 ((~r(s(s(z)), elem!1)) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[10897, 15353])).
% 2.74/2.90 tff(16203,plain,
% 2.74/2.90 (~r(s(s(z)), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16202, 16201, 16173, 1055])).
% 2.74/2.90 tff(16204,plain,
% 2.74/2.90 (s(s(z)) = elem!1),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[782, 16203, 16198])).
% 2.74/2.90 tff(16205,plain,
% 2.74/2.90 (s(s(s(z))) = s(elem!1)),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16204])).
% 2.74/2.90 tff(16206,plain,
% 2.74/2.90 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16205])).
% 2.74/2.90 tff(16207,plain,
% 2.74/2.90 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16206])).
% 2.74/2.90 tff(16208,plain,
% 2.74/2.90 (b(s(s(elem!1)), s(z))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[16201, 16207])).
% 2.74/2.90 tff(16209,plain,
% 2.74/2.90 (~(s(s(elem!1)) = elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[3501, 16204])).
% 2.74/2.90 tff(16210,plain,
% 2.74/2.90 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.74/2.90 inference(symmetry,[status(thm)],[16206])).
% 2.74/2.90 tff(16211,plain,
% 2.74/2.90 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16210])).
% 2.74/2.90 tff(16212,plain,
% 2.74/2.90 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.74/2.90 inference(symmetry,[status(thm)],[16211])).
% 2.74/2.90 tff(16213,plain,
% 2.74/2.90 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16205])).
% 2.74/2.90 tff(16214,plain,
% 2.74/2.90 (r(s(s(s(s(z)))), s(elem!1))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[11, 16213])).
% 2.74/2.90 tff(16215,plain,
% 2.74/2.90 (r(s(s(elem!1)), s(elem!1))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[16214, 16212])).
% 2.74/2.90 tff(16216,plain,
% 2.74/2.90 (r(s(z), s(s(s(z)))) <=> r(s(z), s(elem!1))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16205])).
% 2.74/2.90 tff(16217,plain,
% 2.74/2.90 (r(s(z), s(elem!1))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[257, 16216])).
% 2.74/2.90 tff(16218,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(16219,plain,
% 2.74/2.90 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(16220,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1))))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16219])).
% 2.74/2.90 tff(16221,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 2.74/2.90 inference(transitivity,[status(thm)],[16220, 16218])).
% 2.74/2.90 tff(16222,plain,
% 2.74/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(16223,plain,
% 2.74/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1))))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[16222, 16221])).
% 2.74/2.90 tff(16224,plain,
% 2.74/2.90 (~r(s(z), s(s(elem!1)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16223, 268, 16217, 16215])).
% 2.74/2.90 tff(16225,plain,
% 2.74/2.90 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[3670, 69, 16224])).
% 2.74/2.90 tff(16226,plain,
% 2.74/2.90 (b(s(z), s(s(elem!1)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16225, 3550])).
% 2.74/2.90 tff(16227,plain,
% 2.74/2.90 (~b(s(s(elem!1)), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[12687, 453, 16173, 16208, 16226])).
% 2.74/2.90 tff(16228,plain,
% 2.74/2.90 (r(s(s(elem!1)), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[2240, 16227, 16209])).
% 2.74/2.90 tff(16229,plain,
% 2.74/2.90 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16205])).
% 2.74/2.90 tff(16230,plain,
% 2.74/2.90 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14160, 16226, 16204, 16215, 16217])).
% 2.74/2.90 tff(16231,plain,
% 2.74/2.90 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[687, 16230])).
% 2.74/2.90 tff(16232,plain,
% 2.74/2.90 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[16231, 16229])).
% 2.74/2.90 tff(16233,plain,
% 2.74/2.90 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16205])).
% 2.74/2.90 tff(16234,plain,
% 2.74/2.90 (b(elem!1, s(elem!1))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[1275, 16233])).
% 2.74/2.90 tff(16235,plain,
% 2.74/2.90 (s(elem!1) = s(s(s(z)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[9447, 16204])).
% 2.74/2.90 tff(16236,plain,
% 2.74/2.90 (b(s(elem!1), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[9377, 16235, 1291])).
% 2.74/2.90 tff(16237,plain,
% 2.74/2.90 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(16238,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16237])).
% 2.74/2.90 tff(16239,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.74/2.90 inference(transitivity,[status(thm)],[16238, 3630])).
% 2.74/2.90 tff(16240,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(16241,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[16240, 16239])).
% 2.74/2.90 tff(16242,plain,
% 2.74/2.90 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16241, 453, 16236, 16234, 16232])).
% 2.74/2.90 tff(16243,plain,
% 2.74/2.90 (r(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[643, 16242, 637])).
% 2.74/2.90 tff(16244,plain,
% 2.74/2.90 ((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~(s(s(z)) = elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[3689, 15353])).
% 2.74/2.90 tff(16245,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16244, 16243, 16228, 16208, 16204])).
% 2.74/2.90 tff(16246,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(s(z))))) = elem!1) | (~b(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(16247,plain,
% 2.74/2.90 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16246, 9, 1275, 257, 1291, 637])).
% 2.74/2.90 tff(16248,plain,
% 2.74/2.90 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[518, 16247])).
% 2.74/2.90 tff(16249,plain,
% 2.74/2.90 (~b(s(s(s(s(z)))), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[9834, 16248, 1291, 1275])).
% 2.74/2.90 tff(16250,plain,
% 2.74/2.90 (r(s(s(s(s(z)))), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[254, 16249, 3])).
% 2.74/2.90 tff(16251,plain,
% 2.74/2.90 (~r(s(s(s(s(z)))), s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[15657, 16250])).
% 2.74/2.90 tff(16252,plain,
% 2.74/2.90 (b(s(s(s(s(z)))), s(z))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1098, 16251])).
% 2.74/2.90 tff(16253,plain,
% 2.74/2.90 (~r(s(s(z)), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16202, 16252, 16173, 9])).
% 2.74/2.90 tff(16254,plain,
% 2.74/2.90 (s(s(z)) = elem!1),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[782, 16253, 16198])).
% 2.74/2.90 tff(16255,plain,
% 2.74/2.90 (s(s(s(z))) = s(elem!1)),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16254])).
% 2.74/2.90 tff(16256,plain,
% 2.74/2.90 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16255])).
% 2.74/2.90 tff(16257,plain,
% 2.74/2.90 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16256])).
% 2.74/2.90 tff(16258,plain,
% 2.74/2.90 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16255])).
% 2.74/2.90 tff(16259,plain,
% 2.74/2.90 (b(s(s(s(s(z)))), s(elem!1))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[16248, 16258])).
% 2.74/2.90 tff(16260,plain,
% 2.74/2.90 (b(s(s(elem!1)), s(elem!1))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[16259, 16257])).
% 2.74/2.90 tff(16261,plain,
% 2.74/2.90 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.74/2.90 inference(symmetry,[status(thm)],[16256])).
% 2.74/2.90 tff(16262,plain,
% 2.74/2.90 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16261])).
% 2.74/2.90 tff(16263,plain,
% 2.74/2.90 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 2.74/2.90 inference(symmetry,[status(thm)],[16262])).
% 2.74/2.90 tff(16264,plain,
% 2.74/2.90 (~r(elem!1, s(s(s(s(z)))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[14359, 16252, 1275, 1291, 16248, 8840, 16173, 257])).
% 2.74/2.90 tff(16265,plain,
% 2.74/2.90 (b(elem!1, s(s(s(s(z)))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[1087, 16264, 9])).
% 2.74/2.90 tff(16266,plain,
% 2.74/2.90 (b(elem!1, s(s(elem!1)))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[16265, 16263])).
% 2.74/2.90 tff(16267,plain,
% 2.74/2.90 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16255])).
% 2.74/2.90 tff(16268,plain,
% 2.74/2.90 (b(elem!1, s(elem!1))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[1275, 16267])).
% 2.74/2.90 tff(16269,plain,
% 2.74/2.90 (s(elem!1) = s(s(s(z)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[9447, 16254])).
% 2.74/2.90 tff(16270,plain,
% 2.74/2.90 (b(s(elem!1), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[9377, 16269, 1291])).
% 2.74/2.90 tff(16271,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[10472, 453, 16270, 16268, 16266, 16260])).
% 2.74/2.90 tff(16272,plain,((s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(16273,plain,
% 2.74/2.90 (s(s(s(s(z)))) = elem!1),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16272, 12732, 16176, 228, 637])).
% 2.74/2.90 tff(16274,plain,
% 2.74/2.90 (~b(s(s(z)), elem!1)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[16197, 16176, 16173, 228])).
% 2.74/2.90 tff(16275,plain,
% 2.74/2.90 (elem!1 = s(s(s(s(z))))),
% 2.74/2.90 inference(symmetry,[status(thm)],[16273])).
% 2.74/2.90 tff(16276,plain,
% 2.74/2.90 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16275])).
% 2.74/2.90 tff(16277,plain,
% 2.74/2.90 ((s(s(z)) = elem!1) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.74/2.90 inference(transitivity,[status(thm)],[16276, 1])).
% 2.74/2.90 tff(16278,plain,
% 2.74/2.90 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.74/2.90 inference(symmetry,[status(thm)],[16277])).
% 2.74/2.90 tff(16279,plain,
% 2.74/2.90 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[16278])).
% 2.74/2.90 tff(16280,plain,
% 2.74/2.91 (~(s(s(z)) = elem!1)),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[153, 16279])).
% 2.74/2.91 tff(16281,plain,
% 2.74/2.91 (r(s(s(z)), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[782, 16280, 16274])).
% 2.74/2.91 tff(16282,plain,
% 2.74/2.91 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[15407, 16281])).
% 2.74/2.91 tff(16283,plain,
% 2.74/2.91 (b(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[643, 16282, 637])).
% 2.74/2.91 tff(16284,plain,
% 2.74/2.91 (b(s(elem!1), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1336, 16283, 16273])).
% 2.74/2.91 tff(16285,plain,
% 2.74/2.91 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[4108, 16273])).
% 2.74/2.91 tff(16286,plain,
% 2.74/2.91 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16285])).
% 2.74/2.91 tff(16287,plain,
% 2.74/2.91 ((s(z) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(z))),
% 2.74/2.91 inference(transitivity,[status(thm)],[16286, 173])).
% 2.74/2.91 tff(16288,plain,
% 2.74/2.91 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 2.74/2.91 inference(transitivity,[status(thm)],[16287, 174])).
% 2.74/2.91 tff(16289,plain,
% 2.74/2.91 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(z) = s(elem!1)))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16288])).
% 2.74/2.91 tff(16290,plain,
% 2.74/2.91 (~(s(z) = s(elem!1))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[289, 16289])).
% 2.74/2.91 tff(16291,plain,
% 2.74/2.91 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16285])).
% 2.74/2.91 tff(16292,plain,
% 2.74/2.91 ((~(s(s(s(s(s(z))))) = s(elem!1))) | r(s(z), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[12655, 15353])).
% 2.74/2.91 tff(16293,plain,
% 2.74/2.91 (r(s(z), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16292, 16285])).
% 2.74/2.91 tff(16294,plain,
% 2.74/2.91 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[384, 16293, 228])).
% 2.74/2.91 tff(16295,plain,
% 2.74/2.91 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1656, 16294])).
% 2.74/2.91 tff(16296,plain,
% 2.74/2.91 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16273])).
% 2.74/2.91 tff(16297,plain,
% 2.74/2.91 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.91 inference(symmetry,[status(thm)],[16296])).
% 2.74/2.91 tff(16298,plain,
% 2.74/2.91 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[12732, 16297])).
% 2.74/2.91 tff(16299,plain,
% 2.74/2.91 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[8653, 16284, 16273])).
% 2.74/2.91 tff(16300,plain,
% 2.74/2.91 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1788, 16299, 16298, 16295])).
% 2.74/2.91 tff(16301,plain,
% 2.74/2.91 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[687, 16300])).
% 2.74/2.91 tff(16302,plain,
% 2.74/2.91 (r(s(elem!1), s(s(s(z))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[16301, 16291])).
% 2.74/2.91 tff(16303,plain,
% 2.74/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(16304,plain,
% 2.74/2.91 (((~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(16305,plain,
% 2.74/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16304])).
% 2.74/2.91 tff(16306,plain,
% 2.74/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[16305, 16303])).
% 2.74/2.91 tff(16307,plain,
% 2.74/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(elem!1))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(16308,plain,
% 2.74/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[16307, 16306])).
% 2.74/2.91 tff(16309,plain,
% 2.74/2.91 (~r(s(z), s(elem!1))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16308, 268, 228, 16302])).
% 2.74/2.91 tff(16310,plain,
% 2.74/2.91 (b(s(z), s(elem!1))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[397, 16309, 16290])).
% 2.74/2.91 tff(16311,plain,
% 2.74/2.91 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(elem!1) = s(z)))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16287])).
% 2.74/2.91 tff(16312,plain,
% 2.74/2.91 (~(s(elem!1) = s(z))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[289, 16311])).
% 2.74/2.91 tff(16313,plain,
% 2.74/2.91 (~r(s(s(s(s(s(z))))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[276, 16301, 228])).
% 2.74/2.91 tff(16314,plain,
% 2.74/2.91 (~r(s(elem!1), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[8732, 16313, 16285])).
% 2.74/2.91 tff(16315,plain,
% 2.74/2.91 (b(s(elem!1), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[353, 16314, 16312])).
% 2.74/2.91 tff(16316,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(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(16317,plain,
% 2.74/2.91 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(16318,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(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16317])).
% 2.74/2.91 tff(16319,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(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))),
% 2.74/2.91 inference(transitivity,[status(thm)],[16318, 16316])).
% 2.74/2.91 tff(16320,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(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(16321,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[16320, 16319])).
% 2.74/2.91 tff(16322,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16321, 453, 16315, 16310, 16173, 16284])).
% 2.74/2.91 tff(16323,plain,(b(s(z), s(s(s(z)))) | (s(s(s(s(s(z))))) = elem!1) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16324,plain,
% 2.74/2.91 (b(s(z), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16323, 637, 2])).
% 2.74/2.91 tff(16325,plain,
% 2.74/2.91 (~b(s(s(s(s(z)))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16202, 9, 16173, 700])).
% 2.74/2.91 tff(16326,plain,
% 2.74/2.91 (r(s(s(s(s(z)))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1098, 16325])).
% 2.74/2.91 tff(16327,plain,
% 2.74/2.91 (~r(s(s(s(s(z)))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[15657, 16326])).
% 2.74/2.91 tff(16328,plain,
% 2.74/2.91 (b(s(s(s(s(z)))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[254, 16327, 3])).
% 2.74/2.91 tff(16329,plain,
% 2.74/2.91 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[6968, 453, 16173, 646, 16328])).
% 2.74/2.91 tff(16330,plain,
% 2.74/2.91 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[328, 16329])).
% 2.74/2.91 tff(16331,plain,
% 2.74/2.91 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[7654, 453, 16173, 646, 16328])).
% 2.74/2.91 tff(16332,plain,
% 2.74/2.91 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10556, 16331])).
% 2.74/2.91 tff(16333,plain,
% 2.74/2.91 (~r(s(z), s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2254, 16332, 16326])).
% 2.74/2.91 tff(16334,plain,
% 2.74/2.91 (b(s(z), s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[372, 16333])).
% 2.74/2.91 tff(16335,plain,
% 2.74/2.91 (~r(s(s(s(s(s(z))))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2414, 16330, 16326])).
% 2.74/2.91 tff(16336,plain,
% 2.74/2.91 (b(s(s(s(s(s(z))))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[297, 16335])).
% 2.74/2.91 tff(16337,plain,
% 2.74/2.91 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[15469, 16336, 2090, 700])).
% 2.74/2.91 tff(16338,plain,
% 2.74/2.91 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2570, 16337])).
% 2.74/2.91 tff(16339,plain,
% 2.74/2.91 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[8055, 16338, 16334, 2090])).
% 2.74/2.91 tff(16340,plain,
% 2.74/2.91 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[687, 16339])).
% 2.74/2.91 tff(16341,plain,
% 2.74/2.91 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1982, 16340, 16330])).
% 2.74/2.91 tff(16342,plain,
% 2.74/2.91 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[518, 16341])).
% 2.74/2.91 tff(16343,plain,
% 2.74/2.91 (~r(s(z), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[15458, 700])).
% 2.74/2.91 tff(16344,plain,
% 2.74/2.91 (b(s(z), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[757, 16343])).
% 2.74/2.91 tff(16345,plain,
% 2.74/2.91 (~b(s(s(s(z))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[9027, 16338, 16344, 16336])).
% 2.74/2.91 tff(16346,plain,
% 2.74/2.91 (~(s(s(s(z))) = elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2080, 16345, 16173])).
% 2.74/2.91 tff(16347,plain,
% 2.74/2.91 (b(s(s(s(z))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[74, 16346, 2])).
% 2.74/2.91 tff(16348,plain,
% 2.74/2.91 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[9818, 16347, 16328, 16342])).
% 2.74/2.91 tff(16349,plain,
% 2.74/2.91 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[15395, 16325])).
% 2.74/2.91 tff(16350,plain,
% 2.74/2.91 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1656, 16349])).
% 2.74/2.91 tff(16351,plain,
% 2.74/2.91 (r(elem!1, s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[12998, 16347, 3, 16350, 16327])).
% 2.74/2.91 tff(16352,plain,
% 2.74/2.91 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[427, 16351, 16332])).
% 2.74/2.91 tff(16353,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[466, 16352, 16348, 2073])).
% 2.74/2.91 tff(16354,plain,((s(s(s(s(z)))) = elem!1) | (elem!1 = s(s(s(s(s(z)))))) | r(s(s(s(z))), elem!1) | (~b(s(z), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16355,plain,
% 2.74/2.91 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16354, 700, 2, 16324, 8840, 3])).
% 2.74/2.91 tff(16356,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[643, 16355, 16175, 637])).
% 2.74/2.91 tff(16357,plain,((~r(s(s(z)), elem!1)) | (s(s(s(s(s(z))))) = elem!1) | r(s(s(s(z))), elem!1) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16358,plain,
% 2.74/2.91 (~r(s(s(z)), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16357, 3, 2, 637])).
% 2.74/2.91 tff(16359,plain,
% 2.74/2.91 ((s(elem!1) = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 2.74/2.91 inference(monotonicity,[status(thm)],[76])).
% 2.74/2.91 tff(16360,plain,
% 2.74/2.91 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(s(z))))),
% 2.74/2.91 inference(symmetry,[status(thm)],[16359])).
% 2.74/2.91 tff(16361,plain,
% 2.74/2.91 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(z))) = s(elem!1))),
% 2.74/2.91 inference(transitivity,[status(thm)],[596, 16360, 10379])).
% 2.74/2.91 tff(16362,plain,
% 2.74/2.91 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16361])).
% 2.74/2.91 tff(16363,plain,
% 2.74/2.91 (~(s(s(s(z))) = s(elem!1))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[143, 16362])).
% 2.74/2.91 tff(16364,plain,
% 2.74/2.91 (~r(s(z), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16199, 1132, 11])).
% 2.74/2.91 tff(16365,plain,
% 2.74/2.91 (~(s(s(s(z))) = elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[15848, 16364])).
% 2.74/2.91 tff(16366,plain,
% 2.74/2.91 (~r(s(s(s(s(z)))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[15657, 1132])).
% 2.74/2.91 tff(16367,plain,
% 2.74/2.91 (b(s(s(s(s(z)))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[254, 16366, 3])).
% 2.74/2.91 tff(16368,plain,
% 2.74/2.91 (~b(s(s(s(z))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[7330, 16367, 16173, 922])).
% 2.74/2.91 tff(16369,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[74, 16368, 16365, 2])).
% 2.74/2.91 tff(16370,plain,((~r(s(s(s(s(z)))), s(z))) | r(s(s(s(z))), elem!1) | (~b(s(s(z)), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16371,plain,
% 2.74/2.91 (~r(s(s(s(s(z)))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16370, 11, 922, 3, 2])).
% 2.74/2.91 tff(16372,plain,
% 2.74/2.91 (b(s(s(s(s(z)))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1098, 16371])).
% 2.74/2.91 tff(16373,plain,
% 2.74/2.91 (~b(s(s(s(z))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[7330, 255, 16173, 922])).
% 2.74/2.91 tff(16374,plain,
% 2.74/2.91 (~(s(s(s(z))) = elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[81, 15579])).
% 2.74/2.91 tff(16375,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[74, 16374, 16373, 2])).
% 2.74/2.91 tff(16376,plain,(r(s(s(s(s(z)))), elem!1) | r(s(s(s(z))), elem!1) | (~b(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16377,plain,
% 2.74/2.91 (r(s(s(s(s(z)))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16376, 11, 922, 2, 3])).
% 2.74/2.91 tff(16378,plain,
% 2.74/2.91 (~r(elem!1, s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[8475, 16377, 11])).
% 2.74/2.91 tff(16379,plain,
% 2.74/2.91 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 2.74/2.91 inference(symmetry,[status(thm)],[115])).
% 2.74/2.91 tff(16380,plain,
% 2.74/2.91 ((~b(s(z), elem!1)) <=> (~b(s(z), s(s(s(z)))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16379])).
% 2.74/2.91 tff(16381,plain,
% 2.74/2.91 (~b(s(z), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[13962, 76, 2, 1200, 1764, 16173])).
% 2.74/2.91 tff(16382,plain,
% 2.74/2.91 (~b(s(z), s(s(s(z))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[16381, 16380])).
% 2.74/2.91 tff(16383,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2090, 16382])).
% 2.74/2.91 tff(16384,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(z), s(s(s(z))))) | r(s(s(s(z))), elem!1) | r(elem!1, s(s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16385,plain,
% 2.74/2.91 (~(s(s(s(z))) = elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16384, 16378, 2, 2090, 16372])).
% 2.74/2.91 tff(16386,plain,
% 2.74/2.91 (b(s(s(s(z))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[74, 16385, 2])).
% 2.74/2.91 tff(16387,plain,
% 2.74/2.91 (~(elem!1 = s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[4487, 16385])).
% 2.74/2.91 tff(16388,plain,
% 2.74/2.91 (b(elem!1, s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[4492, 16387, 16378])).
% 2.74/2.91 tff(16389,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[7473, 16388, 16386, 16173, 2090])).
% 2.74/2.91 tff(16390,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | r(s(s(s(z))), elem!1) | (~b(s(s(z)), elem!1)) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16391,plain,
% 2.74/2.91 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16390, 3, 2, 922, 16324])).
% 2.74/2.91 tff(16392,plain,
% 2.74/2.91 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[518, 16391])).
% 2.74/2.91 tff(16393,plain,
% 2.74/2.91 (~b(s(s(s(z))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[7330, 299, 16173, 922])).
% 2.74/2.91 tff(16394,plain,
% 2.74/2.91 (s(s(s(z))) = elem!1),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[74, 16393, 2])).
% 2.74/2.91 tff(16395,plain,
% 2.74/2.91 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16394])).
% 2.74/2.91 tff(16396,plain,
% 2.74/2.91 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 2.74/2.91 inference(symmetry,[status(thm)],[16395])).
% 2.74/2.91 tff(16397,plain,
% 2.74/2.91 ((~b(s(z), elem!1)) <=> (~b(s(z), s(s(s(z)))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16396])).
% 2.74/2.91 tff(16398,plain,
% 2.74/2.91 (~b(s(z), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10980, 299, 16173, 922])).
% 2.74/2.91 tff(16399,plain,
% 2.74/2.91 (~b(s(z), s(s(s(z))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[16398, 16397])).
% 2.74/2.91 tff(16400,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2090, 16399])).
% 2.74/2.91 tff(16401,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(z))))) | r(s(s(s(z))), elem!1) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16402,plain,
% 2.74/2.91 (~b(s(s(s(s(z)))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16401, 922, 2, 16324])).
% 2.74/2.91 tff(16403,plain,
% 2.74/2.91 (~(s(s(s(z))) = elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[4123, 16392, 16402])).
% 2.74/2.91 tff(16404,plain,
% 2.74/2.91 (b(s(s(s(z))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[74, 16403, 2])).
% 2.74/2.91 tff(16405,plain,
% 2.74/2.91 (r(s(s(s(s(z)))), elem!1)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[254, 3, 16402])).
% 2.74/2.91 tff(16406,plain,
% 2.74/2.91 (~r(s(s(s(s(z)))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[15657, 16405])).
% 2.74/2.91 tff(16407,plain,
% 2.74/2.91 (b(s(s(s(s(z)))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1098, 16406])).
% 2.74/2.91 tff(16408,plain,
% 2.74/2.91 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2102, 16407, 16324, 16392])).
% 2.74/2.91 tff(16409,plain,
% 2.74/2.91 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1656, 16408])).
% 2.74/2.91 tff(16410,plain,
% 2.74/2.91 (~r(s(z), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[7287, 268, 15353, 16405])).
% 2.74/2.91 tff(16411,plain,
% 2.74/2.91 (b(s(z), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1677, 69, 16410, 50])).
% 2.74/2.91 tff(16412,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(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(16413,plain,
% 2.74/2.91 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(16414,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(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16413])).
% 2.74/2.91 tff(16415,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(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[16414, 16412])).
% 2.74/2.91 tff(16416,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(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(16417,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(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[16416, 16415])).
% 2.74/2.91 tff(16418,plain,
% 2.74/2.91 (~b(elem!1, s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16417, 453, 16173, 16407, 16411])).
% 2.74/2.91 tff(16419,plain,
% 2.74/2.91 (r(elem!1, s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1087, 16418, 9])).
% 2.74/2.91 tff(16420,plain,
% 2.74/2.91 (~b(s(s(z)), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10938, 453, 16173, 1291, 922])).
% 2.74/2.91 tff(16421,plain,
% 2.74/2.91 (r(s(s(z)), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1350, 69, 16420, 12356])).
% 2.74/2.91 tff(16422,plain,
% 2.74/2.91 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10556, 2934])).
% 2.74/2.91 tff(16423,plain,
% 2.74/2.91 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[427, 16422, 419])).
% 2.74/2.91 tff(16424,plain,
% 2.74/2.91 (b(elem!1, s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[466, 16423, 2073])).
% 2.74/2.91 tff(16425,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(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(16426,plain,
% 2.74/2.91 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(16427,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(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(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[16426])).
% 2.74/2.91 tff(16428,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(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(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[16427, 16425])).
% 2.74/2.91 tff(16429,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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(z))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(16430,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[16429, 16428])).
% 2.74/2.91 tff(16431,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16430, 453, 16173, 16424, 443, 1779])).
% 2.74/2.91 tff(16432,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (elem!1 = s(s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(16433,plain,
% 2.74/2.91 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[16432, 443, 2073, 419, 1291, 523])).
% 2.74/2.91 tff(16434,plain,
% 2.74/2.91 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[687, 16433])).
% 2.74/2.91 tff(16435,plain,
% 2.74/2.91 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2795, 16434, 16421])).
% 2.74/2.91 tff(16436,plain,
% 2.74/2.91 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[5711, 69, 16435, 54])).
% 2.74/2.91 tff(16437,plain,
% 2.74/2.91 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2975, 268, 16434, 16421])).
% 2.74/2.91 tff(16438,plain,
% 2.74/2.91 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[4081, 16437])).
% 2.74/2.91 tff(16439,plain,
% 2.74/2.91 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[309, 16434, 300])).
% 2.74/2.91 tff(16440,plain,
% 2.74/2.91 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[328, 16439])).
% 2.74/2.91 tff(16441,plain,
% 2.74/2.91 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[8186, 16440, 443, 1764])).
% 2.74/2.91 tff(16442,plain,
% 2.74/2.91 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10556, 16441])).
% 2.74/2.91 tff(16443,plain,
% 2.74/2.91 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[427, 16442, 419])).
% 2.74/2.91 tff(16444,plain,
% 2.74/2.91 (b(elem!1, s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[466, 16443, 2073])).
% 2.74/2.91 tff(16445,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(16446,plain,
% 2.74/2.91 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(16447,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(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16446])).
% 2.74/2.92 tff(16448,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(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[16447, 16445])).
% 2.74/2.92 tff(16449,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(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(16450,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[16449, 16448])).
% 2.74/2.92 tff(16451,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16450, 453, 16444, 922, 16438, 16436])).
% 2.74/2.92 tff(16452,plain,((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (elem!1 = s(s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(16453,plain,
% 2.74/2.92 (~b(s(z), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16452, 16419, 8840, 922, 16407, 16409, 16404, 16392])).
% 2.74/2.92 tff(16454,plain,
% 2.74/2.92 (r(s(z), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[372, 16453])).
% 2.74/2.92 tff(16455,plain,
% 2.74/2.92 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[15399, 16454])).
% 2.74/2.92 tff(16456,plain,
% 2.74/2.92 (b(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[643, 16455, 637])).
% 2.74/2.92 tff(16457,plain,
% 2.74/2.92 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[6788, 453, 16173, 16404, 16456])).
% 2.74/2.92 tff(16458,plain,
% 2.74/2.92 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[687, 16457])).
% 2.74/2.92 tff(16459,plain,
% 2.74/2.92 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4084, 16458, 922, 16404, 16456])).
% 2.74/2.92 tff(16460,plain,
% 2.74/2.92 (~(elem!1 = s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4487, 16403])).
% 2.74/2.92 tff(16461,plain,
% 2.74/2.92 (~b(elem!1, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[7473, 16404, 16173, 16324])).
% 2.74/2.92 tff(16462,plain,
% 2.74/2.92 (r(elem!1, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4492, 16461, 16460])).
% 2.74/2.92 tff(16463,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(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(16464,plain,
% 2.74/2.92 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(16465,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16464])).
% 2.74/2.92 tff(16466,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.74/2.92 inference(transitivity,[status(thm)],[16465, 16463])).
% 2.74/2.92 tff(16467,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(16468,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[16467, 16466])).
% 2.74/2.92 tff(16469,plain,
% 2.74/2.92 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16468, 453, 16173, 16404, 16456])).
% 2.74/2.92 tff(16470,plain,
% 2.74/2.92 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2570, 16469])).
% 2.74/2.92 tff(16471,plain,
% 2.74/2.92 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[9415, 16470, 16462])).
% 2.74/2.92 tff(16472,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[466, 16471, 16459, 8840])).
% 2.74/2.92 tff(16473,plain,((s(s(s(s(z)))) = elem!1) | (~b(s(s(z)), elem!1)) | (s(s(s(s(s(z))))) = elem!1) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(16474,plain,
% 2.74/2.92 (s(s(s(s(z)))) = elem!1),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16473, 922, 637, 2])).
% 2.74/2.92 tff(16475,plain,
% 2.74/2.92 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4108, 16474])).
% 2.74/2.92 tff(16476,plain,
% 2.74/2.92 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16475])).
% 2.74/2.92 tff(16477,plain,
% 2.74/2.92 (b(s(s(s(s(z)))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[13422, 16474, 16173])).
% 2.74/2.92 tff(16478,plain,
% 2.74/2.92 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), elem!1)),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16474])).
% 2.74/2.92 tff(16479,plain,
% 2.74/2.92 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.92 inference(symmetry,[status(thm)],[16478])).
% 2.74/2.92 tff(16480,plain,
% 2.74/2.92 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16479])).
% 2.74/2.92 tff(16481,plain,
% 2.74/2.92 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[2, 16480])).
% 2.74/2.92 tff(16482,plain,
% 2.74/2.92 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1656, 16481])).
% 2.74/2.92 tff(16483,plain,
% 2.74/2.92 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2102, 16482, 16324, 16477])).
% 2.74/2.92 tff(16484,plain,
% 2.74/2.92 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[518, 16483])).
% 2.74/2.92 tff(16485,plain,
% 2.74/2.92 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16474])).
% 2.74/2.92 tff(16486,plain,
% 2.74/2.92 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 2.74/2.92 inference(transitivity,[status(thm)],[16485, 1193])).
% 2.74/2.92 tff(16487,plain,
% 2.74/2.92 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16486])).
% 2.74/2.92 tff(16488,plain,
% 2.74/2.92 (~(s(s(s(z))) = elem!1)),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[142, 16487])).
% 2.74/2.92 tff(16489,plain,
% 2.74/2.92 (b(s(s(s(z))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[74, 16488, 2])).
% 2.74/2.92 tff(16490,plain,
% 2.74/2.92 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[16486, 1194])).
% 2.74/2.92 tff(16491,plain,
% 2.74/2.92 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16490])).
% 2.74/2.92 tff(16492,plain,
% 2.74/2.92 (~(elem!1 = s(s(s(z))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[142, 16491])).
% 2.74/2.92 tff(16493,plain,
% 2.74/2.92 (~b(elem!1, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[7473, 16489, 16173, 16324])).
% 2.74/2.92 tff(16494,plain,
% 2.74/2.92 (r(elem!1, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4492, 16493, 16492])).
% 2.74/2.92 tff(16495,plain,
% 2.74/2.92 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4469, 1983, 1170])).
% 2.74/2.92 tff(16496,plain,
% 2.74/2.92 (b(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[643, 16495, 637])).
% 2.74/2.92 tff(16497,plain,
% 2.74/2.92 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4084, 16496, 922, 1291, 256])).
% 2.74/2.92 tff(16498,plain,
% 2.74/2.92 (r(elem!1, s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[466, 16497, 8840])).
% 2.74/2.92 tff(16499,plain,
% 2.74/2.92 (r(elem!1, s(elem!1))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[16498, 8637])).
% 2.74/2.92 tff(16500,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[8690, 268, 16499, 1149, 8114])).
% 2.74/2.92 tff(16501,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (~(s(s(s(s(z)))) = elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(16502,plain,
% 2.74/2.92 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16501, 16494, 922, 16489, 637, 16474, 16484])).
% 2.74/2.92 tff(16503,plain,
% 2.74/2.92 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[687, 16502])).
% 2.74/2.92 tff(16504,plain,
% 2.74/2.92 (b(s(elem!1), s(s(s(z))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[16503, 16476])).
% 2.74/2.92 tff(16505,plain,
% 2.74/2.92 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4526, 443, 1779, 1764])).
% 2.74/2.92 tff(16506,plain,
% 2.74/2.92 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10556, 16505])).
% 2.74/2.92 tff(16507,plain,
% 2.74/2.92 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[8055, 443, 1779, 2090])).
% 2.74/2.92 tff(16508,plain,
% 2.74/2.92 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2570, 16507])).
% 2.74/2.92 tff(16509,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[8666, 16508, 16506, 11])).
% 2.74/2.92 tff(16510,plain,((~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(16511,plain,
% 2.74/2.92 (~b(s(z), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16510, 16484, 16503, 16324, 16477])).
% 2.74/2.92 tff(16512,plain,
% 2.74/2.92 (r(s(z), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[372, 16511])).
% 2.74/2.92 tff(16513,plain,
% 2.74/2.92 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[15399, 16512])).
% 2.74/2.92 tff(16514,plain,
% 2.74/2.92 (b(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[643, 16513, 637])).
% 2.74/2.92 tff(16515,plain,
% 2.74/2.92 (b(s(elem!1), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1336, 16514, 16474])).
% 2.74/2.92 tff(16516,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[12575, 453, 16173, 16515, 16489, 16504])).
% 2.74/2.92 tff(16517,plain,((~b(s(s(z)), elem!1)) | (s(s(s(s(s(z))))) = elem!1) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(16518,plain,
% 2.74/2.92 (~b(s(s(z)), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16517, 637, 2])).
% 2.74/2.92 tff(16519,plain,
% 2.74/2.92 (r(s(s(z)), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[782, 13548, 16518])).
% 2.74/2.92 tff(16520,plain,
% 2.74/2.92 (b(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[643, 16175, 637])).
% 2.74/2.92 tff(16521,plain,
% 2.74/2.92 (s(s(s(s(z)))) = elem!1),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16354, 700, 2, 16324, 8840, 16520])).
% 2.74/2.92 tff(16522,plain,
% 2.74/2.92 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4108, 16521])).
% 2.74/2.92 tff(16523,plain,
% 2.74/2.92 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16522])).
% 2.74/2.92 tff(16524,plain,
% 2.74/2.92 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 2.74/2.92 inference(symmetry,[status(thm)],[16523])).
% 2.74/2.92 tff(16525,plain,
% 2.74/2.92 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16524])).
% 2.74/2.92 tff(16526,plain,
% 2.74/2.92 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16525])).
% 2.74/2.92 tff(16527,plain,
% 2.74/2.92 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[16526, 1307])).
% 2.74/2.92 tff(16528,plain,
% 2.74/2.92 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.74/2.92 inference(symmetry,[status(thm)],[16527])).
% 2.74/2.92 tff(16529,plain,
% 2.74/2.92 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16528])).
% 2.74/2.92 tff(16530,plain,
% 2.74/2.92 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1273, 16521])).
% 2.74/2.92 tff(16531,plain,
% 2.74/2.92 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1436, 16530])).
% 2.74/2.92 tff(16532,plain,
% 2.74/2.92 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[16531, 16529])).
% 2.74/2.92 tff(16533,plain,
% 2.74/2.92 (~(elem!1 = s(s(elem!1)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4223, 16532])).
% 2.74/2.92 tff(16534,plain,
% 2.74/2.92 (~(s(s(elem!1)) = elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3359, 16533])).
% 2.74/2.92 tff(16535,plain,
% 2.74/2.92 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16522])).
% 2.74/2.92 tff(16536,plain,
% 2.74/2.92 (s(s(s(s(z)))) = elem!1),
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% 2.74/2.92 tff(16537,plain,
% 2.74/2.92 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16536])).
% 2.74/2.92 tff(16538,plain,
% 2.74/2.92 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 2.74/2.92 inference(transitivity,[status(thm)],[16537, 1193])).
% 2.74/2.92 tff(16539,plain,
% 2.74/2.92 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16538])).
% 2.74/2.92 tff(16540,plain,
% 2.74/2.92 (~(s(s(s(z))) = elem!1)),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[142, 16539])).
% 2.74/2.92 tff(16541,plain,
% 2.74/2.92 ((elem!1 = s(s(s(s(s(z)))))) <=> (elem!1 = s(elem!1))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16522])).
% 2.74/2.92 tff(16542,plain,
% 2.74/2.92 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(elem!1) = elem!1)),
% 2.74/2.92 inference(transitivity,[status(thm)],[16541, 1027])).
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% 2.74/2.92 ((elem!1 = s(s(s(s(s(z)))))) <=> (elem!1 = s(elem!1))),
% 2.74/2.92 inference(transitivity,[status(thm)],[16542, 1028])).
% 2.74/2.92 tff(16544,plain,
% 2.74/2.92 ((~(elem!1 = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(elem!1)))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16543])).
% 2.74/2.92 tff(16545,plain,
% 2.74/2.92 (~(elem!1 = s(elem!1))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[8840, 16544])).
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% 2.74/2.92 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[16538, 1194])).
% 2.74/2.92 tff(16547,plain,
% 2.74/2.92 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16546])).
% 2.74/2.92 tff(16548,plain,
% 2.74/2.92 (~(elem!1 = s(s(s(z))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[142, 16547])).
% 2.74/2.92 tff(16549,plain,
% 2.74/2.92 (b(s(s(s(z))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[74, 16540, 2])).
% 2.74/2.92 tff(16550,plain,
% 2.74/2.92 (~b(elem!1, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[7473, 16549, 16173, 16324])).
% 2.74/2.92 tff(16551,plain,
% 2.74/2.92 (r(elem!1, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4492, 16550, 16548])).
% 2.74/2.92 tff(16552,plain,
% 2.74/2.92 (b(s(elem!1), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1336, 16521, 16520])).
% 2.74/2.92 tff(16553,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(elem!1, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(16554,plain,
% 2.74/2.92 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(16555,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16554])).
% 2.74/2.92 tff(16556,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.74/2.92 inference(transitivity,[status(thm)],[16555, 16553])).
% 2.74/2.92 tff(16557,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(16558,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(elem!1, s(z))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[16557, 16556])).
% 2.74/2.92 tff(16559,plain,
% 2.74/2.92 (~b(s(s(s(z))), s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16558, 453, 16173, 16552, 16549])).
% 2.74/2.92 tff(16560,plain,
% 2.74/2.92 (r(s(s(s(z))), s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[9480, 16559, 9475])).
% 2.74/2.92 tff(16561,plain,
% 2.74/2.92 (~r(elem!1, s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[9495, 16560, 16551])).
% 2.74/2.92 tff(16562,plain,
% 2.74/2.92 (b(elem!1, s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1069, 16561, 16545])).
% 2.74/2.92 tff(16563,plain,
% 2.74/2.92 ((s(s(s(z))) = elem!1) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | r(s(s(s(z))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4210, 15602])).
% 2.74/2.92 tff(16564,plain,
% 2.74/2.92 (~b(s(s(elem!1)), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16563, 16562, 2, 16540, 16520])).
% 2.74/2.92 tff(16565,plain,
% 2.74/2.92 (r(s(s(elem!1)), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2240, 16564, 16534])).
% 2.74/2.92 tff(16566,plain,
% 2.74/2.92 ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3393, 15353])).
% 2.74/2.92 tff(16567,plain,
% 2.74/2.92 (~r(s(s(elem!1)), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16566, 16565])).
% 2.74/2.92 tff(16568,plain,
% 2.74/2.92 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16523])).
% 2.74/2.92 tff(16569,plain,
% 2.74/2.92 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16568])).
% 2.74/2.92 tff(16570,plain,
% 2.74/2.92 (~(s(s(z)) = s(s(elem!1)))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[2661, 16569])).
% 2.74/2.92 tff(16571,plain,
% 2.74/2.92 ((~r(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4248, 15353])).
% 2.74/2.92 tff(16572,plain,
% 2.74/2.92 (~b(s(s(elem!1)), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16571, 16565, 16570, 700])).
% 2.74/2.92 tff(16573,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1047, 16572, 16567])).
% 2.74/2.92 tff(16574,plain,((~r(s(s(z)), elem!1)) | r(s(s(s(z))), elem!1) | (s(s(s(z))) = s(elem!1)) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(16575,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16574, 16519, 16363, 2, 637])).
% 2.74/2.92 tff(16576,plain,((~(s(s(s(z))) = elem!1)) | r(s(s(s(z))), elem!1) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(16577,plain,
% 2.74/2.92 (~(s(s(s(z))) = elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16576, 637, 2])).
% 2.74/2.92 tff(16578,plain,
% 2.74/2.92 (b(s(s(s(z))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[74, 16577, 2])).
% 2.74/2.92 tff(16579,plain,
% 2.74/2.92 (~(elem!1 = s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4487, 16577])).
% 2.74/2.92 tff(16580,plain,
% 2.74/2.92 (~b(elem!1, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[7473, 16578, 16173, 16324])).
% 2.74/2.92 tff(16581,plain,
% 2.74/2.92 (r(elem!1, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4492, 16580, 16579])).
% 2.74/2.92 tff(16582,plain,
% 2.74/2.92 (s(s(z)) = elem!1),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[782, 16358, 16518])).
% 2.74/2.92 tff(16583,plain,
% 2.74/2.92 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(s(elem!1)), s(z)))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[15930])).
% 2.74/2.92 tff(16584,assumption,(~r(s(s(z)), elem!1)), introduced(assumption)).
% 2.74/2.92 tff(16585,plain,
% 2.74/2.92 (~r(s(s(s(s(z)))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1167, 1099, 701])).
% 2.74/2.92 tff(16586,plain,
% 2.74/2.92 (b(s(s(s(s(z)))), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[254, 16585, 3])).
% 2.74/2.92 tff(16587,plain,
% 2.74/2.92 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[9818, 16586, 1291, 523])).
% 2.74/2.92 tff(16588,plain,
% 2.74/2.92 (r(elem!1, s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[466, 16587, 2073])).
% 2.74/2.92 tff(16589,plain,
% 2.74/2.92 (~b(s(s(z)), elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[7330, 16586, 1291, 2077])).
% 2.74/2.92 tff(16590,plain,
% 2.74/2.92 (s(s(z)) = elem!1),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[782, 16589, 16584])).
% 2.74/2.92 tff(16591,plain,
% 2.74/2.92 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[11100, 16590, 16588, 1149])).
% 2.74/2.92 tff(16592,plain,
% 2.74/2.92 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[687, 16591])).
% 2.74/2.92 tff(16593,plain,
% 2.74/2.92 (~(elem!1 = s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[12708, 701])).
% 2.74/2.92 tff(16594,plain,
% 2.74/2.92 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[7911, 1057, 16593])).
% 2.74/2.92 tff(16595,plain,
% 2.74/2.92 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1656, 16594])).
% 2.74/2.92 tff(16596,plain,
% 2.74/2.92 (~b(elem!1, s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1641, 16595, 1291, 16586])).
% 2.74/2.92 tff(16597,plain,
% 2.74/2.92 (r(elem!1, s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1087, 16596, 9])).
% 2.74/2.92 tff(16598,plain,
% 2.74/2.92 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[427, 16588, 16597])).
% 2.74/2.92 tff(16599,plain,
% 2.74/2.92 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10556, 16598])).
% 2.74/2.92 tff(16600,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2596, 16599, 16592, 1291, 523])).
% 2.74/2.92 tff(16601,plain,(b(s(s(s(s(z)))), s(z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (elem!1 = s(s(s(s(s(z)))))) | r(s(s(z)), elem!1) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(16602,plain,
% 2.74/2.92 (b(s(s(s(s(z)))), s(z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (elem!1 = s(s(s(s(s(z)))))) | r(s(s(z)), elem!1) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = elem!1)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16601, 15353])).
% 2.74/2.92 tff(16603,plain,
% 2.74/2.92 (b(s(s(s(s(z)))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[16602, 523, 16173, 1149, 1291, 2073, 16584, 3])).
% 2.74/2.92 tff(16604,plain,
% 2.74/2.92 (~b(s(s(s(z))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3782, 16603, 2090, 523])).
% 2.74/2.92 tff(16605,plain,
% 2.74/2.92 (r(s(s(s(z))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[134, 16604])).
% 2.74/2.92 tff(16606,plain,
% 2.74/2.92 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2102, 16603, 2090, 523])).
% 2.74/2.92 tff(16607,plain,
% 2.74/2.92 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1656, 16606])).
% 2.74/2.92 tff(16608,plain,
% 2.74/2.92 (~r(s(s(s(s(z)))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[4538, 16607, 16605])).
% 2.74/2.92 tff(16609,plain,
% 2.74/2.92 (~r(s(s(elem!1)), s(z))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[16608, 16583])).
% 2.74/2.92 tff(16610,plain,
% 2.74/2.92 (b(s(s(elem!1)), s(elem!1))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[523, 11775])).
% 2.74/2.92 tff(16611,plain,
% 2.74/2.92 (b(s(z), s(elem!1))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3644, 3468, 2090])).
% 2.74/2.92 tff(16612,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(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(16613,plain,
% 2.74/2.92 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(16614,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[16613])).
% 2.74/2.92 tff(16615,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(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[16614, 16612])).
% 2.74/2.93 tff(16616,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(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(16617,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[16616, 16615])).
% 2.74/2.93 tff(16618,plain,
% 2.74/2.93 (~b(s(s(elem!1)), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16617, 453, 16611, 14132, 16610])).
% 2.74/2.93 tff(16619,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1047, 16618, 16609])).
% 2.74/2.93 tff(16620,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~(s(s(z)) = elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (elem!1 = s(s(s(s(s(z)))))) | r(s(s(z)), elem!1) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(16621,plain,
% 2.74/2.93 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16620, 16582, 16324, 16581, 16578, 8840, 16358, 3])).
% 2.74/2.93 tff(16622,plain,
% 2.74/2.93 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[518, 16621])).
% 2.74/2.93 tff(16623,plain,
% 2.74/2.93 (~r(elem!1, s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[13281, 16622, 16581])).
% 2.74/2.93 tff(16624,plain,
% 2.74/2.93 (~r(s(s(s(s(z)))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[8475, 16622, 16581])).
% 2.74/2.93 tff(16625,plain,
% 2.74/2.93 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[12998, 16623, 3, 16578, 16624])).
% 2.74/2.93 tff(16626,plain,
% 2.74/2.93 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1656, 16625])).
% 2.74/2.93 tff(16627,plain,
% 2.74/2.93 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[15401, 16626, 637, 3, 16624, 16623, 16622])).
% 2.74/2.93 tff(16628,plain,
% 2.74/2.93 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[687, 16627])).
% 2.74/2.93 tff(16629,plain,
% 2.74/2.93 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[3515])).
% 2.74/2.93 tff(16630,plain,
% 2.74/2.93 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 2.74/2.93 inference(symmetry,[status(thm)],[16629])).
% 2.74/2.93 tff(16631,plain,
% 2.74/2.93 (r(elem!1, s(elem!1))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[1149, 16630])).
% 2.74/2.93 tff(16632,plain,
% 2.74/2.93 (r(s(z), s(elem!1))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[257, 14141])).
% 2.74/2.93 tff(16633,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1751, 16632, 16631, 701])).
% 2.74/2.93 tff(16634,plain,((~(s(s(z)) = elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(16635,plain,
% 2.74/2.93 ((~(s(s(z)) = elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16634, 15353])).
% 2.74/2.93 tff(16636,plain,
% 2.74/2.93 (~r(s(z), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16635, 16582, 16581])).
% 2.74/2.93 tff(16637,plain,
% 2.74/2.93 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), elem!1)),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16582])).
% 2.74/2.93 tff(16638,plain,
% 2.74/2.93 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(z)))),
% 2.74/2.93 inference(symmetry,[status(thm)],[16637])).
% 2.74/2.93 tff(16639,plain,
% 2.74/2.93 (b(s(s(s(z))), s(s(z)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[16578, 16638])).
% 2.74/2.93 tff(16640,plain,
% 2.74/2.93 (~b(s(s(s(s(s(z))))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10450, 16628, 16324, 16639])).
% 2.74/2.93 tff(16641,plain,
% 2.74/2.93 (b(s(s(s(s(s(z))))), s(z)) | (~b(elem!1, s(z))) | b(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[7600, 15353])).
% 2.74/2.93 tff(16642,plain,
% 2.74/2.93 (b(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16641, 16640, 16173])).
% 2.74/2.93 tff(16643,plain,
% 2.74/2.93 (s(s(s(z))) = s(elem!1)),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16582])).
% 2.74/2.93 tff(16644,plain,
% 2.74/2.93 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16643])).
% 2.74/2.93 tff(16645,plain,
% 2.74/2.93 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.74/2.93 inference(symmetry,[status(thm)],[16644])).
% 2.74/2.93 tff(16646,plain,
% 2.74/2.93 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16645])).
% 2.74/2.93 tff(16647,plain,
% 2.74/2.93 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16646])).
% 2.74/2.93 tff(16648,plain,
% 2.74/2.93 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.74/2.93 inference(symmetry,[status(thm)],[16647])).
% 2.74/2.93 tff(16649,plain,
% 2.74/2.93 ((~r(s(s(s(s(s(z))))), elem!1)) <=> (~r(s(s(s(elem!1))), elem!1))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16648])).
% 2.74/2.93 tff(16650,plain,
% 2.74/2.93 (r(s(s(s(s(s(z))))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[297, 16640])).
% 2.74/2.93 tff(16651,plain,
% 2.74/2.93 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[15978, 16650])).
% 2.74/2.93 tff(16652,plain,
% 2.74/2.93 (~r(s(s(s(elem!1))), elem!1)),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[16651, 16649])).
% 2.74/2.93 tff(16653,plain,
% 2.74/2.93 (s(elem!1) = s(s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9447, 16582])).
% 2.74/2.93 tff(16654,plain,
% 2.74/2.93 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9847, 16653])).
% 2.74/2.93 tff(16655,plain,
% 2.74/2.93 (~(s(z) = s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9855, 16654])).
% 2.74/2.93 tff(16656,plain,
% 2.74/2.93 (~(s(elem!1) = s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[179, 16655])).
% 2.74/2.93 tff(16657,plain,
% 2.74/2.93 (~b(s(s(s(elem!1))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[6811, 16652, 16173, 2, 16324, 16656, 16642, 16628])).
% 2.74/2.93 tff(16658,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[6796, 16657, 16652, 2, 16642, 16636, 2076, 16628])).
% 2.74/2.93 tff(16659,plain,((s(s(s(s(z)))) = elem!1) | r(s(s(s(z))), elem!1) | r(elem!1, s(z)) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(16660,plain,
% 2.74/2.93 (s(s(s(s(z)))) = elem!1),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16659, 637, 2076, 2])).
% 2.74/2.93 tff(16661,plain,
% 2.74/2.93 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[4108, 16660])).
% 2.74/2.93 tff(16662,plain,
% 2.74/2.93 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16661])).
% 2.74/2.93 tff(16663,plain,
% 2.74/2.93 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.74/2.93 inference(transitivity,[status(thm)],[16662, 10379])).
% 2.74/2.93 tff(16664,plain,
% 2.74/2.93 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16663])).
% 2.74/2.93 tff(16665,plain,
% 2.74/2.93 (~(s(s(s(z))) = s(elem!1))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[111, 16664])).
% 2.74/2.93 tff(16666,plain,
% 2.74/2.93 (elem!1 = s(s(s(s(z))))),
% 2.74/2.93 inference(symmetry,[status(thm)],[16660])).
% 2.74/2.93 tff(16667,plain,
% 2.74/2.93 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16666])).
% 2.74/2.93 tff(16668,plain,
% 2.74/2.93 ((s(s(z)) = elem!1) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.74/2.93 inference(transitivity,[status(thm)],[16667, 1])).
% 2.74/2.93 tff(16669,plain,
% 2.74/2.93 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.74/2.93 inference(symmetry,[status(thm)],[16668])).
% 2.74/2.93 tff(16670,plain,
% 2.74/2.93 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16669])).
% 2.74/2.93 tff(16671,plain,
% 2.74/2.93 (~(s(s(z)) = elem!1)),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[153, 16670])).
% 2.74/2.93 tff(16672,plain,
% 2.74/2.93 (r(s(s(z)), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[782, 16671, 16518])).
% 2.74/2.93 tff(16673,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16574, 16672, 16665, 2, 637])).
% 2.74/2.93 tff(16674,plain,((s(s(s(s(s(z))))) = elem!1) | r(s(s(s(z))), elem!1) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(16675,plain,
% 2.74/2.93 (s(s(s(s(s(z))))) = elem!1),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16674, 2076, 2])).
% 2.74/2.93 tff(16676,plain,
% 2.74/2.93 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16675])).
% 2.74/2.93 tff(16677,plain,
% 2.74/2.93 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.74/2.93 inference(transitivity,[status(thm)],[16676, 3483])).
% 2.74/2.93 tff(16678,plain,
% 2.74/2.93 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16677])).
% 2.74/2.93 tff(16679,plain,
% 2.74/2.93 (~(s(s(s(s(z)))) = elem!1)),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[319, 16678])).
% 2.74/2.93 tff(16680,plain,
% 2.74/2.93 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16675])).
% 2.74/2.93 tff(16681,plain,
% 2.74/2.93 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 2.74/2.93 inference(transitivity,[status(thm)],[16680, 1193])).
% 2.74/2.93 tff(16682,plain,
% 2.74/2.93 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16681])).
% 2.74/2.93 tff(16683,plain,
% 2.74/2.93 (~(s(s(s(z))) = elem!1)),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[111, 16682])).
% 2.74/2.93 tff(16684,plain,
% 2.74/2.93 (b(s(s(s(z))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[74, 16683, 2])).
% 2.74/2.93 tff(16685,plain,
% 2.74/2.93 ((~r(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~(s(s(s(s(s(z))))) = elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10957, 15353])).
% 2.74/2.93 tff(16686,plain,
% 2.74/2.93 (~r(s(s(s(s(z)))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16685, 16684, 16173, 16675])).
% 2.74/2.93 tff(16687,plain,
% 2.74/2.93 (b(s(s(s(s(z)))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[254, 16686, 16679])).
% 2.74/2.93 tff(16688,plain,
% 2.74/2.93 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[16677, 3609])).
% 2.74/2.93 tff(16689,plain,
% 2.74/2.93 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16688])).
% 2.74/2.93 tff(16690,plain,
% 2.74/2.93 (~(elem!1 = s(s(s(s(z)))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[319, 16689])).
% 2.74/2.93 tff(16691,plain,
% 2.74/2.93 (elem!1 = s(s(s(s(s(z)))))),
% 2.74/2.93 inference(symmetry,[status(thm)],[16675])).
% 2.74/2.93 tff(16692,plain,
% 2.74/2.93 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16691])).
% 2.74/2.93 tff(16693,plain,
% 2.74/2.93 ((s(s(z)) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.74/2.93 inference(transitivity,[status(thm)],[16692, 4133])).
% 2.74/2.93 tff(16694,plain,
% 2.74/2.93 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.74/2.93 inference(symmetry,[status(thm)],[16693])).
% 2.74/2.93 tff(16695,plain,
% 2.74/2.93 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16694])).
% 2.74/2.93 tff(16696,plain,
% 2.74/2.93 (~(s(s(z)) = elem!1)),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[52, 16695])).
% 2.74/2.93 tff(16697,plain,
% 2.74/2.93 (~b(s(s(z)), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[7330, 16687, 16173, 16684])).
% 2.74/2.93 tff(16698,plain,
% 2.74/2.93 (r(s(s(z)), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[782, 16697, 16696])).
% 2.74/2.93 tff(16699,plain,
% 2.74/2.93 (~b(s(s(s(s(z)))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16202, 16698, 16173, 16690])).
% 2.74/2.93 tff(16700,plain,
% 2.74/2.93 (r(s(s(s(s(z)))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1098, 16699])).
% 2.74/2.93 tff(16701,plain,
% 2.74/2.93 (b(s(s(s(s(s(z))))), s(z)) <=> b(elem!1, s(z))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16675])).
% 2.74/2.93 tff(16702,plain,
% 2.74/2.93 (b(elem!1, s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.74/2.93 inference(symmetry,[status(thm)],[16701])).
% 2.74/2.93 tff(16703,plain,
% 2.74/2.93 (b(s(s(s(s(s(z))))), s(z))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[16173, 16702])).
% 2.74/2.93 tff(16704,plain,
% 2.74/2.93 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(s(z))), elem!1)),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16675])).
% 2.74/2.93 tff(16705,plain,
% 2.74/2.93 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.93 inference(symmetry,[status(thm)],[16704])).
% 2.74/2.93 tff(16706,plain,
% 2.74/2.93 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16705])).
% 2.74/2.93 tff(16707,plain,
% 2.74/2.93 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[2, 16706])).
% 2.74/2.93 tff(16708,plain,
% 2.74/2.93 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[2570, 16707])).
% 2.74/2.93 tff(16709,plain,
% 2.74/2.93 (~r(s(z), s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[15458, 16698])).
% 2.74/2.93 tff(16710,plain,
% 2.74/2.93 (b(s(z), s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[757, 16709])).
% 2.74/2.93 tff(16711,plain,
% 2.74/2.93 (~b(s(s(s(z))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9027, 16710, 16708, 16703])).
% 2.74/2.93 tff(16712,plain,
% 2.74/2.93 (r(elem!1, s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[13704, 16711, 2, 16700, 16687, 16173])).
% 2.74/2.93 tff(16713,plain,
% 2.74/2.93 (~(s(s(s(z))) = elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[12720, 2077, 221])).
% 2.74/2.93 tff(16714,plain,
% 2.74/2.93 (~r(s(s(s(z))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[4885, 701, 228])).
% 2.74/2.93 tff(16715,plain,
% 2.74/2.93 (~(s(s(z)) = elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16634, 701, 228, 1149])).
% 2.74/2.93 tff(16716,plain,
% 2.74/2.93 (b(s(s(s(z))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[74, 16713, 16714])).
% 2.74/2.93 tff(16717,plain,
% 2.74/2.93 (~b(s(s(z)), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16196, 2077, 701, 228, 16716])).
% 2.74/2.93 tff(16718,plain,
% 2.74/2.93 (r(s(s(z)), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[782, 16717, 16715])).
% 2.74/2.93 tff(16719,plain,
% 2.74/2.93 (~b(s(s(s(s(z)))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10897, 9, 701, 2077, 16718])).
% 2.74/2.93 tff(16720,plain,
% 2.74/2.93 (r(s(s(s(s(z)))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1098, 16719])).
% 2.74/2.93 tff(16721,plain,
% 2.74/2.93 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1611, 16720, 228, 701])).
% 2.74/2.93 tff(16722,plain,
% 2.74/2.93 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[518, 16721])).
% 2.74/2.93 tff(16723,plain,
% 2.74/2.93 (~r(s(s(s(s(z)))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1167, 16720, 701])).
% 2.74/2.93 tff(16724,plain,
% 2.74/2.93 (~b(s(s(s(z))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[7267, 16723, 10664, 221, 16722, 16720, 16593])).
% 2.74/2.93 tff(16725,plain,
% 2.74/2.93 (r(s(s(s(z))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[134, 16724])).
% 2.74/2.93 tff(16726,plain,
% 2.74/2.93 (~(s(z) = elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1125, 16593])).
% 2.74/2.93 tff(16727,plain,
% 2.74/2.93 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[547, 16726])).
% 2.74/2.93 tff(16728,plain,
% 2.74/2.93 (~r(s(s(s(z))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[4885, 701, 257])).
% 2.74/2.93 tff(16729,plain,
% 2.74/2.93 (~(s(s(z)) = elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16634, 701, 257, 1149])).
% 2.74/2.93 tff(16730,plain,
% 2.74/2.93 (~(s(s(s(z))) = s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[11953, 16729])).
% 2.74/2.93 tff(16731,plain,
% 2.74/2.93 (~b(elem!1, s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9830, 16586, 1291, 523])).
% 2.74/2.93 tff(16732,plain,
% 2.74/2.93 (~(elem!1 = s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[13264, 16597, 16586, 3, 1149, 523, 16728, 16727])).
% 2.74/2.93 tff(16733,plain,
% 2.74/2.93 (r(elem!1, s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1069, 16732, 16731])).
% 2.74/2.93 tff(16734,plain,
% 2.74/2.93 (~r(s(s(s(z))), s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9495, 16733, 1149])).
% 2.74/2.93 tff(16735,plain,
% 2.74/2.93 (b(s(s(s(z))), s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9480, 16734, 16730])).
% 2.74/2.93 tff(16736,plain,
% 2.74/2.93 (~b(s(s(s(s(s(z))))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[13277, 16735, 16728, 1149, 523, 16727, 16586, 2073, 1291])).
% 2.74/2.93 tff(16737,plain,
% 2.74/2.93 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[2596, 16599, 1291, 523])).
% 2.74/2.93 tff(16738,plain,
% 2.74/2.93 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[687, 16737])).
% 2.74/2.93 tff(16739,plain,
% 2.74/2.93 (~r(s(s(s(s(s(z))))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[276, 16738, 257])).
% 2.74/2.93 tff(16740,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[297, 16739, 16736])).
% 2.74/2.93 tff(16741,plain,(b(s(s(s(s(z)))), s(z)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(16742,plain,
% 2.74/2.93 (elem!1 = s(s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16741, 16722, 1149, 228, 16719, 16716, 3, 701])).
% 2.74/2.93 tff(16743,plain,
% 2.74/2.93 (s(s(s(s(s(z))))) = elem!1),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[8839, 16742])).
% 2.74/2.93 tff(16744,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10967, 16743, 16725, 16714, 228, 10664, 16713])).
% 2.74/2.93 tff(16745,plain,((s(s(s(s(z)))) = elem!1) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | b(s(z), s(s(s(z)))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(16746,plain,
% 2.74/2.93 ((s(s(s(s(z)))) = elem!1) | (~r(elem!1, s(s(s(z))))) | b(s(z), s(s(s(z)))) | (~b(elem!1, s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16745, 15353])).
% 2.74/2.93 tff(16747,plain,
% 2.74/2.93 (b(s(z), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16746, 16712, 16679, 16173])).
% 2.74/2.93 tff(16748,plain,
% 2.74/2.93 (~(s(elem!1) = s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[5852, 16675])).
% 2.74/2.93 tff(16749,plain,
% 2.74/2.93 (~(s(z) = s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[5029, 16748])).
% 2.74/2.93 tff(16750,plain,
% 2.74/2.93 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16675])).
% 2.74/2.93 tff(16751,plain,
% 2.74/2.93 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16750])).
% 2.74/2.93 tff(16752,plain,
% 2.74/2.93 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.74/2.93 inference(symmetry,[status(thm)],[16751])).
% 2.74/2.93 tff(16753,plain,
% 2.74/2.93 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16752])).
% 2.74/2.93 tff(16754,plain,
% 2.74/2.93 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(s(elem!1)))),
% 2.74/2.93 inference(symmetry,[status(thm)],[16753])).
% 2.74/2.93 tff(16755,plain,
% 2.74/2.93 ((~(elem!1 = s(s(s(s(s(s(s(z))))))))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16754])).
% 2.74/2.93 tff(16756,plain,
% 2.74/2.93 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16675])).
% 2.74/2.93 tff(16757,plain,
% 2.74/2.93 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[16756, 3858])).
% 2.74/2.93 tff(16758,plain,
% 2.74/2.93 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(s(s(s(s(z)))))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16757])).
% 2.74/2.93 tff(16759,plain,
% 2.74/2.93 (~(elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[2729, 16758])).
% 2.74/2.93 tff(16760,plain,
% 2.74/2.93 (~(elem!1 = s(s(elem!1)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[16759, 16755])).
% 2.74/2.93 tff(16761,plain,
% 2.74/2.93 (~(s(elem!1) = elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3351, 16760])).
% 2.74/2.93 tff(16762,plain,
% 2.74/2.93 (~(elem!1 = s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[8957, 16761])).
% 2.74/2.93 tff(16763,plain,
% 2.74/2.93 ((~(s(s(s(s(s(z))))) = elem!1)) | (~b(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | r(elem!1, s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[7402, 15353])).
% 2.74/2.93 tff(16764,plain,
% 2.74/2.93 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16763, 16700, 16173, 16675, 2076])).
% 2.74/2.93 tff(16765,plain,
% 2.74/2.93 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[518, 16764])).
% 2.74/2.93 tff(16766,plain,
% 2.74/2.93 (~b(elem!1, s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9830, 16765, 16687, 16684])).
% 2.74/2.93 tff(16767,plain,
% 2.74/2.93 (r(elem!1, s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1069, 16766, 16762])).
% 2.74/2.93 tff(16768,plain,
% 2.74/2.93 (~r(s(z), s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[15735, 16767])).
% 2.74/2.93 tff(16769,plain,
% 2.74/2.93 (b(s(z), s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[397, 16768, 16749])).
% 2.74/2.93 tff(16770,plain,
% 2.74/2.93 (~(s(s(s(z))) = s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[11953, 16696])).
% 2.74/2.93 tff(16771,plain,
% 2.74/2.93 (~r(s(s(s(z))), s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9495, 16767, 16712])).
% 2.74/2.93 tff(16772,plain,
% 2.74/2.93 (b(s(s(s(z))), s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9480, 16771, 16770])).
% 2.74/2.93 tff(16773,plain,
% 2.74/2.93 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[13292, 16772, 16769, 16747])).
% 2.74/2.93 tff(16774,plain,
% 2.74/2.93 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[15395, 16699])).
% 2.74/2.93 tff(16775,plain,
% 2.74/2.93 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1656, 16774])).
% 2.74/2.93 tff(16776,plain,
% 2.74/2.93 (~b(elem!1, s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1641, 16775, 16684, 16687])).
% 2.74/2.93 tff(16777,plain,
% 2.74/2.93 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[13015, 16776, 16675])).
% 2.74/2.93 tff(16778,plain,
% 2.74/2.93 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[328, 16777])).
% 2.74/2.93 tff(16779,plain,
% 2.74/2.93 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9485, 16679])).
% 2.74/2.93 tff(16780,plain,
% 2.74/2.93 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[11671, 16772, 16703, 16708])).
% 2.74/2.93 tff(16781,plain,
% 2.74/2.93 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[659, 16780, 16779])).
% 2.74/2.93 tff(16782,plain,
% 2.74/2.93 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10607, 16781, 16778])).
% 2.74/2.93 tff(16783,plain,
% 2.74/2.93 (s(elem!1) = s(s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9382, 16782, 16773])).
% 2.74/2.93 tff(16784,plain,
% 2.74/2.93 (s(s(s(s(z)))) = s(elem!1)),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[16783, 2373])).
% 2.74/2.93 tff(16785,plain,
% 2.74/2.93 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[4144, 16683])).
% 2.74/2.93 tff(16786,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16785, 16784])).
% 2.74/2.93 tff(16787,plain,(r(elem!1, s(z)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(16788,plain,
% 2.74/2.93 (r(elem!1, s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16787, 2])).
% 2.74/2.93 tff(16789,plain,
% 2.74/2.93 (b(s(s(s(z))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10359, 221, 16788, 3, 16174])).
% 2.74/2.93 tff(16790,plain,
% 2.74/2.93 (s(s(s(s(s(z))))) = elem!1),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16323, 221, 2])).
% 2.74/2.93 tff(16791,plain,
% 2.74/2.93 (~r(s(s(s(s(z)))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16685, 16789, 16173, 16790])).
% 2.74/2.93 tff(16792,plain,
% 2.74/2.93 (b(s(s(s(s(z)))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[254, 16791, 3])).
% 2.74/2.93 tff(16793,plain,
% 2.74/2.93 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9834, 16792, 16789, 12732])).
% 2.74/2.93 tff(16794,plain,
% 2.74/2.93 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[518, 16793])).
% 2.74/2.93 tff(16795,plain,
% 2.74/2.93 (~r(s(s(s(s(z)))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16199, 16794, 228])).
% 2.74/2.93 tff(16796,plain,
% 2.74/2.93 (b(s(s(s(s(z)))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1098, 16795])).
% 2.74/2.93 tff(16797,plain,
% 2.74/2.93 (~r(s(s(z)), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16202, 16796, 16173, 9])).
% 2.74/2.93 tff(16798,plain,
% 2.74/2.93 (~b(s(elem!1), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[15606, 16794, 16790, 16789, 12732, 3])).
% 2.74/2.93 tff(16799,plain,
% 2.74/2.93 (~(s(elem!1) = s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9377, 16798, 16789])).
% 2.74/2.93 tff(16800,plain,
% 2.74/2.93 (~(s(s(z)) = elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9447, 16799])).
% 2.74/2.93 tff(16801,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[782, 16800, 16797, 4])).
% 2.74/2.93 tff(16802,plain,(b(s(z), s(s(s(z)))) | b(s(s(z)), elem!1) | (s(s(s(s(z)))) = elem!1) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(16803,plain,
% 2.74/2.93 (b(s(z), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16802, 4, 3, 2])).
% 2.74/2.93 tff(16804,plain,
% 2.74/2.93 (r(s(z), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[15848, 76])).
% 2.74/2.93 tff(16805,plain,
% 2.74/2.93 (~r(elem!1, s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1157, 16804, 16788])).
% 2.74/2.93 tff(16806,plain,
% 2.74/2.93 (~b(s(s(s(s(z)))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16384, 16805, 2, 2090, 76])).
% 2.74/2.93 tff(16807,plain,
% 2.74/2.93 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[15395, 16806])).
% 2.74/2.93 tff(16808,plain,
% 2.74/2.93 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1656, 16807])).
% 2.74/2.93 tff(16809,plain,
% 2.74/2.93 (r(s(s(s(s(z)))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1098, 16806])).
% 2.74/2.93 tff(16810,plain,
% 2.74/2.93 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16199, 16809, 16804])).
% 2.74/2.93 tff(16811,plain,
% 2.74/2.93 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[518, 16810])).
% 2.74/2.93 tff(16812,plain,
% 2.74/2.93 (s(s(s(s(s(z))))) = elem!1),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16576, 76, 2])).
% 2.74/2.93 tff(16813,plain,
% 2.74/2.93 (elem!1 = s(s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[5538, 16812])).
% 2.74/2.93 tff(16814,plain,
% 2.74/2.93 (~r(elem!1, s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[12993, 16809, 16788])).
% 2.74/2.93 tff(16815,plain,
% 2.74/2.93 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[5534, 16814, 16813])).
% 2.74/2.93 tff(16816,plain,
% 2.74/2.93 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[328, 16815])).
% 2.74/2.93 tff(16817,plain,
% 2.74/2.93 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1788, 16816, 16811, 16808])).
% 2.74/2.93 tff(16818,plain,
% 2.74/2.93 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[687, 16817])).
% 2.74/2.93 tff(16819,plain,
% 2.74/2.93 (r(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[4066, 16818, 76])).
% 2.74/2.93 tff(16820,plain,
% 2.74/2.93 (b(s(s(s(z))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[2080, 76, 16173])).
% 2.74/2.93 tff(16821,plain,
% 2.74/2.93 (~b(s(z), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[2894, 16811, 16820, 16808])).
% 2.74/2.93 tff(16822,plain,
% 2.74/2.93 (~b(s(z), s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1758, 16821, 162])).
% 2.74/2.93 tff(16823,plain,
% 2.74/2.93 (~(s(s(z)) = elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3644, 16822, 2090])).
% 2.74/2.93 tff(16824,plain,
% 2.74/2.93 (r(s(s(z)), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[782, 16823, 4])).
% 2.74/2.93 tff(16825,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[15407, 16824, 16819])).
% 2.74/2.93 tff(16826,plain,((~(s(s(s(z))) = elem!1)) | b(s(s(z)), elem!1) | (~b(s(z), s(s(s(z))))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(16827,plain,
% 2.74/2.93 (~(s(s(s(z))) = elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16826, 4, 16803, 2])).
% 2.74/2.93 tff(16828,plain,
% 2.74/2.93 (b(s(s(s(z))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[74, 16827, 2])).
% 2.74/2.93 tff(16829,plain,
% 2.74/2.93 (~r(s(s(z)), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16357, 637, 2, 3])).
% 2.74/2.93 tff(16830,plain,
% 2.74/2.93 (~(elem!1 = s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[4487, 16827])).
% 2.74/2.93 tff(16831,plain,
% 2.74/2.93 (~b(elem!1, s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[7473, 16828, 16173, 16803])).
% 2.74/2.93 tff(16832,plain,
% 2.74/2.93 (r(elem!1, s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[4492, 16831, 16830])).
% 2.74/2.93 tff(16833,plain,
% 2.74/2.93 (s(s(z)) = elem!1),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[782, 16829, 4])).
% 2.74/2.93 tff(16834,plain,
% 2.74/2.93 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16620, 16833, 16803, 16832, 16828, 8840, 16829, 3])).
% 2.74/2.93 tff(16835,plain,
% 2.74/2.93 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[518, 16834])).
% 2.74/2.93 tff(16836,plain,
% 2.74/2.93 (~r(s(s(s(s(z)))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[8475, 16835, 16832])).
% 2.74/2.93 tff(16837,plain,
% 2.74/2.93 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[512, 16836, 16835])).
% 2.74/2.93 tff(16838,plain,
% 2.74/2.93 (s(elem!1) = s(s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9447, 16833])).
% 2.74/2.93 tff(16839,plain,
% 2.74/2.93 (b(s(s(s(s(z)))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[254, 16836, 3])).
% 2.74/2.93 tff(16840,plain,
% 2.74/2.93 (~b(s(s(s(z))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14225, 453, 16173, 16828])).
% 2.74/2.93 tff(16841,plain,
% 2.74/2.93 (~b(s(s(s(z))), s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[14232, 16833, 16840])).
% 2.74/2.93 tff(16842,plain,
% 2.74/2.93 (r(s(s(s(z))), elem!1) | (~(s(elem!1) = s(s(elem!1)))) | b(s(s(s(z))), s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9349, 15602])).
% 2.74/2.93 tff(16843,plain,
% 2.74/2.93 (~(s(elem!1) = s(s(elem!1)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16842, 16841, 2])).
% 2.74/2.93 tff(16844,plain,
% 2.74/2.93 (~(s(elem!1) = elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[8905, 16843])).
% 2.74/2.93 tff(16845,plain,
% 2.74/2.93 (~(elem!1 = s(elem!1))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[8957, 16844])).
% 2.74/2.93 tff(16846,plain,
% 2.74/2.93 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[607, 16844])).
% 2.74/2.93 tff(16847,plain,
% 2.74/2.93 ((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (elem!1 = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9717, 15354])).
% 2.74/2.93 tff(16848,plain,
% 2.74/2.93 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16847, 16839, 16788, 16828, 637, 16835, 16841, 16846, 16832, 16845])).
% 2.74/2.93 tff(16849,plain,
% 2.74/2.93 (r(s(elem!1), s(s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(z))) | (~(s(elem!1) = s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (elem!1 = s(s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9444, 15357])).
% 2.74/2.93 tff(16850,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16849, 16848, 16839, 16788, 16828, 16838, 16835, 16830, 8840, 16837])).
% 2.74/2.93 tff(16851,plain,((s(s(s(s(s(z))))) = elem!1) | (s(s(s(s(z)))) = elem!1) | r(s(s(s(z))), elem!1) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(16852,plain,
% 2.74/2.93 (s(s(s(s(s(z))))) = elem!1),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16851, 4, 2, 3])).
% 2.74/2.93 tff(16853,plain,
% 2.74/2.93 (~r(s(s(s(s(z)))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16685, 16852, 16173, 16828])).
% 2.74/2.93 tff(16854,plain,
% 2.74/2.93 (elem!1 = s(s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[5538, 16852])).
% 2.74/2.93 tff(16855,plain,
% 2.74/2.93 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16854])).
% 2.74/2.93 tff(16856,plain,
% 2.74/2.93 ((s(s(z)) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.74/2.93 inference(transitivity,[status(thm)],[16855, 4133])).
% 2.74/2.93 tff(16857,plain,
% 2.74/2.93 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.74/2.93 inference(symmetry,[status(thm)],[16856])).
% 2.74/2.93 tff(16858,plain,
% 2.74/2.93 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16857])).
% 2.74/2.93 tff(16859,plain,
% 2.74/2.93 (~(s(s(z)) = elem!1)),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[52, 16858])).
% 2.74/2.93 tff(16860,plain,
% 2.74/2.93 (r(s(s(z)), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[782, 16859, 4])).
% 2.74/2.93 tff(16861,plain,
% 2.74/2.93 (~b(s(s(s(s(z)))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16202, 16860, 16173, 9])).
% 2.74/2.93 tff(16862,plain,
% 2.74/2.93 (r(s(s(s(s(z)))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1098, 16861])).
% 2.74/2.93 tff(16863,plain,
% 2.74/2.93 (~r(elem!1, s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[12993, 16862, 16788])).
% 2.74/2.93 tff(16864,plain,
% 2.74/2.93 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[15395, 16861])).
% 2.74/2.93 tff(16865,plain,
% 2.74/2.93 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1656, 16864])).
% 2.74/2.93 tff(16866,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[12998, 16865, 16863, 3, 16828, 16853])).
% 2.74/2.93 tff(16867,plain,(b(s(s(z)), elem!1) | (s(s(s(s(z)))) = elem!1) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(16868,plain,
% 2.74/2.93 (b(s(s(z)), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16867, 3, 2])).
% 2.74/2.93 tff(16869,plain,
% 2.74/2.93 (s(s(s(s(s(z))))) = elem!1),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16473, 16868, 3, 2])).
% 2.74/2.93 tff(16870,plain,
% 2.74/2.93 (elem!1 = s(s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[5538, 16869])).
% 2.74/2.93 tff(16871,plain,
% 2.74/2.93 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16870])).
% 2.74/2.93 tff(16872,plain,
% 2.74/2.93 ((s(s(s(z))) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[16871, 57])).
% 2.74/2.93 tff(16873,plain,
% 2.74/2.93 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 2.74/2.93 inference(symmetry,[status(thm)],[16872])).
% 2.74/2.93 tff(16874,plain,
% 2.74/2.93 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16873])).
% 2.74/2.93 tff(16875,plain,
% 2.74/2.93 (~(s(s(s(z))) = elem!1)),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[111, 16874])).
% 2.74/2.93 tff(16876,plain,
% 2.74/2.93 (b(s(s(s(z))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[74, 16875, 2])).
% 2.74/2.93 tff(16877,plain,
% 2.74/2.93 (~b(s(s(s(s(z)))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[7330, 16876, 16173, 16868])).
% 2.74/2.93 tff(16878,plain,
% 2.74/2.93 (~r(s(s(s(s(z)))), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16685, 16876, 16173, 16869])).
% 2.74/2.93 tff(16879,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[254, 16878, 16877, 3])).
% 2.74/2.93 tff(16880,plain,((s(s(s(s(z)))) = elem!1) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(16881,plain,
% 2.74/2.93 (s(s(s(s(z)))) = elem!1),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16880, 2])).
% 2.74/2.93 tff(16882,plain,
% 2.74/2.93 (elem!1 = s(s(s(s(z))))),
% 2.74/2.93 inference(symmetry,[status(thm)],[16881])).
% 2.74/2.93 tff(16883,plain,
% 2.74/2.93 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16882])).
% 2.74/2.93 tff(16884,plain,
% 2.74/2.93 ((s(s(z)) = elem!1) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.74/2.93 inference(transitivity,[status(thm)],[16883, 1])).
% 2.74/2.93 tff(16885,plain,
% 2.74/2.93 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.74/2.93 inference(symmetry,[status(thm)],[16884])).
% 2.74/2.93 tff(16886,plain,
% 2.74/2.93 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16885])).
% 2.74/2.93 tff(16887,plain,
% 2.74/2.93 (~(s(s(z)) = elem!1)),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[153, 16886])).
% 2.74/2.93 tff(16888,plain,
% 2.74/2.93 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16881])).
% 2.74/2.93 tff(16889,plain,
% 2.74/2.93 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[16888, 55])).
% 2.74/2.93 tff(16890,plain,
% 2.74/2.93 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.74/2.93 inference(transitivity,[status(thm)],[16889, 56])).
% 2.74/2.93 tff(16891,plain,
% 2.74/2.93 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16890])).
% 2.74/2.93 tff(16892,plain,
% 2.74/2.93 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[319, 16891])).
% 2.74/2.93 tff(16893,plain,
% 2.74/2.93 (~b(s(s(z)), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16517, 16892, 2])).
% 2.74/2.93 tff(16894,plain,
% 2.74/2.93 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[4108, 16881])).
% 2.74/2.93 tff(16895,plain,
% 2.74/2.93 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16894])).
% 2.74/2.93 tff(16896,plain,
% 2.74/2.93 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 2.74/2.93 inference(transitivity,[status(thm)],[16895, 10379])).
% 2.74/2.93 tff(16897,plain,
% 2.74/2.93 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[16896])).
% 2.74/2.93 tff(16898,plain,
% 2.74/2.93 (~(s(s(s(z))) = s(elem!1))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[111, 16897])).
% 2.74/2.93 tff(16899,plain,
% 2.74/2.93 (~r(s(s(z)), elem!1)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[16574, 16892, 2, 16898])).
% 2.74/2.93 tff(16900,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[782, 16899, 16893, 16887])).
% 2.74/2.93 tff(16901,plain,(r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(16902,plain,
% 2.74/2.93 (~r(s(z), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[15833, 16901])).
% 2.74/2.93 tff(16903,plain,
% 2.74/2.93 (b(s(z), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[227, 16902])).
% 2.74/2.93 tff(16904,plain,
% 2.74/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(16905,plain,
% 2.74/2.94 (((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(16906,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16905])).
% 2.74/2.94 tff(16907,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 2.74/2.94 inference(transitivity,[status(thm)],[16906, 16904])).
% 2.74/2.94 tff(16908,plain,
% 2.74/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(16909,plain,
% 2.74/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[16908, 16907])).
% 2.74/2.94 tff(16910,plain,
% 2.74/2.94 (~r(s(s(s(z))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16909, 268, 15353, 16901])).
% 2.74/2.94 tff(16911,plain,
% 2.74/2.94 (b(s(s(s(z))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[134, 16910])).
% 2.74/2.94 tff(16912,plain,
% 2.74/2.94 (~r(s(s(s(s(z)))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[15839, 16911, 16901])).
% 2.74/2.94 tff(16913,plain,
% 2.74/2.94 (b(s(s(s(s(z)))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[254, 3, 16912])).
% 2.74/2.94 tff(16914,plain,
% 2.74/2.94 (~b(s(s(s(s(z)))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[3782, 523, 16903, 16911])).
% 2.74/2.94 tff(16915,plain,
% 2.74/2.94 (r(s(s(s(s(z)))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1098, 16914])).
% 2.74/2.94 tff(16916,plain,
% 2.74/2.94 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[15395, 16914])).
% 2.74/2.94 tff(16917,plain,
% 2.74/2.94 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1656, 16916])).
% 2.74/2.94 tff(16918,plain,
% 2.74/2.94 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[14561, 16917, 16173, 16901, 299, 637, 523])).
% 2.74/2.94 tff(16919,plain,
% 2.74/2.94 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[328, 16918])).
% 2.74/2.94 tff(16920,plain,
% 2.74/2.94 (~r(s(s(s(s(s(z))))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2414, 16919, 16915])).
% 2.74/2.94 tff(16921,plain,
% 2.74/2.94 (b(s(s(s(s(s(z))))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[297, 16920])).
% 2.74/2.94 tff(16922,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(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))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(16923,plain,
% 2.74/2.94 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(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))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(16924,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(z))))) | (~b(s(s(s(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(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(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(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)))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16923])).
% 2.74/2.94 tff(16925,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(z))))) | (~b(s(s(s(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(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(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(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))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[16924, 16922])).
% 2.74/2.94 tff(16926,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(z))))) | (~b(s(s(s(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(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(16927,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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(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)))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[16926, 16925])).
% 2.74/2.94 tff(16928,plain,
% 2.74/2.94 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16927, 453, 523, 16917, 16921, 16911, 16903])).
% 2.74/2.94 tff(16929,plain,
% 2.74/2.94 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[687, 16928])).
% 2.74/2.94 tff(16930,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(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(16931,plain,
% 2.74/2.94 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(16932,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(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16931])).
% 2.74/2.94 tff(16933,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(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.74/2.94 inference(transitivity,[status(thm)],[16932, 16930])).
% 2.74/2.94 tff(16934,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(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(16935,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[16934, 16933])).
% 2.74/2.94 tff(16936,plain,
% 2.74/2.94 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16935, 453, 16173, 16921, 16903])).
% 2.74/2.94 tff(16937,plain,
% 2.74/2.94 (r(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[643, 16936, 637])).
% 2.74/2.94 tff(16938,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1566, 16937, 16929, 16901])).
% 2.74/2.94 tff(16939,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(s(z))))) = elem!1) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(16940,plain,
% 2.74/2.94 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16939, 637, 16913])).
% 2.74/2.94 tff(16941,plain,
% 2.74/2.94 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[518, 16940])).
% 2.74/2.94 tff(16942,plain,
% 2.74/2.94 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1982, 256, 16941])).
% 2.74/2.94 tff(16943,plain,
% 2.74/2.94 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[328, 16942])).
% 2.74/2.94 tff(16944,plain,
% 2.74/2.94 (~(s(s(s(z))) = elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[15848, 16902])).
% 2.74/2.94 tff(16945,plain,
% 2.74/2.94 (~(elem!1 = s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[4487, 16944])).
% 2.74/2.94 tff(16946,plain,
% 2.74/2.94 (~b(elem!1, s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[7497, 453, 16173, 16911, 16903])).
% 2.74/2.94 tff(16947,plain,
% 2.74/2.94 (r(elem!1, s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[4492, 16946, 16945])).
% 2.74/2.94 tff(16948,plain,
% 2.74/2.94 (~r(elem!1, s(s(s(s(z)))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[13281, 16941, 16947])).
% 2.74/2.94 tff(16949,plain,
% 2.74/2.94 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1566, 256, 16901])).
% 2.74/2.94 tff(16950,plain,
% 2.74/2.94 (b(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[643, 16949, 637])).
% 2.74/2.94 tff(16951,plain,
% 2.74/2.94 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[6664, 16950, 3, 16948, 16943, 16912])).
% 2.74/2.94 tff(16952,plain,
% 2.74/2.94 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10556, 16951])).
% 2.74/2.94 tff(16953,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[3216, 268, 16941, 256, 16952])).
% 2.74/2.94 tff(16954,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(16955,plain,
% 2.74/2.94 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16954, 637, 3])).
% 2.74/2.94 tff(16956,plain,
% 2.74/2.94 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[687, 16955])).
% 2.74/2.94 tff(16957,plain,
% 2.74/2.94 (~b(s(z), s(s(s(s(s(z))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[5584, 453, 16956, 16911, 16903])).
% 2.74/2.94 tff(16958,plain,
% 2.74/2.94 (r(s(z), s(s(s(s(s(z))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[372, 16957])).
% 2.74/2.94 tff(16959,plain,
% 2.74/2.94 (~b(s(s(s(s(s(z))))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[7909, 453, 16956, 16911, 16903])).
% 2.74/2.94 tff(16960,plain,
% 2.74/2.94 (b(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16641, 16959, 16173])).
% 2.74/2.94 tff(16961,plain,
% 2.74/2.94 (~r(s(s(z)), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[15861, 16903, 16901])).
% 2.74/2.94 tff(16962,plain,
% 2.74/2.94 (b(s(s(z)), s(z)) <=> b(elem!1, s(z))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[3468])).
% 2.74/2.94 tff(16963,plain,
% 2.74/2.94 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 2.74/2.94 inference(symmetry,[status(thm)],[16962])).
% 2.74/2.94 tff(16964,plain,
% 2.74/2.94 (b(s(s(z)), s(z))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[16173, 16963])).
% 2.74/2.94 tff(16965,plain,
% 2.74/2.94 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), elem!1)),
% 2.74/2.94 inference(monotonicity,[status(thm)],[3468])).
% 2.74/2.94 tff(16966,plain,
% 2.74/2.94 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.94 inference(symmetry,[status(thm)],[16965])).
% 2.74/2.94 tff(16967,plain,
% 2.74/2.94 (b(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[299, 16966])).
% 2.74/2.94 tff(16968,plain,
% 2.74/2.94 (r(s(z), s(s(z))) <=> r(s(z), elem!1)),
% 2.74/2.94 inference(monotonicity,[status(thm)],[3468])).
% 2.74/2.94 tff(16969,plain,
% 2.74/2.94 (r(s(z), elem!1) <=> r(s(z), s(s(z)))),
% 2.74/2.94 inference(symmetry,[status(thm)],[16968])).
% 2.74/2.94 tff(16970,plain,
% 2.74/2.94 (r(s(z), s(s(z)))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[15353, 16969])).
% 2.74/2.94 tff(16971,plain,
% 2.74/2.94 (b(s(s(s(s(s(z))))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[297, 292])).
% 2.74/2.94 tff(16972,plain,
% 2.74/2.94 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[3587, 11097])).
% 2.74/2.94 tff(16973,plain,
% 2.74/2.94 (b(s(z), s(elem!1))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[3644, 3468, 16903])).
% 2.74/2.94 tff(16974,plain,
% 2.74/2.94 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[3537])).
% 2.74/2.94 tff(16975,plain,
% 2.74/2.94 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.74/2.94 inference(symmetry,[status(thm)],[16974])).
% 2.74/2.94 tff(16976,plain,
% 2.74/2.94 ((~r(s(s(s(s(s(z))))), s(z))) <=> (~r(s(s(s(elem!1))), s(z)))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16975])).
% 2.74/2.94 tff(16977,plain,
% 2.74/2.94 (~r(s(s(s(elem!1))), s(z))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[292, 16976])).
% 2.74/2.94 tff(16978,plain,
% 2.74/2.94 (b(s(s(s(elem!1))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[856, 16977])).
% 2.74/2.94 tff(16979,plain,
% 2.74/2.94 (~b(elem!1, s(s(s(elem!1))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[7460, 16978, 16173, 16973])).
% 2.74/2.94 tff(16980,plain,
% 2.74/2.94 (r(elem!1, s(s(s(elem!1))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1428, 16979, 3736])).
% 2.74/2.94 tff(16981,plain,
% 2.74/2.94 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[16980, 16972])).
% 2.74/2.94 tff(16982,plain,
% 2.74/2.94 (~r(s(z), s(s(s(s(s(z))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[9047, 16981, 16970])).
% 2.74/2.94 tff(16983,plain,
% 2.74/2.94 (b(s(z), s(s(s(s(s(z))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[372, 16982])).
% 2.74/2.94 tff(16984,plain,
% 2.74/2.94 (r(s(s(z)), s(s(s(z))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[16947, 11094])).
% 2.74/2.94 tff(16985,plain,
% 2.74/2.94 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2795, 16981, 16984])).
% 2.74/2.94 tff(16986,plain,
% 2.74/2.94 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[687, 16985])).
% 2.74/2.94 tff(16987,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[9007, 16986, 16983, 16911, 16971])).
% 2.74/2.94 tff(16988,plain,(r(s(s(s(s(s(z))))), s(z)) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(16989,plain,
% 2.74/2.94 (r(s(s(s(s(s(z))))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[16988, 3468])).
% 2.74/2.94 tff(16990,plain,
% 2.74/2.94 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2476, 16989, 16970])).
% 2.74/2.94 tff(16991,plain,
% 2.74/2.94 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[4081, 16990])).
% 2.74/2.94 tff(16992,plain,
% 2.74/2.94 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2505, 16991, 16967, 16964])).
% 2.74/2.94 tff(16993,plain,
% 2.74/2.94 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10556, 16992])).
% 2.74/2.94 tff(16994,plain,
% 2.74/2.94 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[16993, 3536])).
% 2.74/2.94 tff(16995,plain,
% 2.74/2.94 (r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[3478])).
% 2.74/2.94 tff(16996,plain,
% 2.74/2.94 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(symmetry,[status(thm)],[16995])).
% 2.74/2.94 tff(16997,plain,
% 2.74/2.94 (b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[3478])).
% 2.74/2.94 tff(16998,plain,
% 2.74/2.94 ((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) <=> (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[16997])).
% 2.74/2.94 tff(16999,plain,
% 2.74/2.94 (r(s(elem!1), elem!1)),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[16901, 15883])).
% 2.74/2.94 tff(17000,plain,
% 2.74/2.94 (b(s(elem!1), s(z))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[16911, 5605])).
% 2.74/2.94 tff(17001,plain,
% 2.74/2.94 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[15909, 17000, 16999, 3476, 3825, 16973])).
% 2.74/2.94 tff(17002,plain,
% 2.74/2.94 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[3875, 17001, 15881])).
% 2.74/2.94 tff(17003,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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(17004,plain,
% 2.74/2.94 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(17005,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[17004])).
% 2.74/2.94 tff(17006,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[17005, 17003])).
% 2.74/2.94 tff(17007,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(17008,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(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[17007, 17006])).
% 2.74/2.94 tff(17009,plain,
% 2.74/2.94 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[17008, 453, 16173, 5607, 17002])).
% 2.74/2.94 tff(17010,plain,
% 2.74/2.94 (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[17009, 16998])).
% 2.74/2.94 tff(17011,plain,
% 2.74/2.94 (r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[6308, 17010])).
% 2.74/2.94 tff(17012,plain,
% 2.74/2.94 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[17011, 16996])).
% 2.74/2.94 tff(17013,plain,
% 2.74/2.94 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[15978, 16989])).
% 2.74/2.94 tff(17014,plain,
% 2.74/2.94 (b(s(s(s(s(s(z))))), elem!1)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[643, 17013, 7191])).
% 2.74/2.94 tff(17015,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(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(17016,plain,
% 2.74/2.94 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(17017,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[17016])).
% 2.74/2.94 tff(17018,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[17017, 17015])).
% 2.74/2.94 tff(17019,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(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(17020,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(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[17019, 17018])).
% 2.74/2.95 tff(17021,plain,
% 2.74/2.95 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17020, 453, 16173, 17014, 17002])).
% 2.74/2.95 tff(17022,plain,
% 2.74/2.95 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[11422, 17021])).
% 2.74/2.95 tff(17023,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(17024,plain,
% 2.74/2.95 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(17025,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17024])).
% 2.74/2.95 tff(17026,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.95 inference(transitivity,[status(thm)],[17025, 17023])).
% 2.74/2.95 tff(17027,plain,
% 2.74/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(17028,plain,
% 2.74/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[17027, 17026])).
% 2.74/2.95 tff(17029,plain,
% 2.74/2.95 ($false),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17028, 268, 17022, 17012, 16994])).
% 2.74/2.95 tff(17030,plain,((~(s(s(z)) = elem!1)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.95 tff(17031,plain,
% 2.74/2.95 (~(s(s(z)) = elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17030, 16913])).
% 2.74/2.95 tff(17032,plain,
% 2.74/2.95 (b(s(s(z)), elem!1)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[782, 17031, 16961])).
% 2.74/2.95 tff(17033,plain,
% 2.74/2.95 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[7654, 453, 16173, 16960, 16913])).
% 2.74/2.95 tff(17034,plain,
% 2.74/2.95 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[10556, 17033])).
% 2.74/2.95 tff(17035,plain,
% 2.74/2.95 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[947, 17034, 16913, 17032, 16960])).
% 2.74/2.95 tff(17036,plain,
% 2.74/2.95 (r(elem!1, s(s(s(s(s(z))))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[466, 17035, 8840])).
% 2.74/2.95 tff(17037,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(17038,plain,
% 2.74/2.95 (((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(17039,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17038])).
% 2.74/2.95 tff(17040,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.74/2.95 inference(transitivity,[status(thm)],[17039, 17037])).
% 2.74/2.95 tff(17041,plain,
% 2.74/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), elem!1)))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(17042,plain,
% 2.74/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[17041, 17040])).
% 2.74/2.95 tff(17043,plain,
% 2.74/2.95 ($false),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17042, 268, 15353, 17036, 16958])).
% 2.74/2.95 tff(17044,plain,((s(s(s(s(s(z))))) = elem!1) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.95 tff(17045,plain,
% 2.74/2.95 (s(s(s(s(s(z))))) = elem!1),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17044, 3])).
% 2.74/2.95 tff(17046,plain,
% 2.74/2.95 (elem!1 = s(s(s(s(s(z)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[5538, 17045])).
% 2.74/2.95 tff(17047,plain,
% 2.74/2.95 (b(elem!1, s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17046])).
% 2.74/2.95 tff(17048,plain,
% 2.74/2.95 (b(s(s(s(s(s(z))))), s(z))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[16173, 17047])).
% 2.74/2.95 tff(17049,plain,
% 2.74/2.95 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[7616, 453, 16173, 17032, 16913])).
% 2.74/2.95 tff(17050,plain,
% 2.74/2.95 (r(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[2370, 69, 2359, 17049])).
% 2.74/2.95 tff(17051,plain,
% 2.74/2.95 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[12865, 17046, 17032])).
% 2.74/2.95 tff(17052,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(17053,plain,
% 2.74/2.95 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(17054,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[17053])).
% 2.74/2.95 tff(17055,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.74/2.95 inference(transitivity,[status(thm)],[17054, 17052])).
% 2.74/2.95 tff(17056,plain,
% 2.74/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(17057,plain,
% 2.74/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[17056, 17055])).
% 2.74/2.95 tff(17058,plain,
% 2.74/2.95 (~r(s(s(z)), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[17057, 268, 376, 6934])).
% 2.74/2.95 tff(17059,plain,
% 2.74/2.95 (b(s(s(z)), s(z))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[720, 69, 717, 17058])).
% 2.74/2.95 tff(17060,plain,
% 2.74/2.95 (~r(s(z), s(s(z)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[7637, 268, 376, 6934])).
% 2.74/2.95 tff(17061,plain,
% 2.74/2.95 (b(s(z), s(s(z)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[757, 17060])).
% 2.74/2.95 tff(17062,plain,
% 2.74/2.95 ($false),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[9547, 453, 17061, 374, 17059, 8943])).
% 2.74/2.95 tff(17063,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.95 tff(17064,plain,
% 2.74/2.95 (~r(s(z), s(s(s(s(z)))))),
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% 2.74/2.95 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
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% 2.74/2.95 tff(17067,plain,
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% 2.74/2.95 inference(modus_ponens,[status(thm)],[16913, 17066])).
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% 2.74/2.96 tff(17141,plain,
% 2.74/2.96 (~r(s(s(s(z))), s(elem!1))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[9495, 17134, 16947])).
% 2.74/2.96 tff(17142,plain,
% 2.74/2.96 (b(s(s(s(z))), s(elem!1))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[9480, 17141, 17140])).
% 2.74/2.96 tff(17143,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[13292, 17142, 17136, 17093, 16903])).
% 2.74/2.96 % SZS output end Proof
% 2.74/2.96 % E exiting
%------------------------------------------------------------------------------